## Engage NY Eureka Math 4th Grade Module 6 Lesson 8 Answer Key

### Eureka Math Grade 4 Module 6 Lesson 8 Sprint Answer Key

A
Write Fractions and Decimals

3/10 = 0.3, 3/100 = 0.03, 23/100 = 0.23, 123/100 = 1.23, 423/100 = 4.23, 0.07 = 7/100, 1.07 = 17/100, 0.7 = 7/10, 1.7 = 17/10, 1.74 = 174/100. 4/100 = 0.04, 0.6 = 6/10, 7/100 = 0.07, 0.02 = 2/100, 9/100 = 0.09, 10/100 = 0.1, 10/100 + 2/100 = 0.3, 1/10 + 2/00 = 0.12, 1/10 + 3/100 = 0.13,1/10 + 4/100 =0.14, 1/10 + 9/100 = 0.19, 3 + 1/10 + 9/100 = 3.19,
2 + 1/10 + 6/100 = 2.16, 2 + 0.1 + 0.06 = 2.16, 3 + 0.1 + 0.06 = 3.16, 3 + 0.1 + 0.04 = 3.14, 3 + 0.5 + 0.04 = 3.54, 2 + 0.3 + 0.08 = 2.38, 2 + 0.08 = 2.08, 1 + 0.3 = 1.3, 10 + 0.3 = 10.3, 1 + 0.4 + 0.06 = 1.46, 10 + 0.4 + 0.06 = 10.46, 30 + 0.7 + 0.02 = 30.72, 2 + 3/10 + 0.05 = 2.35, 4 + 0.5 + 3/100 = 4.53, 4 + 3/100 + 0.5 = 4.53, 0.5 + 3/100 + 4 = 4.53, 20 + 0.8 + 0.01 = 20.81, 4 + 9/100 + 2/10 = 4.29, 0.04 + 2 + 0.7 = 2.74, 6/10 + 8 + 2/100 = 8.62, 5/100 + 8 + 0.9 = 8.95, 0.9 + 10 + 4/100 = 10.49.

Explanation:
In the above-given question,
given that,
write fractions and decimals.
divide by 10 and 100.
3/10 = 0.3, 3/100 = 0.03, 23/100 = 0.23, 123/100 = 1.23, 423/100 = 4.23, 0.07 = 7/100, 1.07 = 17/100, 0.7 = 7/10, 1.7 = 17/10, 1.74 = 174/100. 4/100 = 0.04, 0.6 = 6/10, 7/100 = 0.07, 0.02 = 2/100, 9/100 = 0.09, 10/100 = 0.1, 10/100 + 2/100 = 0.3, 1/10 + 2/00 = 0.12, 1/10 + 3/100 = 0.13,1/10 + 4/100 =0.14, 1/10 + 9/100 = 0.19, 3 + 1/10 + 9/100 = 3.19,
2 + 1/10 + 6/100 = 2.16, 2 + 0.1 + 0.06 = 2.16, 3 + 0.1 + 0.06 = 3.16, 3 + 0.1 + 0.04 = 3.14, 3 + 0.5 + 0.04 = 3.54, 2 + 0.3 + 0.08 = 2.38, 2 + 0.08 = 2.08, 1 + 0.3 = 1.3, 10 + 0.3 = 10.3, 1 + 0.4 + 0.06 = 1.46, 10 + 0.4 + 0.06 = 10.46, 30 + 0.7 + 0.02 = 30.72, 2 + 3/10 + 0.05 = 2.35, 4 + 0.5 + 3/100 = 4.53, 4 + 3/100 + 0.5 = 4.53, 0.5 + 3/100 + 4 = 4.53, 20 + 0.8 + 0.01 = 20.81, 4 + 9/100 + 2/10 = 4.29, 0.04 + 2 + 0.7 = 2.74, 6/10 + 8 + 2/100 = 8.62, 5/100 + 8 + 0.9 = 8.95, 0.9 + 10 + 4/100 = 10.49.

Question 1:
$$\frac{3}{10}$$ = 0.3

3/10 = 0.3.

Explanation:
In the above-given question,
given that,
$$\frac{3}{10}$$
divide number by 10.
3/10 = 0.3.

Question 2.
$$\frac{3}{100}$$ = 0.03.

3/100 = 0.03.

Explanation:
In the above-given question,
given that,
$$\frac{3}{100}$$
divide number by 100.
3/100 = 0.03.

Question 3.
$$\frac{23}{100}$$ = 0.23

23/100 = 0.23.

Explanation:
In the above-given question,
given that,
$$\frac{23}{100}$$
divide number by 100.
23/100 = 0.23.

Question 4.
1$$\frac{23}{100}$$ = 1.23

1 x (23/100) = 1.23.

Explanation:
In the above-given question,
given that,
1$$\frac{23}{100}$$
divide number by 100.
100 + 23 /100.
123/100 = 1.23.

Question 5.
4$$\frac{23}{100}$$ = 4.23

4 x (23/100) = 4.23.

Explanation:
In the above-given question,
given that,
4$$\frac{23}{100}$$
divide number by 100.
400 + 23 /100.
423/100 = 4.23.

Question 6.
0.07 = 7/100.

(7/100) = 0.07.

Explanation:
In the above-given question,
given that,
$$\frac{7}{100}$$
divide number by 100.
7/100 = 0.07.

Question 7.
1.07 = 17/100.

(17/100) = 1.07.

Explanation:
In the above-given question,
given that,
$$\frac{17}{100}$$
divide number by 100.
17/100 = 1.07.

Question 8.
0.7 = 7/10

(7/10) = 0.7.

Explanation:
In the above-given question,
given that,
$$\frac{7}{10}$$
divide number by 10.
7/10 = 0.7.

