# Into Math Grade 5 Module 15 Lesson 1 Answer Key Understand Decimal Multiplication Patterns

We included HMH Into Math Grade 5 Answer Key PDF Module 15 Lesson 1 Understand Decimal Multiplication Patterns to make students experts in learning maths.

## HMH Into Math Grade 5 Module 15 Lesson 1 Answer Key Understand Decimal Multiplication Patterns

I Can multiply decimals by powers of 10 that are both greater than and less than 1.

DNA is the genetic code that determines many of your traits. It is found rolled up inside your body’s cells. Uncoiled, each strand of DNA is 71.0 inches long. This measurement is equivalent to about 1.8 meters. What is the length of 10 uncoiled DNA strands placed end-to-end in inches and in meters?

Length of 10 Uncoiled, each strand of DNA = 710 inches or 18 meters.

Explanation:
Number of inches of Uncoiled, each strand of DNA = 71.0 inches long.
Number of inches of 10 Uncoiled, each strand of DNA = 10 × Number of inches of Uncoiled, each strand of DNA
= 10 × 71.0 inches
= 710 inches.
Number of meters of Uncoiled, each strand of DNA =1.8 meters.
Number of meters of 10 Uncoiled, each strand of DNA = 10 × Number of meters of Uncoiled, each strand of DNA
= 10 × 1.8 meters
= 18 meters.

Turn and Talk In each instance, what happens to the place-value positions of the digits and the placement of the decimal point?
In each instance, the place-value positions of the digits and the placement of the decimal point changes as it moves right side of the number.

Explanation:
In each instance, the place-value positions of the digits and the placement of the decimal point changes as it moves right side of the number.

Build Understanding
Question 1.
A discount store sells all items for $0.98 each. Items can be bought in boxes of 10, 100, or 1,000. Jolene wants to know how much each box will cost. Use the pattern to answer the questions. 1 × 0.98 = 0.98 10 × 0.98 = 9.8 100 × 0.98 = 98 1,000 × 0.98 = 980 A. How much will it cost to buy 1 box of 10 items? 1 box of 100 items? 1 box of 1,000 items? Answer: Cost of 10 items in a box =$9.8.
Cost of 100 items in a box = $98.0. Cost of 1000 items in a box =$980.0.

Explanation:
Cost of all items a discount store sells = $0.98 each. Cost of 10 items in a box = 10 × Cost of all items a discount store sells = 10 ×$0.98
= $9.8 Cost of 100 items in a box = 100 × Cost of all items a discount store sells = 100 ×$0.98
= $98.0 Cost of 1000 items in a box = 1000 × Cost of all items a discount store sells = 1000 ×$0.98
= $980.0 B. What is the value of the digit 9 in 0.98? in 9.80? in 98? in 980? Answer: The value of the digit 9 in 0.98 = 9 Oneth. The value of the digit 9 in 9.8 = 90. The value of the digit 9 in 980 = 900. Explanation: The value of the digit 9 in 0.98 = 9 Oneth. The value of the digit 9 in 9.8 = 90. The value of the digit 9 in 980 = 900. C. In which direction do the digits shift as you multiply by increasing powers of 10? Answer: Right side direction the digits shift as you multiply by increasing powers of 10. Explanation: The direction where the digits shift as you multiply by increasing powers of 10 is to its right side. D. How does the shifting of the digits affect the position of the decimal point as you multiply by increasing powers of 10? Answer: Yes, the shifting of the digits affect the position of the decimal point as you multiply by increasing powers of 10. Explanation: The shifting of the digits affect the position of the decimal point as you multiply by increasing powers of 10 because digits values will be changed. E. Show the movement of the decimal point in the pattern above. Answer: Explanation: 10 ×$0.98 = $9.8 100 ×$0.98 = $98.00 1000 ×$0.98 = $980.00 Here how many zeros are after 1, that many times the deciml point moves to the right of the number while multiplication. Turn and Talk If you multiply a number by 100, how will the placement of the decimal point change? Find at least two ways in which the pattern above shows that this is true. Answer: 100 ×$0.98 = $98.00. => 10 ×$0.98 = $9.8 × 10 =$98.00.

Explanation:
Two ways:
100 × $0.98 =$98.00.
=> 10 × $0.98 =$9.8 × 10 = $98.00. Question 2. Mrs. Gymni sells jump ropes on her website for$2.35 each. She sold 102 jump ropes last week. How much did she earn?

