McGraw Hill My Math Grade 5 Chapter 6 Lesson 14 Answer Key Divide Decimals by Powers of Ten

All the solutions provided in McGraw Hill My Math Grade 5 Answer Key PDF Chapter 6 Lesson 14 Divide Decimals by Powers of Ten will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 5 Answer Key Chapter 6 Lesson 14 Divide Decimals by Powers of Ten

You can divide decimals by powers of ten, such a 10, 100, and 1,000. Powers of ten can be written with exponents.

Math in My World

Example 1

Laura needs to make 10 payments to pay for her new motorized scooter. How much will each payment be if the scooter costs $219.50?

One Way: Divide.
Find $219.50 ÷ 10.

Another Way: Move the decimal point.
Dividing a decimal by 10 moves the decimal point one place to the left.

So, each payment will be ____________.
Check Use multiplication. 21.95 × 10 =
To divide a decimal by a power of ten, move the decimal point to the left same number of zeros in the power of ten. This is also the same number as the exponent on 10.
Answer:
Explanation:
Laura needs to make 10 payments to pay for her new motorized scooter.
Cost of scooter $219.50
Total amount of each payment of the scooter,
Move the decimal point.
Dividing a decimal by 10 moves the decimal point one place to the left.

$219.50 ÷ 10 = $21.95

Example 2

In the past 10² years, scientists measured the movement of the continents to be 190.5 centimeters. If the continents moved the same amount each year, how much did the continents move in one year?

Helpful Hint
The quotient of a number and a power of ten that is greater than 1 will always be less than the original number.

Since 10² = 100, find 190.5 ÷ 100.

Dividing a decimal by 100 moved the decimal point two places to the left.

So, 190.5 ÷ 10² = ____________. The continents moved ___________ centimeters in one year.
Check Use multiplication. 1.905 × 100 =
Answer:
1.905 cm
Explanation:
Scientists measured the movement of the continents to be 190.5 centimeters.
If the continents moved the same amount each year,
Total measure of the continents move in one year
190.5 ÷ 10² = 1.905 cm
10² = 10 x 10 = 100 cm
Dividing a decimal by 100 moved the decimal point two places to the left.
190.5 ÷ 100 = 1.905 cm
Check Use multiplication. 1.905 × 100 = 190.5 cm

Talk Math

Use the number of zeros in the number 10 to explain why 4.5 ÷ 10 = 0.45.

Answer:
0.45
Explanation:
Dividing a decimal by 10 moves the decimal point one place to the left.
the number 10 to explain why 4.5 ÷ 10 = 0.45 as shown below.

Guided Practice

Divide. Check your answer using multiplication.

Question 1.
7.2 ÷ 10 = ______________
Answer:
0.72
Explanation:
Dividing a decimal by 10 moves the decimal point one place to the left.
the number 10 to explain why 7.2 ÷ 10 = 0.72 as shown below.

Question 2.
21.5 ÷ 10² = ______________
Answer:
0.215
Explanation:
Dividing a decimal by 100 moves the decimal point two place to the left.
10² = 10 x 10 = 100, the number 100 to explain.
21.5 ÷ 100 = 0.215 as shown below.

Question 3.
19.2 ÷ 10³ = ______________
Answer:
0.0192
Explanation:
Dividing a decimal by 1000 moves the decimal point three place to the left.
10³ = 10 x 10 x 10 = 1000, the number 1000 to explain.
19.2 ÷ 1000 = 0.0192 as shown below.

Independent Practice

Divide. Check your answer using multiplication.