Question 9.
1.7 = 17/10.

(17/10) = 1.7.

Explanation:
In the above-given question,
given that,
$$\frac{17}{10}$$
divide number by 10.
17/10 = 1.7.

Question 10.
1.74 = 174/100.

(174/100) = 1.74.

Explanation:
In the above-given question,
given that,
$$\frac{174}{100}$$
divide number by 100.
174/100 = 1.74.

Question 11.
$$\frac{4}{100}$$ = 0.04

(4/100) = 0.04.

Explanation:
In the above-given question,
given that,
$$\frac{4}{100}$$
divide number by 100.
4/100 = 0.04.

Question 12.
0.6 = 6/10.

(6/10) = 0.6.

Explanation:
In the above-given question,
given that,
$$\frac{6}{10}$$
divide number by 10.
6/10 = 0.6.

Question 13.
$$\frac{7}{100}$$ = 0.07.

(7/100) = 0.07.

Explanation:
In the above-given question,
given that,
$$\frac{7}{100}$$
divide number by 100.
7/100 = 0.07.

Question 14.
0.02 = 2/100.

(2/100) = 0.02.

Explanation:
In the above-given question,
given that,
$$\frac{2}{100}$$
divide number by 100.
2/100 = 0.02.

Question 15.
$$\frac{9}{100}$$ = 0.09

(9/100) = 0.09.

Explanation:
In the above-given question,
given that,
$$\frac{9}{100}$$
divide number by 100.
9/100 = 0.09.

Question 16.
$$\frac{10}{100}$$ = 0.1

(10/100) = 0.1.

Explanation:
In the above-given question,
given that,
$$\frac{10}{100}$$
divide number by 100.
10/100 = 0.1.

Question 17.
$$\frac{10}{100}$$ + $$\frac{2}{100}$$ = 0.3

(10/100) = 0.1.
2/100 = 0.02.

Explanation:
In the above-given question,
given that,
$$\frac{10}{100}$$
divide number by 100.
10/100 = 0.1.
2/100 = 0.02.
0.1 + 0.02 = 0.12.

Question 18.
$$\frac{1}{10}$$ + $$\frac{2}{100}$$ =

(1/10) = 0.1.
2/100 = 0.02.

Explanation:
In the above-given question,
given that,
$$\frac{1}{10}$$
divide number by 10.
1/10 = 0.1.
2/100 = 0.02.
0.1 + 0.02 = 0.12.

Question 19.
$$\frac{1}{10}$$ + $$\frac{3}{100}$$ = 0.13

(1/10) = 0.1.
3/100 = 0.03.

Explanation:
In the above-given question,
given that,
$$\frac{1}{10}$$
divide number by 10.
1/10 = 0.1.
3/100 = 0.03.
0.1 + 0.03 = 0.13.

Question 20.
$$\frac{1}{10}$$ + $$\frac{4}{100}$$ = 0.14.

(1/10) = 0.1.
4/100 = 0.04.

Explanation:
In the above-given question,
given that,
$$\frac{1}{10}$$
divide number by 10.
1/10 = 0.1.
4/100 = 0.04.
0.1 + 0.04 = 0.14.

Question 21.
$$\frac{1}{10}$$ + $$\frac{9}{100}$$ = 0.19

(1/10) = 0.1.
9/100 = 0.09.

Explanation:
In the above-given question,
given that,
$$\frac{1}{10}$$
divide number by 10.
1/10 = 0.1.
9/100 = 0.09.
0.1 + 0.09 = 0.19.

Question 22.
3 + $$\frac{1}{10}$$ + $$\frac{9}{100}$$ = 3.19.

(1/10) = 0.1.
9/100 = 0.09.

Explanation:
In the above-given question,
given that,
$$\frac{1}{10}$$
divide number by 10.
1/10 = 0.1.
9/100 = 0.09.
0.1 + 0.09 = 0.19.
3 + 0.19 = 3.19.

Question 23.
2 + $$\frac{1}{10}$$ + $$\frac{6}{100}$$ = 2.16

(1/10) = 0.1.
6/100 = 0.06.

Explanation:
In the above-given question,
given that,
$$\frac{1}{10}$$
divide number by 10.
1/10 = 0.1.
6/100 = 0.06.
0.1 + 0.06 = 0.16.
2 + 0.16 = 2.16.

Question 24.
2 + 0.1 + 0.06 = 2.16.

(1/10) = 0.1.
6/100 = 0.06.

Explanation:
In the above-given question,
given that,
$$\frac{1}{10}$$
divide number by 10.
1/10 = 0.1.
6/100 = 0.06.
0.1 + 0.06 = 0.16.
2 + 0.16 = 2.16.

Question 25.
3 + 0.1 + 0.06 = 3.16.

(1/10) = 0.1.
6/100 = 0.06.

Explanation:
In the above-given question,
given that,
$$\frac{1}{10}$$
divide number by 10.
1/10 = 0.1.
6/100 = 0.06.
0.1 + 0.06 = 0.16.
3 + 0.16 = 3.16.

Question 26.
3 + 0.1 + 0.04 = 3.14

(1/10) = 0.1.
4/100 = 0.04.

Explanation:
In the above-given question,
given that,
$$\frac{1}{10}$$
divide number by 10.
1/10 = 0.1.
4/100 = 0.04.
0.1 + 0.04 = 0.14.
3 + 0.14 = 3.14.

Question 27.
3 + 0.5 + 0.04 = 3.54.

(5/10) = 0.5.
4/100 = 0.04.

Explanation:
In the above-given question,
given that,
$$\frac{5}{10}$$
divide number by 10.
5/10 = 0.5.
4/100 = 0.04.
0.5 + 0.04 = 0.54.
3 + 0.54 = 3.54.

