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

All the solutions provided in McGraw Hill My Math Grade 5 Answer Key PDF Chapter 6 Lesson 6 Multiply 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 6 Multiply Decimals by Powers of Ten

Math in My World

Example 1

Josh will need to make 10 payments of $32.25 to purchase a new skimboard. What is the total cost of the skimboard?

Find $32.25 × 10

Multiplying a decimal by 10 moves the decimal point one place to the right.

So, the skimboard costs __________.
Numbers like 10, 100, and 1,000 are powers often. They can be written with exponents with a base of ten.

There is 1 zero in 10. The exponent on 10¹ is 1.
There are 2 zeros in 100. The exponent on 10² is 2.
There are 3 zeros in 1,000. The exponent on 10³ is 3.

To multiply a decimal by a power of ten,
move the decimal point to the right the same number of zeros in the power of ten.
This is also the same number as the exponent on 10.
Answer:
$322.5
Explanation:
Josh will need to make 10 payments of $32.25 to purchase a new skim board.
The total cost of the skim board is,

10 x $32.25 = $322.5

Example 2

Find 24.7 × 10².
One Way: Multiply
Since 10² = 100, find 24.7 × 100.

Another Way: Move the decimal point.
Multiplying a decimal by 100 moves the decimal point two places to the right.

So, 24.7 × 10² = _____________.
Answer:
24,70
Explanation:
Multiply
10² = 10 x 10 = 100,
find 24.7 × 100.
Move the decimal point.
Multiplying a decimal by 100 moves the decimal point two places to the right.

So, 24.7 × 10² = 2,470

Talk Math

Explain how you can mentally find the cost of 10 text messages that each cost $0.25.

Answer:
$2.5
Explanation:
Cost of one text message = $0.25
Cost of ten text messages = 10 x $0.25
Multiplying a decimal by 10 moves the decimal point two places to the right.
10 x $0.25 = $2.5

Guided Practice

Multiply.

Question 1.
0.54 × 10 = ____________
Answer:
5.4
Explanation:
To multiply a decimal by a power of ten,
move the decimal point to the right the same number of zeros in the power of ten.
This is also the same number as the exponent on 10.

Question 2.
8.32 × 100 = _____________
Answer:
832
Explanation:
To multiply a decimal by a power of ten,
move the decimal point to the right the same number of zeros in the power of ten.
This is also the same number as the exponent on 10.
8.32 × 100 = 832.

Question 3.
7.46 × 1,000 = ____________
Answer:
7460.00
Explanation:
To multiply a decimal by a power of ten,
move the decimal point to the right the same number of zeros in the power of ten.
This is also the same number as the exponent on 10.

Independent Practice

Multiply.

Question 4.
1.63 × 10 = ____________
Answer:
16.3
Explanation:
To multiply a decimal by a power of ten,
move the decimal point to the right the same number of zeros in the power of ten.
This is also the same number as the exponent on 10.

Question 5.
0.853 × 10³ = ____________
Answer:
853
Explanation:
To multiply a decimal by a power of ten,
move the decimal point to the right the same number of zeros in the power of ten.
This is also the same number as the exponent on 10.
10³ = 10 x 10 x 10 = 1000
0.853 x 1000 = 853

Question 6.
0.397 × 10¹ = _____________
Answer:
3.97
Explanation:
To multiply a decimal by a power of ten,
move the decimal point to the right the same number of zeros in the power of ten.
This is also the same number as the exponent on 10.
10¹ = 10
0.397 × 10 =3.97

Question 7.
1.76 × 100 = ____________
Answer:
176
Explanation:
To multiply a decimal by a power of ten,
move the decimal point to the right the same number of zeros in the power of ten.
This is also the same number as the exponent on 10.
1.76 × 100 =176

Question 8.
0.78 × 10² = _____________
Answer:
78
Explanation:
To multiply a decimal by a power of ten,
move the decimal point to the right the same number of zeros in the power of ten.
This is also the same number as the exponent on 10.
10² = 10 x 10 = 100
0.78 × 100 =78