Question 4.
5.62 ÷ 100 = ____________
Answer:
0.0562
Explanation:

Dividing a decimal by 100 moves the decimal point two places to the left.
5.62 ÷ 100 = 0.0562

Question 5.
18.7 ÷ 100 = _____________
Answer:
0.187
Explanation:

Dividing a decimal by 100 moves the decimal point two places to the left.
18.7 ÷ 100 = 0.187

Question 6.
6.3 ÷ 10³ = ______________
Answer:
0.0063
Explanation:

Dividing a decimal by 1000 moves the decimal point three places to the left.
10³ = 10 x 10 x 10 = 1000, the number 1000 to explain.
6.3 ÷ 10³ = 0.0063

Question 7.
0.05 ÷ 1 = _____________
Answer:
0.05
Explanation:

Any number except 0 divided by itself is one.
Any number divided by one is the same number.
0.05 ÷ 1 = 0.05

Question 8.
0.012 ÷ 10² = ______________
Answer:
0.00012
Explanation:
Dividing a decimal by 100 moves the decimal point two places to the left.
10² = 10 x 10 = 100, the number 100 to explain.
0.012 ÷ 10² = 0.00012

Question 9.
2.46 ÷ 10¹ = ______________
Answer:
0.246
Explanation:
Dividing a decimal by 10 moves the decimal point one place to the left.
10¹ = 10 = 10, the number 10 to explain.
2.46 ÷ 10¹ = 2.46

Question 10.
8.72 ÷ 100 = ______________
Answer:
0.0872
Explanation:
Dividing a decimal by 100 moves the decimal point two places to the left.
8.72 ÷ 100 = 0.0872

Question 11.
98.6 ÷ 10² = ______________
Answer:
0.986
Explanation:

Dividing a decimal by 100 moves the decimal point two places to the left.
10² = 10 x 10 = 100, the number 100 to explain.
98.6 ÷ 100 = 0.986

Question 12.
5.71 ÷ 1 = _____________
Answer:
5.71
Explanation:

Any number except 0 divided by itself is one.
Any number divided by one is the same number.
5.71 ÷ 1 = 5.71

Question 13.
437 ÷ 1,000 = _____________
Answer:
0.437
Explanation:
Dividing a decimal by 1000 moves the decimal point three places to the left.
437 ÷ 1,000 = 0.437

Problem Solving

Question 14.
Herbert bought red beans to make chili to sell at a fundraiser. The total price of the red beans was $13.90. How much did it cost for each can?

Answer:
$1.39
Explanation:
The total price of the red beans was $13.90.
The cost of each can $13.90 ÷ 10
Dividing a decimal by 10 moves the decimal point one place to the left.
Cost of each can = $1.39

Question 15.
Mathematical PRACTICE Model Math Sarah was trying to decide what kind of cat food to buy at the store. Smiley Cat costs $7.90 for 10 pounds. Purr Plus costs $0.85 per pound. Which brand is the better buy? Explain your reasoning.

Answer:
Purr Plus brand is better than Smiley Cat.
Explanation:
Smiley Cat costs $7.90 for 10 pounds.
$7.90 ÷ 10 = $0.79
Dividing a decimal by 10 moves the decimal point one place to the left.
Purr Plus costs $0.85 per pound.
When we compare both the brands Purr Plus brand is better than Smiley Cat.

Question 16.
In Alaska, scientists are studying the melting of glaciers. They found that in the past 10 years, the glaciers receded about 59.05 feet. If the glaciers receded at the same rate each year, how much did they recede in one year?
Answer:
5.905 feet.
Explanation:
Scientists found that in the past 10 years, the glaciers receded about 59.05 feet.
If the glaciers receded at the same rate each year,
Number of feet they recede in one year,
59.05 ÷ 10 = 5.905 feet.
Dividing a decimal by 10 moves the decimal point one place to the left.

HOT Problems

Question 17.
Mathematical PRACTICE Which One Doesn’t Belong? Circle the expression that does not belong with the other three. Explain your reasoning.

Answer:

Explanation:
To divide a decimal by a power of ten,
move the decimal point to the left same number of zeros in the power of ten.
This is also the same number as the exponent on 10.
Any number except 0 divided by itself is one.
Any number divided by one is the same number.

