5.15.1Name Multiplication Multiplication

Patterns with Patterns with DecimalsDecimalsLearning Target:Learning Target: Find products involving decimals Find products involving decimals

and powers of 10.and powers of 10.Success Criteria:Success Criteria: • I can explain how to multiply a decimal by a power of 10.• I can explain how to multiply a decimal by a power of 10.• I can explain patterns in the placement of the decimal • I can explain patterns in the placement of the decimal

point when multiplying a decimal by a power of 10.point when multiplying a decimal by a power of 10.

Explore and Grow

Chapter 5 ⎜ Lesson 1 175

Use the relationship between positions in a place value chart to find each product.

What patterns do you notice?

Structure Describe the placement of the decimal point when multiplying a decimal by 10, 100, 0.1, and 0.01.

Hundreds Tens Ones . Tenths Hundredths Thousandths

2.5 × 1 22 .. 55

2.5 × 10

2.5 × 100

Hundreds Tens Ones . Tenths Hundredths Thousandths

2.5 × 1 22 .. 55

2.5 × 0.1

2.5 × 0.01

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Think and Grow: Understand Multiplicative ComparisonThink and Grow: Use Patterns to Find Products

176

9.2 × 1 = 9.2

9.2 × 0.1 = 0.92

9.2 × 0.01 =

So, 9.2 × 0.01 = .

Notice the pattern: When you multiply by 0.1, the decimal point moves oneplace to the left. When you multiply by 0.01, the decimal point moves two places to the left.

Find the product.

wwSSSSShhhoooowwwww aaaaandddddddd GGGGrrrrrrrooowwwwSSSSSSSShhhhhhhhoooooooowwwwwwww aaaaaaaannnnnnnndddddddd GGGGGGGGrrrrrrrroooooooowwwwwwwwShow and GrowShow and Grow

1. 1. 2.51 × 104 = 2. 2. 0.7 × 0.01 =

Use place value concepts. Every time you multiply a number by 1

— 10

= 0.1,

each digit in the number shifts one position to the right in a place value chart.

Use place value concepts. Every time you multiply a number by 10, each digit in the number shifts one position to the left in a place value chart.

0.38 × 1 = 0.38

0.38 × 101 = 0.38 × 10 = 3.8

0.38 × 102 = 0.38 × 100 = 38.

0.38 × 103 = 0.38 × 1,000 =

So, 0.38 × 103 = .

Notice the pattern: In each product, the number of places the decimal pointmoves to the right is the same as the exponent.

Example Find 0.38 × 10 3.

Example Find 9.2 × 0.01.

Hundreds Tens Ones . Tenths Hundredths

00 .. 33 88

33 .. 88

33 88 ..

33 88 00 ..

Ones . Tenths Hundredths Thousandths

99 .. 22

00 .. 99 22

00 .. 00 99 22

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177Chapter 5 ⎜ Lesson 1

Name

Find the product.

7. 7. A contractor installs a new floor of a room using 1,000 squaretiles. Each tile has an area of 1.25 square feet. What is the areaof the floor?

Reasoning Complete the equation.

3. 3. 4.1 × 10 2 =

8. 8. 3.14 × = 0.314

10. 10. × 0.01 = 1.879

5. 5. 16.579 × 104 =

4. 4. 7.03 × 0.1 =

9. 9. × 103 = 6,209

11. 11. 0.045 × = 45

6. 6. 843.7 × 0.01 =

Apply and Grow: Practice©

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Think and Grow: Modeling Real Life

178

Show and GrowShow and Grow GGGGrrrrrrowwwwwwGGhhhhhhoww aannnddddddddh ddddddSSShhhhhhoowwwwwwww nd GrrowGGS GGGGGGGGrrrrrrrroooooooowwwwwwwwGGGGGGaaaaaaaannnnnnnndddddddd dddSSSSSSSShhhhhhhhoooooooowwwwwwww SShhhhhSh ww a r wwShow and GrowShow and Grow12. 12. The London Eye is a 443-foot-tall

Ferris wheel. A model is 0.01 times as tall as the actual Ferris wheel. How much taller is the actualLondon Eye than the model?

14. 14. DIG DEEPER An eel travels at a speed of 2 miles per hour. A starfish travels one hundredth the speed of the eel. A falcontravels 10,000 times as fast as the starfish. How many more miles per hour can the falcon travel than the eel?

13. 13. Each day, you ride your bike from home to school and back. Your school is 0.9 mile from home. How far do you ride your bike in 10 days?

Example A flea is 1.5 millimeters long. A magnified image of the flea is 100 times as long as its actual length. How much longer is the flea in the image than its actual length?

Subtract the length of the flea from the length of theflea in the image.

The flea in the image is millimeters longer than its actual length.

− 1.5

Find the length of the flea in the image by multiplying the length of the flea by 100.

Multiplying 1.5 by 100, or 102, shifts the digits positions to the left in a

place value chart. So, the decimal point moves places to the right.

1.5 × 100 = 1.5 × 102 =

The length of the flea in the image is millimeters.

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Name 5.15.1Homework

& PracticeLearning Target:Learning Target: Find products involving Find products involving decimals and powers of 10.decimals and powers of 10.

179Chapter 5 ⎜ Lesson 1

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0.5 × 0.1 =

So, 0.5 × 0.1 = .

Find the product.

3.02 × 104 = 3.02 × 10,000 =

So, 3.02 × 104 = .

1. 1. 5.201 × 10 =

3. 3. 0.095 × 103 =

5. 5. 0.26 × 104 =

2. 2. 26.7 × 0.01 =

4. 4. 37.84 × 0.1 =

6. 6. 15.9 × 0.01 =

Example Find 3.02 × 104.

Example Find 0.5 × 0.1.

30,200

30200.

0.05

.05

When multiplying a number by a power of 10, the number of

places the decimal point moves tothe right is the same as the

exponent.

When multiplying a number by 0.1, the decimal point moves 1 place to

the left. When multiplying a number by 0.01, the decimal point moves

2 places to the left.

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180

9. 9. Writing Explain how you can use mental math to find 5.4 × 103 and5.4 × 0.01.

10. 10. DIG DEEPER What is Newton’s number?

11. 11. Modeling Real Life A house cat weighs 9.22 pounds. Hercules the liger is the world’s largest cat, and weighs 100 times the weight of the house cat. How much more does Hercules weigh than the house cat?

12. 12. DIG DEEPER A Tyrannosaurus rex weighed about1.4 tons more than one tenth the weight of a Patagotitan mayorum. About how much did the Tyrannosaurus rex weigh?

Find the product.

Review & Refresh13. 13. Newton and Descartes have a $50.00 gift card to a pet store.

Newton’s total is $18.95 and Descartes’s total is $24.38. How much money do they have left on their gift card?

7. 7. 0.8 × 0.01 = 8. 8. 3.1 × 104 =

ghst cat, and weighs

hs 9.22 pounds. cat, and weighs

100 times my number is 12.6 more

than 5,000.

A Patagotitan mayorum was a type of a titanosaur that

weighed about 76 tons.

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