Question 9.
76.5 × 10³ = _____________
Answer:
76,500
Explanation:
To multiply a decimal by a power of ten,
move the decimal point to the right the same number of zeros in the power of ten.
This is also the same number as the exponent on 10.
10³ = 10 x 10 x 10 = 100
76.5 × 1000 = 76500

Question 10.
0.81 × 10 = ____________
Answer:
8.1
Explanation:
To multiply a decimal by a power of ten,
move the decimal point to the right the same number of zeros in the power of ten.
This is also the same number as the exponent on 10.
0.81 × 10 = 8.1

Question 11.
1.23 × 10² = _____________
Answer:
123
Explanation:
To multiply a decimal by a power of ten,
move the decimal point to the right the same number of zeros in the power of ten.
This is also the same number as the exponent on 10.
10² = 100
1.23 × 100 = 123

Question 12.
0.48 × 100 = ___________
Answer:
48
Explanation:
To multiply a decimal by a power of ten,
move the decimal point to the right the same number of zeros in the power of ten.
This is also the same number as the exponent on 10.
0.48 × 100 =48

Algebra Find each unknown.

Question 13.
0.93 × 10 = a
a = _____________
Answer:
a = 9.3
Explanation:
To multiply a decimal by a power of ten,
move the decimal point to the right the same number of zeros in the power of ten.
This is also the same number as the exponent on 10.
0.93 × 10 = 9.3

Question 14.
22.94 × 10² = n
n = _____________
Answer:
n = 2,294
Explanation:
To multiply a decimal by a power of ten,
move the decimal point to the right the same number of zeros in the power of ten.
This is also the same number as the exponent on 10.
10² = 10 x 10 = 100
22.94 × 100 = 2294

Question 15.
0.05 × 1,000 = w
w = _____________
Answer:
w = 50
Explanation:
To multiply a decimal by a power of ten,
move the decimal point to the right the same number of zeros in the power of ten.
This is also the same number as the exponent on 10.
0.05 × 1000 = 50

Problem Solving

Question 16.
A music store has 10 flutes. Each flute costs $325.50. What is the cost of all 10 flutes?
Answer:
$3,255
Explanation:
A music store has 10 flutes.
Each flute costs $325.50.
The cost of all 10 flutes = 10 x $325.50 = $3,255

Question 17.
Mathematical PRACTICE Make a Plan One carton of milk costs $0.99. What is the total cost of 102 cartons of milk?
Answer:
$100.98
Explanation:
One carton of milk costs $0.99.
102 cartons can be split into 100 cartons plus 2 cartons.
Cost 100 cartoons = 100 x $0.99 = $99
Cost of 2 cartoons = 2 x $0.99 = $1.98
The total cost of 102 cartons of milk = $99 + $1.98 = $100.98

Question 18.
Titus’s and Cam’s hourly charges for yard work are shown. Suppose Titus and Cam each worked 10 hours. How much money did they earn together?

Answer:
Explanation:
Titus and Cam each worked 10 hours.
Titus earns for 10 days = 10 x $8.25 = $82.5
Cam earns for 10 days = 10 x $5.58 = $55.8
Total money they earn together = $82.5 + $55.8 = $138.3

Question 19.
The length of Jenny’s dog is 10 times the length of her hamster. The length of her hamster is 8.4 centimeters. What is the length of her dog?

Answer:
Explanation:
The length of Jenny’s dog is 10 times the length of her hamster.
The length of her hamster is 8.4 centimeters.
The length of her dog is 8.4 x 10 = 84 centimeters.