A. Complete the pattern.
100 × 2.35 = _____________
101 × 2.35 = _____________
102 × 2.35 = _____________
103 × 2.35 = _____________
The pattern:
100 × 2.35 = 2.35.
101 × 2.35 = 23.5.
102 × 2.35 = 235.0.
103 × 2.35 = 2350.0.

Explanation:
100 × 2.35 = 2.35.
101 × 2.35 = 10 × 2.35 = 23.5.
102 × 2.35 = 100 × 2.35 = 235.0.
103 × 2.35 = 1000 × 2.35 = 2350.0.

B. Which equation shows 2.35 multiplied by 10 once?
Write this equation using a factor of 10.
Equation: 1 × 10 × 2.35 = 2.35.

Explanation:
100 × 2.35 = 2.35.
Factor of 10:
1 × 10 = 10.
=> 1 × 10 × 2.35 = 2.35.

How does the placement of the decimal point in the product compare to its placement in 2.35?
The number present before the decimal point is called the whole number part, and present after the decimal point is called the decimal number part. the placement of the decimal point in the product compare to its placement in 2.35 are the same.

Explanation:
The placement of the decimal point in the product compare to its placement in 2.35 is that a decimal number has two parts namely the whole number and decimal number part.

C. Which equation shows 2.35 multiplied by 10 three times?
Write this equation using factors of 10.
Equation: 103 × 2.35 = 2350.0

Explanation:
103 × 2.35 = 10 × 10 × 10 × 2.35
= 100 × 10 × 2.35
= 1000 × 2.35
= 2350.0.

How does the placement of the decimal point in the product compare to its placement in 2.35?
The placement of the decimal point in the product compare to its placement in 2.35 differs as it becomes greater by 10 times decimal Point.

Explanation:
As the place moves to the left, the value of the number becomes greater by 10 times Decimal Point. Another important idea for decimals and place value is the decimal point. The decimal point is a dot between digits in a number

D. How much did Mrs. Gymni earn last week from selling 102 jump ropes?
Amount she earned = 232.65.

Explanation:
Cost of jump ropes Mrs. Gymni sells on her website = $2.35 each. Amount of jump ropes She sold last week = 102 Amount she earned = (102 × 2.35) – (100 × 2.35) = (100 × 2.35) – (1 × 2.35) = 235 – 2.35 = 232.65 Turn and Talk How does the change in the position of the decimal point relate to the exponent on the 10? Answer: The change in the position of the decimal point relate to the exponent on the 10 because when multiplication is done by 10 to any number, there a place to left left moves the decimal point according to the number of zeros. Explanation: The change in the position of the decimal point relate to the exponent on the 10 because when multiplication is done by 10 to any number, there a place to left left moves the decimal point according to the number of zeros. Question 3. The first-place finisher in a magazine drive raised$935 in sales. Most participants raised $$\frac{1}{10}$$ of that amount. The least amount raised was $$\frac{1}{100}$$ of that amount.

Use the pattern to answer the questions.
1 × 935 = 935
0.1 × 935 = 93.5
0.01 × 935 = 9.35
A. What is the value of the digit 5 in 935? in 93.5? in 9.35?
The value of the digit 5 in 935 = 5 (5 × 1)
The value of the digit 5 in 93.5 = 0.5 (5 × 0.1)
The value of the digit 5 in 9.35 = 0.05 (5 × 0.01)

Explanation:
The value of the digit 5 in 935 = 5 (5 × 1)
The value of the digit 5 in 93.5 = 0.5 (5 × 0.1)
The value of the digit 5 in 9.35 = 0.05 (5 × 0.01)

B. How do the digits shift as you multiply by 1, 0.1, and 0.01?
When multiplying by 0.1, 0.01 and 0.001, the point is moved to the left as many digits as there are zeros in the multiplier.

Explanation:
When multiplying by 0.1, 0.01 and 0.001, the point is moved to the left as many digits as there are zeros in the multiplier. If this is difficult to remember at first, you can use the first method, in which multiplication is done as with regular numbers.

C. How does the shifting of the digits affect the position of the decimal point as you multiply by 1, 0.1, and 0.01?
The shifting of the digits affect the position of the decimal point as you multiply by 1, 0.1, and 0.01 as the point is moved to the left as many digits as there are zeros in the multiplier.