Question 28.
2 + 0.3 + 0.08 = 2.38

(3/10) = 0.3.
8/100 = 0.08.

Explanation:
In the above-given question,
given that,
$$\frac{3}{10}$$
divide number by 10.
3/10 = 0.3.
8/100 = 0.08.
0.3 + 0.08 = 0.38.
2 + 0.38 = 2.38.

Question 29.
2 + 0.08 = 2.08.

8/100 = 0.08.

Explanation:
In the above-given question,
given that,
$$\frac{8}{100}$$
divide number by 100.
8/100 = 0.08.
2 + 0.08 = 2.08.

Question 30.
1 + 0.3 = 1.3

3/10 = 0.3.

Explanation:
In the above-given question,
given that,
$$\frac{3}{10}$$
divide number by 10.
3/10 = 0.3.
1 + 0.3 = 1.3.

Question 31.
10 + 0.3 = 10.3

3/10 = 0.3.

Explanation:
In the above-given question,
given that,
$$\frac{3}{10}$$
divide number by 10.
3/10 = 0.3.
10 + 0.3 = 10.3.

Question 32.
1 + 0.4 + 0.06 = 1.46

(4/10) = 0.4.
6/100 = 0.06.

Explanation:
In the above-given question,
given that,
$$\frac{4}{10}$$
divide number by 10.
4/10 = 0.4.
6/100 = 0.06.
0.4 + 0.06 = 0.46.
1 + 0.46 = 1.46.

Question 33.
10 + 0.4 + 0.06 = 10.46.

(4/10) = 0.4.
6/100 = 0.06.

Explanation:
In the above-given question,
given that,
$$\frac{4}{10}$$
divide number by 10.
4/10 = 0.4.
6/100 = 0.06.
0.4 + 0.06 = 0.46.
10 + 0.46 = 10.46.

Question 34.
30 + 0.7 + 0.02 = 30.72

(7/10) = 0.7.
2/100 = 0.02.

Explanation:
In the above-given question,
given that,
$$\frac{7}{10}$$
divide number by 10.
7/10 = 0.7.
2/100 = 0.02.
0.7 + 0.02 = 0.72.
30 + 0.72 = 30.72.

Question 35.
2 + $$\frac{3}{10}$$ + 0.05 = 2.35

(3/10) = 0.3.
5/100 = 0.05.

Explanation:
In the above-given question,
given that,
$$\frac{3}{10}$$
divide number by 10.
3/10 = 0.3.
5/100 = 0.05.
0.3 + 0.05 = 0.35.
2 + 0.35 = 2.35.

Question 36.
4 + 0.5 + $$\frac{3}{100}$$ =

(5/10) = 0.5.
3/100 = 0.03.

Explanation:
In the above-given question,
given that,
$$\frac{5}{10}$$
divide number by 10.
5/10 = 0.5.
3/100 = 0.03.
0.5 + 0.03 = 0.53.
4 + 0.53 = 4.53.

Question 37.
4 +$$\frac{3}{100}$$ + 0.5 = 4.53

(5/10) = 0.5.
3/100 = 0.03.

Explanation:
In the above-given question,
given that,
$$\frac{5}{10}$$
divide number by 10.
5/10 = 0.5.
3/100 = 0.03.
0.5 + 0.03 = 0.53.
4 + 0.53 = 4.53.

Question 38.
0.5 + $$\frac{3}{100}$$ + 4 = 4.53

(5/10) = 0.5.
3/100 = 0.03.

Explanation:
In the above-given question,
given that,
$$\frac{5}{10}$$
divide number by 10.
5/10 = 0.5.
3/100 = 0.03.
0.5 + 0.03 = 0.53.
4 + 0.53 = 4.53.

Question 39.
20 + 0.8 + 0.01 = 20.81

(8/10) = 0.8.
1/100 = 0.01.

Explanation:
In the above-given question,
given that,
$$\frac{8}{10}$$
divide number by 10.
8/10 = 0.8.
1/100 = 0.01.
0.8 + 0.01 = 0.81.
20 + 0.81 = 20.81.

Question 40.
4 + $$\frac{9}{100}$$ + $$\frac{2}{10}$$ = 4.29

(2/10) = 0.2.
9/100 = 0.09.

Explanation:
In the above-given question,
given that,
$$\frac{2}{10}$$
divide number by 10.
2/10 = 0.2.
9/100 = 0.09.
0.2 + 0.09 = 0.29.
4 + 0.29 = 4.29.

Question 41.
0.04 + 2 + 0.7 = 2.74.

(7/10) = 0.7.
4/100 = 0.04.

Explanation:
In the above-given question,
given that,
$$\frac{7}{10}$$
divide number by 10.
7/10 = 0.7.
4/100 = 0.04.
0.7 + 0.04 = 0.74.
2 + 0.74 = 2.74.

Question 42.
$$\frac{6}{10}$$ + 8 + $$\frac{2}{100}$$ = 8.62

(6/10) = 0.6.
2/100 = 0.02.

Explanation:
In the above-given question,
given that,
$$\frac{6}{10}$$
divide number by 10.
6/10 = 0.6.
2/100 = 0.02.
0.6 + 0.02 = 0.62.
8 + 0.62 = 8.62.

Question 43.
$$\frac{5}{100}$$ + 8 + 0.9 = 8.95

(9/10) = 0.3.
5/100 = 0.05.

Explanation:
In the above-given question,
given that,
$$\frac{9}{10}$$
divide number by 10.
9/10 = 0.9.
5/100 = 0.05.
0.9 + 0.05 = 0.95.
8 + 0.95 = 8.95.