Question 18.
Building on the Essential Question Describe the relationship between the number of places a decimal point is moved to the left and the change in the value of the number.
Answer:
As the place moves to the left, the value of the number becomes greater by 10 times.
Explanation:
Dividing a decimal by 10 moves the decimal point one place to the left
The decimal point is a dot between digits in a number.
Numbers to the left of the decimal point are greater than 1.

McGraw Hill My Math Grade 5 Chapter 6 Lesson 14 My Homework Answer Key

Practice

Divide. Check your answer using multiplication.

Question 1.
8.3 ÷ 100 = ___________
Answer:
0.083
Explanation:
Dividing a decimal by 100 moves the decimal point two places to the left.
8.3 ÷ 100 = 0.083

Question 2.
208 ÷ 10² = _______________
Answer:
2.08
Explanation:
Dividing a whole by 100 moves the decimal point two places to the right.
10² = 10 x 10 = 100, the number 100 to explain.
208 ÷ 100 = 2.08

Question 3.
0.07 ÷ 1 = ______________
Answer:
Explanation:
Any number except 0 divided by itself is one.
Any number divided by one is the same number.
0.07 ÷ 1 = 0.07

Question 4.
32.7 ÷ 1,000 = ____________
Answer:
0.0327
Explanation:
Dividing a decimal by 1000 moves the decimal point three places to the left.
32.7 ÷ 1,000 = 0.0327

Problem Solving

Use the table to answer Exercises 5-7.

Question 5.
Each row of the grocery store parking lot has 10 parking spots of equal width. What is the width for each spot?
Answer:
Grocery store =  3.192 m
Hardware store = 3.196 m
Mall = 3.130 m
Explanation:
Dividing a decimal by 10 moves the decimal point one place to the left.
Grocery store = 31.92 ÷ 10 = 3.192 m
Hardware store = 31.96 ÷ 10 = 3.196 m
Mall = 31.30 ÷ 10 = 3.130 m

Question 6.
How much space is given for each parking spot at the Mall parking lot if each spot has an equal width?
Answer:
3.130 m
Explanation:
Space given for each parking spot at the Mall parking lot,
31.30 ÷ 10 = 3.130 m
Dividing a decimal by 10 moves the decimal point one place to the left.

Question 7.
Which location gives the greatest space for each parking spot?
Answer:
Hardware store.
Explanation:
Dividing a decimal by 10 moves the decimal point one place to the left.
Grocery store = 31.92 ÷ 10 = 3.192 m
Hardware store = 31.96 ÷ 10 = 3.196 m
Mall = 31.30 ÷ 10 = 3.130 m
When compare all the three spaces allotted in the location,
Hardware store is given the greatest space for each parking spot.

Question 8.
Mathematical PRACTICE Model Math Christy purchased 6.75 pounds of licorice. How much licorice does she need to put in each bag if she divides the total amount into 10 equal-sized bags?
Answer:
0.675 pounds.
Explanation:
Christy purchased 6.75 pounds of licorice.
Number of pounds she need to put in each bag,
if she divides the total amount into 10 equal-sized bags.
6.75 ÷ 10 = 0.675
Dividing a decimal by 10 moves the decimal point one place to the left.

Question 9.
Mathematical PRACTICE Explain to a Friend Tell what number you must divide 180 by to get 1.8.
Answer:
180 Divided by 100.
Explanation:
100 because there are two zeros, as we move the decimal over twice.

Test Practice

Question 10.
Tomas buys a trumpet for $108.90. He will make 10 equal payments to pay for the trumpet. What is the amount of each payment that Tomas will make?
(A) $1.09
(B) $10.89
(C) $19.90
(D) $108.90
Answer:
Option(B)
Explanation:
Tomas buys a trumpet for $108.90.
He will make 10 equal payments to pay for the trumpet.
The total amount of each payment that Tomas will make for the trumpet,
$108.90 ÷ 10 = $10.89
Dividing a decimal by 10 moves the decimal point one place to the left.