Explanation:
The shifting of the digits affect the position of the decimal point as you multiply by 1, 0.1, and 0.01 as the point is moved to the left as many digits as there are zeros in the multiplier. The value of digits also changes.

D. How much did most participants raise? ___________
How much was the least amount raised? ___________
Most participants raised = $93.5. The least amount raised =$9.35.

Explanation:
The first-place finisher in a magazine drive raised $935 in sales. Most participants raised = $$\frac{1}{10}$$ of that amount. = $$\frac{1}{10}$$ ×$935
= $93.5. The least amount raised = $$\frac{1}{100}$$ of that amount. = $$\frac{1}{100}$$ ×$935
= $9.35. Check Understanding Chromosome 13 in the human body contains a DNA molecule that is about 3.19 centimeters long. Question 1. What is the length of 1,000 of these molecules? Answer: Length of 1,000 of these molecules = 3190. Explanation: Length of Chromosome 13 = 3.19 centimeters long. Length of 1,000 of these molecules = 1000 × Length of Chromosome 13 = 1000 × 3.19 = 3190. Question 2. What is the combined length of 102 of these molecules? Answer: The combined length of 102 of these molecules = 319. Explanation: Length of 10 molecules = 10 × 3.19 = 31.9. The combined length of 102 of these molecules = (10 × 10 × 3.19) = 319. Question 3. What is 0.1 of the length of chromosome 13? Answer: 0.1 of the length of chromosome 13 = 31.9. Explanation: 0.1 of the length of chromosome 13 = 3.19 ÷ 0.1 = 31.9. On Your Own Question 4. STEM The length of a single DNA molecule is 3.4 nanometers. What is the combined length of 100 DNA molecules? Answer: The combined length of 100 DNA molecules = 340. Explanation: Length of a single DNA molecule = 3.4 nanometers. The combined length of 100 DNA molecules = 100 × 3.4 = 340. Find the value of the expression. Question 5. 102 × 38,256.77 Answer: 102 × 38,256.77 = 38,25,677. Explanation: 102 × 38,256.77 = 10 × 10 × 38,256.77 = 38,25,677. Question 6. 100 × 932.56 Answer: 100 × 932.56 = 93,256. Explanation: 100 × 932.56 = 93,256. Question 7. 0.01 × 7,143.5 Answer: 0.01 × 7,143.5 = 71.435. Explanation: 0.01 × 7,143.5 = 71.435. Question 8. 1,000 × 42.35 Answer: 1,000 × 42.35 = 42,350. Explanation: 1,000 × 42.35 = 42,350. Question 9. 103 × 5,976 Answer: 103 × 5,976 = 59,76,000. Explanation: 103 × 5,976 = 10 × 10 × 10 × 5,976 = 59,76,000. Question 10. 0.1 × 3,654 Answer: 0.1 × 3,654 = 365.4. Explanation: 0.1 × 3,654 = 365.4. Find the value that makes the equation true. Question 11. 103 × _________ = 34,000 Answer: 103 × 34 = 34,000. Explanation: 103 × ?? = 34,000 => ?? = 34000 ÷ 103 => ?? = 34. Question 12. 843 = 100 × _________ Answer: 843 = 100 × 8.43 Explanation: 843 = 100 × ?? => 843 ÷ 100= ?? => 8.43 = ?? Question 13. 0.01 × _______ = 76.55 Answer: 0.01 × 7,655 = 76.55 Explanation: 0.01 × ?? = 76.55 => ?? = 76.55 ÷ 0.01 => ?? = 7,655. Question 14. An author sells books on a website for$8.95 each.
A teacher orders 10 books. How much will the teacher pay?
Number of books teacher orders = 10.
Total cost of the books = $89.5. Explanation: Cost of the books an author sells on a website =$8.95 each.
Number of books teacher orders = 10.
Total cost of the books = Cost of the books an author sells on a website × Number of books teacher orders
= $8.95 × 10 =>$89.5.

A library orders 103 books. How much will the library pay?
Total cost of the books = $8950. Explanation: Cost of the books an author sells on a website =$8.95 each.
Number of books library orders = 103
Total cost of the books = Cost of the books an author sells on a website × Number of books library orders
= $8.95 × 103 =$8.95 × 10 × 10 × 10
= $89.5 × 10 × 10 =$895 × 10
= \$8950.