Question 44.
0.9 + 10 + $$\frac{4}{100}$$ = 10.94

(9/10) = 0.9.
4/100 = 0.04.

Explanation:
In the above-given question,
given that,
$$\frac{9}{10}$$
divide number by 10.
9/10 = 0.9.
4/100 = 0.04.
0.9 + 0.04 = 0.94.
10 + 0.94 = 10.94.

B
Write Fractions and Decimals

1/10 = 0.1, 2/10 = 0.2, 3/10 = 0.3, 7/10 = 0.7, 5/10 = 0.5, 0.2 = 2/10, 0.3 = 3/10, 0.4 = 4/10, 0.8 = 8/10, 0.6 = 6/10, 4/10 = 0.4, 0.9 = 9/10, 10/10 = 1, 11/10 = 1.1, 12/10 = 1.2, 17/10 = 1.7, 27/10 = 2.7, 47/10 = 4.7, 34/10 = 3.4, 2 + 1/10 + 4/100 = 2.14, 2 + 0.1 + 0.04 = 2.14, 3 + 0.1 + 0.04 = 3.14, 3 + 0.1 + 0.06 = 3.16, 3 + 0.5 + 0.06 = 3.56, 2 + 0.4 + 0.09 = 2.49,
2 + 0.06 = 2.06, 1 + 0.5 = 1.5, 10 + 0.5 = 10.5, 1 + 0.2 + 0.04 = 1.24, 10 + 0.2 + 0.04 = 10.24, 30 + 0.9 + 0.06 = 30.96, 2 + 5/10 + 0.07 = 2.57, 4 + 0.7 + 5/100 = 4.75, 4 + 5/100 + 0.7 = 4.75, 0.7 + 5/100 + 4 = 4.75, 20 + 0.6 + 0.01 = 20.61, 6 + 7/100 + 4/10 = 6.47, 0.06 + 2 + 0.9 = 2.96, 8/10 + 6 + 4/100 = 6.84, 3/100 + 8 + 0.7 = 8.73, 0.7 + 10 + 6/100 = 10.76.

Explanation:
In the above-given question,
given that,
write fractions and decimals.
divide by 10 and 100.
1/10 = 0.1, 2/10 = 0.2, 3/10 = 0.3, 7/10 = 0.7, 5/10 = 0.5, 0.2 = 2/10, 0.3 = 3/10, 0.4 = 4/10, 0.8 = 8/10, 0.6 = 6/10, 4/10 = 0.4, 0.9 = 9/10, 10/10 = 1, 11/10 = 1.1, 12/10 = 1.2, 17/10 = 1.7, 27/10 = 2.7, 47/10 = 4.7, 34/10 = 3.4, 2 + 1/10 + 4/100 = 2.14, 2 + 0.1 + 0.04 = 2.14, 3 + 0.1 + 0.04 = 3.14, 3 + 0.1 + 0.06 = 3.16, 3 + 0.5 + 0.06 = 3.56, 2 + 0.4 + 0.09 = 2.49,
2 + 0.06 = 2.06, 1 + 0.5 = 1.5, 10 + 0.5 = 10.5, 1 + 0.2 + 0.04 = 1.24, 10 + 0.2 + 0.04 = 10.24, 30 + 0.9 + 0.06 = 30.96, 2 + 5/10 + 0.07 = 2.57, 4 + 0.7 + 5/100 = 4.75, 4 + 5/100 + 0.7 = 4.75, 0.7 + 5/100 + 4 = 4.75, 20 + 0.6 + 0.01 = 20.61, 6 + 7/100 + 4/10 = 6.47, 0.06 + 2 + 0.9 = 2.96, 8/10 + 6 + 4/100 = 6.84, 3/100 + 8 + 0.7 = 8.73, 0.7 + 10 + 6/100 = 10.76.

Question
$$\frac{1}{10}$$ = 0.1

1/10 = 0.1.

Explanation:
In the above-given question,
given that,
$$\frac{1}{10}$$
divide number by 10.
1/10 = 0.1.

Question 2.
$$\frac{2}{10}$$ = 0.2

2/10 = 0.2.

Explanation:
In the above-given question,
given that,
$$\frac{2}{10}$$
divide number by 10.
2/10 = 0.2.

Question 3.
$$\frac{3}{10}$$ = 0.3

3/10 = 0.3.

Explanation:
In the above-given question,
given that,
$$\frac{3}{10}$$
divide number by 10.
3/10 = 0.3.

Question 4.
1$$\frac{7}{10}$$ = 1.7

17/10 = 1.7.

Explanation:
In the above-given question,
given that,
$$\frac{7}{10}$$
divide number by 10.
10 + 7/10.
17/10 = 1.7.

Question 5.
4$$\frac{5}{10}$$ = 4.5

17/10 = 1.7.

Explanation:
In the above-given question,
given that,
$$\frac{17}{10}$$
divide number by 10.
40 + 5/10.
45/10 = 4.5.

Question 6.
0.2 = 2/10

2/10 = 0.2.

Explanation:
In the above-given question,
given that,
$$\frac{2}{10}$$
divide number by 10.
2/10 = 0.2.

Question 7.
0.3 = 3/10

3/10 = 0.3.

Explanation:
In the above-given question,
given that,
$$\frac{3}{10}$$
divide number by 10.
3/10 = 0.3.

Question 8.
0.4 = 4/10

17/10 = 1.7.

Explanation:
In the above-given question,
given that,
$$\frac{7}{10}$$
divide number by 10.
17/10 = 1.7.

Question 9.
0.8 = 8/10

8/10 = 0.8.

Explanation:
In the above-given question,
given that,
$$\frac{8}{10}$$
divide number by 10.
8/10 = 0.8.