HOT Problem

Question 20.
Mathematical PRACTICE Use Number Sense Find 0.346 × 10² × 10.
Answer:
346
Explanation:
To multiply a decimal by a power of ten,
move the decimal point to the right the same number of zeros in the power of ten.
This is also the same number as the exponent on 10.
10² = 10 x 10 = 100
10 x 100 = 1000
0.346 × 1000 = 346

Question 21.
Building on the Essential Question How does the exponent of each power of ten correspond with placing a decimal?
Answer:
A number to the power of -10 multiplying by 10 moves the decimal point 1 place to the right.
Explanation:
The power ten will be the number of places the original decimal point was moved,
it will be negative as it was moved towards the right side.
A number is written as a row of digits,
with each position in the row corresponding to a certain power of 10.
A decimal point in the row divides it into those powers of 10 equal to or greater than 0 and those less than 0, i.e., negative powers of 10.

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

Practice

Multiply.

Question 1.
0.13 × 10 = ___________
Answer:
1.3
Explanation:
To multiply a decimal by a power of ten,
move the decimal point to the right the same number of zeros in the power of ten.
This is also the same number as the exponent on 10.
0.13 × 10 = 1.3

Question 2.
1.4 × 1,000 = ______________
Answer:
1,400
Explanation:
To multiply a decimal by a power of ten,
move the decimal point to the right the same number of zeros in the power of ten.
This is also the same number as the exponent on 10.
1.4 × 1000 = 1400

Question 3.
4.81 × 10³ = ______________
Answer:
4,810
Explanation:
To multiply a decimal by a power of ten,
move the decimal point to the right the same number of zeros in the power of ten.
This is also the same number as the exponent on 10.
10³ = 10 x 10 x 10 = 1000
4.81 x 1000 = 4810

Question 4.
0.72 × 10² = ______________
Answer:
72
Explanation:
To multiply a decimal by a power of ten,
move the decimal point to the right the same number of zeros in the power of ten.
This is also the same number as the exponent on 10.
10² = 10 x 10 = 100
0.72 × 100 = 72

Question 5.
0.179 × 1,000 = _______________
Answer:
179
Explanation:
To multiply a decimal by a power of ten,
move the decimal point to the right the same number of zeros in the power of ten.
This is also the same number as the exponent on 10.
0.179 × 1000 = 179

Question 6.
67.2 × 10¹ = ______________
Answer:
672
Explanation:
To multiply a decimal by a power of ten,
move the decimal point to the right the same number of zeros in the power of ten.
This is also the same number as the exponent on 10.
10¹ = 10
67.2 × 10 = 672

Problem Solving

For Exercises 7 and 8, use the table which shows a school store’s prices.

Question 7.
How much would it cost to buy 10 pens from the school store?
Answer:
$8
Explanation:
Cost of 1 pen = $0.80
Cost of ten pens = 10 x $0.80= $8

Question 8.
How much will it cost for 10 pencils and one notebook?
Answer:
$5
Explanation:
Cost of 1 pen = $0.50
Cost of ten pens = 10 x $0.50= $5

Question 9.
The school purchased 100 trophies to give to the honor roll students. If one trophy costs $4.32, how much would it cost for all of the trophies?

Answer:
$432
Explanation:
The school purchased 100 trophies to give to the honor roll students.
If one trophy costs $4.32,
Cost of 100 trophies = 100 x $4.32 = $432

Question 10.
Mathematical PRACTICE Find the Error Rico is finding 7.5 × 100. Find and correct his mistake.

Answer:
750
Explanation:
To multiply a decimal by a power of ten,
move the decimal point to the right the same number of zeros in the power of ten.
This is also the same number as the exponent on 10.
7.5 x 100 = 750
But Rico moved the decimal point to the left.

Test Practice

Question 11.
Elyse is cutting strips of paper for a scrapbook page. Each strip is 1.5 centimeters wide. How wide will 10 strips of paper be?
(A) 1.5 centimeters
(B) 15 centimeters
(C) 150 centimeters
(D) 1,500 centimeters
Answer:
Option(B)
Explanation:
Each strip is 1.5 centimeters wide.
Total width of 10 strips of paper be 10 x 1.5 = 15 centimeters.