Complete the pattern.
Question 15.
0.01 × 72.3 = _________
0.1 × 72.3 = _________
1 × 72.3 = _________
10 × 72.3 = _________
The pattern:
0.01 × 72.3 = 0.723
0.1 × 72.3 = 7.23.
1 × 72.3 = 72.3.
10 × 72.3 = 723.

Explanation:
0.01 × 72.3 = 0.723
0.1 × 72.3 = 7.23.
1 × 72.3 = 72.3.
10 × 72.3 = 723.

Question 16.
100 × 3.58 = __________
101 × 3.58= __________
102 × 3.58 = __________
103 × 3.58 = __________
The pattern:
100 × 3.58 = 3.58.
101 × 3.58= 35.8.
102 × 3.58 = 358.
103 × 3.58 = 3580.

Explanation:
100 × 3.58 = 3.58.
101 × 3.58= 35.8.
102 × 3.58 = 358.
103 × 3.58 = 3580.

Question 17.
Attend to Precision How would you explain to another student how to multiply 725 by 0.01?
Here we need to understand that 725 is multiplied by 0.01
=> Number of dots in the number that many dots it goes to left side in 725.
=> 725 × 0.01 = 7.25.

Explanation:
Multiply 725 by 0.01:
Here we need to understand that 725 is multiplied by 0.01
=> Number of dots in the number that many dots it goes to left side in 725.
=> 725 × 0.01 = 7.25.

Find the value of the expression.
Question 18.
10 × 565.54
10 × 565.54 = 5655.4.

Explanation:
10 × 565.54 = 5655.4.

Question 19.
0.01 × 9,764.6
0.01 × 9,764.6 = 97.646.

Explanation:
0.01 × 9,764.6= 97.646.

Question 20.
103 × 76.34
103 × 76.34 = 76,340.

Explanation:
103 × 76.34 = 10 × 10 × 10 × 76.34
= 76,340.

Find the value that makes the equation true.
Question 21.
10 × _________ = 4,276.4
10 × 427.64 = 4,276.4

Explanation:
10 × ?? = 4,276.4
=> ?? = 4276.4 ÷ 10
=> ?? = 427.64

Question 22.
0.1 × __________ = 7,354
0.1 × 73,540 = 7,354.

Explanation:
0.1 × ?? = 7,354
=> ?? = 7354 ÷ 0.1
=> ?? = 73,540.

Question 23.
103 × ________ = 78,660
103 × 78.66 = 78,660

Explanation:
103 × ?? = 78,660
=> ?? = 78660 ÷ 103
=> ?? = 78.66.

Question 24.
Four different boxes weigh a total of 245 pounds.
One box weighs $$\frac{1}{10}$$ of the total amount. How much does this box weigh?
Weigh of one box = 24.5 Pounds.

Explanation:
Total Number of pounds of all four boxes = 245.
One box weighs $$\frac{1}{10}$$ of the total amount.
=> Weigh of one box = $$\frac{1}{10}$$ × Total Number of pounds of all four boxes
= $$\frac{1}{10}$$ × 245
= 24.5 Pounds.

Another box weighs $$\frac{1}{100}$$ of the total amount. How much does this box weigh?
Weight of another box = 2.45 Pounds.

Explanation:
Total Number of pounds of all four boxes = 245.
Another box weighs $$\frac{1}{100}$$ of the total amount.
Weight of another box = $$\frac{1}{100}$$  × Total Number of pounds of all four boxes
= $$\frac{1}{100}$$ × 245
= 2.45 Pounds.

Complete the pattern.
Question 25.
100 × 345.89 = __________
101 × 345.89 = __________
102 × 345.89 = __________
103 × 345.89 = __________
100 × 345.89 = 345.89.
101 × 345.89 = 3458.9
102 × 345.89 = 34589.
103 × 345.89 = 345890.

Explanation:
The pattern:
100 × 345.89 = 345.89.
101 × 345.89 = 3458.9
102 × 345.89 = 34589.
103 × 345.89 = 345890.

Question 26.
10 × 144.2 = __________
1 × 144.2 = __________
0.1 × 144.2 = __________
0.01 × 144.2 = __________
10 × 144.2 = 1442.
1 × 144.2 = 144.2
0.1 × 144.2 = 14.42.
0.01 × 144.2 = 1.442.

Explanation:
The pattern:
10 × 144.2 = 1442.
1 × 144.2 = 144.2
0.1 × 144.2 = 14.42.
0.01 × 144.2 = 1.442.

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