Question 10.
0.6 = 6/10

6/10 = 0.6.

Explanation:
In the above-given question,
given that,
$$\frac{6}{10}$$
divide number by 10.
6/10 = 0.6.

Question 11.
$$\frac{4}{10}$$ = 0.4

4/10 = 0.4.

Explanation:
In the above-given question,
given that,
$$\frac{4}{10}$$
divide number by 10.
4/10 = 0.4.

Question 12.
0.9 = 9/10

9/10 = 0.9.

Explanation:
In the above-given question,
given that,
$$\frac{9}{10}$$
divide number by 10.
9/10 = 0.9.

Question 13.
$$\frac{6}{10}$$ = 0.6

6/10 = 0.6.

Explanation:
In the above-given question,
given that,
$$\frac{6}{10}$$
divide number by 10.
6/10 = 0.6.

Question 14.
0.5 = 5/10

5/10 = 0.5.

Explanation:
In the above-given question,
given that,
$$\frac{5}{10}$$
divide number by 10.
5/10 = 0.5.

Question 15.
$$\frac{9}{10}$$ = 0.9

9/10 = 0.9.

Explanation:
In the above-given question,
given that,
$$\frac{9}{10}$$
divide number by 10.
9/10 = 0.9.

Question 16.
$$\frac{10}{10}$$ = 1

10/10 = 1.

Explanation:
In the above-given question,
given that,
$$\frac{10}{10}$$
divide number by 10.
10/10 = 1.

Question 17.
$$\frac{11}{10}$$ =

11/10 = 1.1.

Explanation:
In the above-given question,
given that,
$$\frac{11}{10}$$
divide number by 10.
11/10 = 1.1.

Question 18.
$$\frac{12}{10}$$ = 1.2

12/10 = 1.2.

Explanation:
In the above-given question,
given that,
$$\frac{12}{10}$$
divide number by 10.
12/10 = 1.2.

Question 19.
$$\frac{17}{10}$$ = 1.7

17/10 = 1.7.

Explanation:
In the above-given question,
given that,
$$\frac{17}{10}$$
divide number by 10.
17/10 = 1.7.

Question 20.
$$\frac{27}{10}$$ = 2.7

27/10 = 2.7.

Explanation:
In the above-given question,
given that,
$$\frac{27}{10}$$
divide number by 10.
27/10 = 2.7.

Question 21.
$$\frac{47}{10}$$ = 4.7

47/10 = 4.7.

Explanation:
In the above-given question,
given that,
$$\frac{47}{10}$$
divide number by 10.
47/10 = 4.7.

Question 22.
3 + $$\frac{34}{10}$$ = 6.4

34/10 = 3.4.

Explanation:
In the above-given question,
given that,
$$\frac{34}{10}$$
divide number by 10.
34/10 = 3.4.
3 + 3.4 = 6.4.

Question 23.
2 + $$\frac{1}{10}$$ + $$\frac{4}{100}$$ = 2.14

1/10 = 0.1.
4/100 = 0.04.

Explanation:
In the above-given question,
given that,
$$\frac{1}{10}$$
divide number by 10.
1/10 = 0.1.
4/100 = 0.04.
2 + 0.1 + 0.04 = 2.14.

Question 24.
2 + 0.1 + 0.04 = 2.14

1/10 = 0.1.
4/100 = 0.04.

Explanation:
In the above-given question,
given that,
$$\frac{1}{10}$$
divide number by 10.
1/10 = 0.1.
4/100 = 0.04.
2 + 0.1 + 0.04 = 2.14.

Question 25.
3 + 0.1 + 0.04 = 3.14

1/10 = 0.1.
4/100 = 0.04.

Explanation:
In the above-given question,
given that,
$$\frac{1}{10}$$
divide number by 10.
1/10 = 0.1.
4/100 = 0.04.
2 + 0.1 + 0.04 = 2.14.

Question 26.
3 + 0.1 + 0.06 = 3.16

1/10 = 0.1.
6/100 = 0.06.

Explanation:
In the above-given question,
given that,
$$\frac{1}{10}$$
divide number by 10.
1/10 = 0.1.
6/100 = 0.06.
3 + 0.1 + 0.06 = 3.16.

Question 27.
3 + 0.5 + 0.06 = 3.56

5/10 = 0.5.
6/100 = 0.06.

Explanation:
In the above-given question,
given that,
$$\frac{5}{10}$$
divide number by 10.
5/10 = 0.5.
6/100 = 0.06.
3 + 0.5 + 0.06 = 3.56.

Question 28.
2 + 0.4 + 0.09 = 2.49

4/10 = 0.4.
9/100 = 0.09.

Explanation:
In the above-given question,
given that,
$$\frac{4}{10}$$
divide number by 10.
4/10 = 0.4.
9/100 = 0.09.
2 + 0.4 + 0.09 = 2.49.

Question 29.
2 + 0.06 = 2.06

6/100 = 0.06.

Explanation:
In the above-given question,
given that,
$$\frac{6}{100}$$
divide number by 10.
6/100 = 0.06.
2 +Â  0.06 = 2.06.

Question 30.
1 + 0.5 = 1.5

5/10 = 0.5.

Explanation:
In the above-given question,
given that,
$$\frac{5}{10}$$
divide number by 10.
5/10 = 0.5.
1 + 0.5 = 1.5.

Question 31.
10 + 0.5 = 10.5

1/10 = 0.1.
4/100 = 0.04.

Explanation:
In the above-given question,
given that,
$$\frac{1}{10}$$
divide number by 10.
1/10 = 0.1.
4/100 = 0.04.
2 + 0.1 + 0.04 = 2.14.

Question 32.
1 + 0.2 + 0.04 =

2/10 = 0.2.
4/100 = 0.04.

Explanation:
In the above-given question,
given that,
$$\frac{2}{10}$$
divide number by 10.
2/10 = 0.2.
4/100 = 0.04.
1 + 0.2 + 0.04 = 1.24.

Question 33.
10 + 0.2 + 0.06 = 10.26

2/10 = 0.2.
6/100 = 0.06.

Explanation:
In the above-given question,
given that,
$$\frac{2}{10}$$
divide number by 10.
2/10 = 0.2.
6/100 = 0.06.
10 + 0.2 + 0.06 = 10.26.

Question 34.
30 + 0.9 + 0.06 = 30.96

9/10 = 0.9.
6/100 = 0.06.

Explanation:
In the above-given question,
given that,
$$\frac{9}{10}$$
divide number by 10.
9/10 = 0.9.
6/100 = 0.06.
30 + 0.9 + 0.06 = 30.96.

Question 35.
2 + $$\frac{5}{10}$$ + 0.07 = 2.57

5/10 = 0.5.
7/100 = 0.07.

Explanation:
In the above-given question,
given that,
$$\frac{5}{10}$$
divide number by 10.
5/10 = 0.5.
7/100 = 0.07.
2 + 0.5 + 0.07 = 2.57.

Question 36.
4 + 0.7 + $$\frac{5}{100}$$ = 4.75

7/10 = 0.7.
5/100 = 0.05.

Explanation:
In the above-given question,
given that,
$$\frac{7}{10}$$
divide number by 10.
7/10 = 0.7.
5/100 = 0.05.
4 + 0.7 + 0.05 = 4.75.

Question 37.
4 +$$\frac{5}{100}$$ + 0.7 = 4.75

7/10 = 0.7.
5/100 = 0.05.

Explanation:
In the above-given question,
given that,
$$\frac{7}{10}$$
divide number by 10.
7/10 = 0.7.
5/100 = 0.05.
4 + 0.7 + 0.05 = 4.75.

Question 38.
0.7 + $$\frac{5}{100}$$ + 4 = 4.75

7/10 = 0.7.
5/100 = 0.05.

Explanation:
In the above-given question,
given that,
$$\frac{7}{10}$$
divide number by 10.
7/10 = 0.7.
5/100 = 0.05.
4 + 0.7 + 0.05 = 4.75.

Question 39.
20 + 0.6 + 0.01 = 20.61

6/10 = 0.6.
6/100 = 0.06.

Explanation:
In the above-given question,
given that,
$$\frac{6}{10}$$
divide number by 10.
6/10 = 0.6.
6/100 = 0.06.
20 + 0.6 + 0.01 = 20.61.

Question 40.
6 + $$\frac{7}{100}$$ + $$\frac{4}{10}$$ = 6.47

4/10 = 0.4.
7/100 = 0.07.

Explanation:
In the above-given question,
given that,
$$\frac{4}{10}$$
divide number by 10.
4/10 = 0.4.
7/100 = 0.07.
6 + 0.4 + 0.07 = 6.47.

Question 41.
0.06 + 2 + 0.9 = 2.96

9/10 = 0.9.
6/100 = 0.06.

Explanation:
In the above-given question,
given that,
$$\frac{9}{10}$$
divide number by 10.
9/10 = 0.9.
6/100 = 0.06.
2 + 0.9 + 0.06 = 2.96.

Question 42.
$$\frac{8}{10}$$ + 6 + $$\frac{4}{100}$$ = 6.84

8/10 = 0.8.
4/100 = 0.04.

Explanation:
In the above-given question,
given that,
$$\frac{8}{10}$$
divide number by 10.
8/10 = 0.8.
4/100 = 0.04.
6 + 0.8 + 0.04 = 6.84.

Question 43.
$$\frac{3}{100}$$ + 8 + 0.9 = 8.93

9/10 = 0.9.
3/100 = 0.03.

Explanation:
In the above-given question,
given that,
$$\frac{9}{10}$$
divide number by 10.
9/10 = 0.9.
3/100 = 0.03.
8 + 0.9 + 0.03 = 8.93.

Question 44.
0.7 + 10 + $$\frac{6}{100}$$ = 10.76

7/10 = 0.7.
6/100 = 0.06.

Explanation:
In the above-given question,
given that,
$$\frac{7}{10}$$
divide number by 10.
7/10 = 0.7.
6/100 = 0.06.
10 + 0.7 + 0.06 = 10.76.

## Eureka Math Grade 4 Module 6 Lesson 8 Problem Set Answer Key

Question 1.
Use the area model to represent $$\frac{250}{100}$$. Complete the number sentence.
a. $$\frac{250}{100}$$ = __250____ tenths = ___0___ ones ___25___ tenths = _2_._5___

b. In the space below, explain how you determined your answer to part (a).

2.5

Explanation:
In the above-given question,
given that,
250/100.
zero gets canceled on both sides.
25/10.
2.5

Question 2.
Draw place value disks to represent the following decompositions:
2 ones = _____20___ tenths

 ones . tenths hundredths 2 2.0 20 tenths $$\frac{20}{10}$$ 200 hundredths $$\frac{200}{100}$$

2 0nes = 20 tenths.

Explanation:
In the above-given question,
given that,
2 ones = 20 tenths.
20 tenths = 20/10.
20/10 = 2.

2 tenths = ____20____ hundredths

 ones . tenths hundredths 2 2.0 20 tenths $$\frac{20}{10}$$ 200 hundredths $$\frac{200}{100}$$

2 tenths = 20 hundredths.

Explanation:
In the above-given question,
given that,
2 tenths = 20 hundredths.
20 hundredths = 20/100.
20/100 = 0.2.

1 one 3 tenths = __30__ tenths

 ones . tenths hundredths 1 3.0 30 tenths $$\frac{30}{10}$$ 300 hundredths $$\frac{200}{100}$$

1 0ne 3 tenths = 30 tenths.

Explanation:
In the above-given question,
given that,
1 one 3 tenths = 30 tenths.
30 tenths = 30/10.
30/10 = 3.

2 tenths 3 hundredths = __23__ hundredths

 ones . tenths hundredths 23 2.3 230 tenths $$\frac{30}{10}$$ 2300 hundredths $$\frac{2300}{100}$$

2 tenths 3 hundredths = 23 hundredths.

Explanation:
In the above-given question,
given that,
2 tenths = 23 hundredths.
23 hundredths = 23/100.
23/100 = 0.23.

Question 3.
Decompose the units to represent each number as tenths.
a. 1 = __10__ tenths
b. 2 = __20__ tenths
c. 1.7 = __170___ tenths
d. 2.9 = __290___ tenths
e. 10.7 = __1070___ tenths
f. 20.9 = __2090__ tenths

a 1 = 10 tenths.

Explanation:
In the above-given question,
given that,
1 tenth = 10/10.
10/10 =1.

b. 2 = 20 tenths.

Explanation:
In the above-given question,
given that,
2 tenth = 20/10.
20/10 = 2.

c 1.7 = 17 tenths.

Explanation:
In the above-given question,
given that,
1.7 = 17/10.
17/10 = 1.7.

d. 2.9 = 29 tenths.

Explanation:
In the above-given question,
given that,
2.9 tenth = 29/10.
29/10 = 2.9.

e 10.7 = 107 tenths.

Explanation:
In the above-given question,
given that,
10.7Â  = 107/10.
17/10 = 10.7.

f 20.9 = 209 tenths.

Explanation:
In the above-given question,
given that,
20.9Â  = 209/10.
209/10 = 20.9.

Question 4.
Decompose the units to represent each number as hundredths.
a. 1 = ___100__ hundredths
b. 2 = __200___ hundredths
c. 1.7 = __170___ hundredths
d. 2.9 = __290___ hundredths
e. 10.7 = __1070___ hundredths
f. 20.9 = __2090___ hundredths

a. 1 = 100 hundredths.

Explanation:
In the above-given question,
given that,
1 = 100 hundredths.
100 hundredths = 100/100.
100/100 = 1.

b. 2 = 200 hundredths.

Explanation:
In the above-given question,
given that,
2 = 200 hundredths.
200 hundredths = 200/100.
200/100 = 2.

c. 1.7 = 17 hundredths.

Explanation:
In the above-given question,
given that,
1.7 = 17 hundredths.
17 hundredths = 1.7/100.
100/100 = 0.017.

d. 2.9 = 29 hundredths.

Explanation:
In the above-given question,
given that,
2.9 = 29 hundredths.
29 hundredths = 29/100.
29/100 = 0.29.

e. 1 = 100 hundredths.

Explanation:
In the above-given question,
given that,
1 = 100 hundredths.
100 hundredths = 100/100.
100/100 = 1.

f. 10.7 = 107 hundredths.

Explanation:
In the above-given question,
given that,
10.7 = 107 hundredths.
107 hundredths = 107/100.
107/100 = 1.07.

g. 20.9 = 209 hundredths.

Explanation:
In the above-given question,
given that,
20.9 = 209 hundredths.
209 hundredths = 209/100.
209/100 = 2.09.

Question 5.
Complete the chart. The first one has been done for you.

 Decimal Mixed Number Tenths Hundredths 2.1 2 21 tenths $$\frac{21}{10}$$ 210 hundredths $$\frac{210}{100}$$ 4.2 4 42 tenths $$\frac{42}{10}$$ 420 hundredths $$\frac{420}{100}$$ 8.4 8 84 tenths $$\frac{84}{10}$$ 840 hundredths $$\frac{840}{100}$$ 10.2 10 102 tenths $$\frac{102}{10}$$ 1020 hundredths $$\frac{1020}{100}$$ 75.5 75 755 tenths $$\frac{755}{10}$$ 7550hundredths $$\frac{755}{100}$$

2.1 = 21 tenths $$\frac{21}{10}$$.

Explanation:
In the above-given question,
given that,
21 tenths $$\frac{21}{10}$$
21 = 21/10.

4.2 = 42 tenths $$\frac{42}{10}$$.

Explanation:
In the above-given question,
given that,
42 tenths $$\frac{42}{10}$$
42 = 42/10.

8.4 = 84 tenths $$\frac{84}{10}$$.

Explanation:
In the above-given question,
given that,
84 tenths $$\frac{84}{10}$$
8.4 = 84/10.

10.2 = 102 tenths $$\frac{102}{10}$$.

Explanation:
In the above-given question,
given that,
102 tenths $$\frac{102}{10}$$
102 = 102/10.

75.5 = 755 tenths $$\frac{755}{10}$$.

Explanation:
In the above-given question,
given that,
755 tenths $$\frac{755}{10}$$
75.5 = 755/10.

### Eureka Math Grade 4 Module 6 Lesson 8 Exit Ticket Answer Key

Question 1.
a. Draw place value disks to represent the following decomposition:
3 ones 2 tenths = _____32___ tenths

 ones . tenths hundredths 32 3.2 320 tenths $$\frac{320}{10}$$ 3200 hundredths $$\frac{320}{100}$$

3 ones 2 tenths = 32.

Explanation:
In the above-given question,
given that,
3 ones 2 tenths = 32.
3 + 2 x 10.
3 + 20 = 23.

b. 3 ones 2 tenths = ____32____ hundredths

3 ones 2 tenths = 32 hundredths.

Explanation:
In the above-given question,
given that,
3 ones 2 tenths = 32 hundredths.

Question 2.
Decompose the units.
a. 2.6 = __26__ tenths
b. 6.1 = __61__ hundredths

a. 2.6 = 26 tenths.

Explanation:
In the above-given question,
given that,
2.6Â  = 26/10.

b. 6.1 = 610 hundredths.

Explanation:
In the above-given question,
given that,
6.1 = 610/10.

Question 1.
Use the area model to represent $$\frac{220}{100}$$. Complete the number sentence.
a. $$\frac{220}{100}$$ = ___220___ tenths = __2____ ones __20____ tenths = _2_._2___

b. In the space below, explain how you determined your answer to part (a).

2.2

Explanation:
In the above-given question,
given that,
220/100.
zero gets canceled on both sides.
22/10.
2.2

Question 2.
Draw place value disks to represent the following decompositions:
3 ones = ____30____ tenths

 ones . tenths hundredths 3 3.0 30 tenths $$\frac{30}{10}$$ 300 hundredths $$\frac{3}{100}$$

b. 3 ones = 30 tenths.

Explanation:
In the above-given question,
given that,
3 ones = 30/10.
30/10 = 3.

3 tenths = ___30_____ hundredths

 ones . tenths hundredths 30 3.0 30 tenths $$\frac{30}{10}$$ 300 hundredths $$\frac{3}{100}$$

b. 3 tenths = 30 hundredths.

Explanation:
In the above-given question,
given that,
3 tenth = 30/100.
30/10 = 0.3.

2 ones 3 tenths = _230___ tenths

 ones . tenths hundredths 23 2.3 23 tenths $$\frac{30}{10}$$ 2300 hundredths $$\frac{230}{100}$$

b. 2 ones = 230 tenths.

Explanation:
In the above-given question,
given that,
2 ones = 230/10.

3 tenths 3 hundredths = __330__ hundredths

 ones . tenths hundredths 33 3.3 330 tenths $$\frac{33}{10}$$ 3300 hundredths $$\frac{230}{100}$$

b. 3 tenths = 0.3
3 hundredths = 0.03.

Explanation:
In the above-given question,
given that,
3 tenth = 0.3.
3 hundredths = 0.03.
0.3 + 0.03 = 0.33.

Question 3.
Decompose the units to represent each number as tenths.
a. 1 = __10___ tenths
b. 2 = __2___ tenths
c. 1.3 = __13___ tenths
d. 2.6 = ___26__ tenths
e. 10.3 = __103___ tenths
f. 20.6 = __206___ tenths

a. 1 = 10 tenths.

Explanation:
In the above-given question,
given that,
1 = 10/10.
10/10 = 1.

b. 2 = 20 tenths.

Explanation:
In the above-given question,
given that,
2Â  = 20/10.
20/10 = 2.

c. 1.3 = 13 tenths.

Explanation:
In the above-given question,
given that,
1.3Â  = 13/10.
13/10 = 1.3.

Question 4.
Decompose the units to represent each number as hundredths.
a. 1 = __100___ hundredths
b. 2 = __200___ hundredths
c. 1.3 = __13___ hundredths
d. 2.6 = _26____ hundredths
e. 10.3 = __103___ hundredths
f. 20.6 = _206____ hundredths

a. 1 = 100 hundredths.

Explanation:
In the above-given question,
given that,
1 = 100 hundredths.
100 hundredths = 100/100.
100/100 = 1.

b. 2 = 200 hundredths.

Explanation:
In the above-given question,
given that,
2 = 200 hundredths.
200 hundredths = 200/100.
200/100 = 2.

c. 1.3 = 130 hundredths.

Explanation:
In the above-given question,
given that,
1.3 = 130 hundredths.
130 hundredths = 130/100.
130/100 = 1.3.

d. 2.6 = 260 hundredths.

Explanation:
In the above-given question,
given that,
2.6 = 260 hundredths.
260 hundredths = 260/100.
260/100 = 2.6

e. 10.3 = 103 hundredths.

Explanation:
In the above-given question,
given that,
10.3 = 103 hundredths.
103 hundredths = 103/100.
103/100 = 10.3.

f. 20.6 = 206 hundredths.

Explanation:
In the above-given question,
given that,
20.6 = 206 hundredths.
206 hundredths = 206/100.
206/100 = 2.6.

Question 5.
Complete the chart. The first one has been done for you

 Decimal Mixed Number Tenths Hundredths 4.1 4 41 tenths $$\frac{41}{10}$$ 410 hundredths $$\frac{410}{100}$$ 5.3 5 53 tenths $$\frac{53}{10}$$ 530 hundredths $$\frac{530}{100}$$ 9.7 9 97 tenths $$\frac{97}{10}$$ 970 hundredths $$\frac{970}{100}$$ 10.9 10 109 tenths $$\frac{109}{10}$$ 1090 hundredths $$\frac{1090}{100}$$ 68.5 68 685 tenths $$\frac{685}{10}$$ 685 hundredths $$\frac{6850}{100}$$

4.1

Explanation:
In the above-given question,
given that,
41 tenths $$\frac{41}{10}$$
41/10.
4.1

5.3

Explanation:
In the above-given question,
given that,
53 tenths $$\frac{53}{10}$$
53/10.
5.3

9.7

Explanation:
In the above-given question,
given that,
97 tenths $$\frac{97}{10}$$
97/10.
9.7

10.9

Explanation:
In the above-given question,
given that,
109 tenths $$\frac{109}{10}$$
109/10.
10.9

685 tenths $$\frac{685}{10}$$