# Place Value with Decimals

Lesson 2

Math

Unit 1

Lesson 2 of 13

## Objective

Use whole numbers to denote powers of 10. Explain patterns in the number of zeros when multiplying any powers of 10 by any other powers of 10.

## Common Core Standards

### Core Standards

• 5.NBT.A.2 — Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

• 4.NBT.A.1

## Criteria for Success

1. Use exponents to denote powers of 10.
2. Convert between exponential form, standard form, and multiplication sentences that represent powers of 10.
3. Look for and express regularity in repeated calculations of powers of 10 multiplied by other powers of 10, and explain patterns in the number of zeros in the product (MP.8).
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### Problem 1

a.   How many do you see? How do you see them?

b.   Instead of writing $$10 \times 10$$, we can write $$10^2$$, which we read “ten to the power of two.” The two is the exponent and tells us how many times we multiply 10 by itself. How would you represent the number of the smallest spokes in the image above as a power of 10?

#### Guiding Questions

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#### References

Illustrative Mathematics Grade 5 > Unit 6 > Lesson 2 > Warm-up

Grade 5 > Unit 6 > Lesson 2 > Warm-up, accessed on June 14, 2022, 5 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

### Problem 2

a.   Write each of the following as a product of tens and in standard form.

1. $$10^4$$
2. $$10^6$$

b.   Write each of the following as a power of 10.

1. 10 × 10 × 10 × 10 × 10
2. 1,000,000,000

#### Guiding Questions

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### Problem 3

a.   Solve.

1. 10 × 10,000 = ______
2. 1,000 × 1,000 = ______
3. 1,000,000 × 100 = ______

b.   How were powers of 10 useful in solving Part (a)?

#### Guiding Questions

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#### References

Illustrative Mathematics Grade 5 > Unit 6 > Lesson 2 > Activity 2

Grade 5 > Unit 6 > Lesson 2 > Activity 2, accessed on June 14, 2022, 5:12 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

## Problem Set & Homework

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### Discussion of Problem Set

• Look at the last row in #2. What did you get? How did you get that?
• Look at #4e. How did you solve this even though it’s beyond what we’ve done already?

### Problem 1

Fill in the following chart.

 Standard Form Repeated Multiplication Sentence Exponential Form $${10\times10\times10\times10}$$ $${10^2}$$ $${1,000,000}$$

### Problem 2

What pattern do you notice between the standard form and repeated multiplication sentences in the table in #1?

### Student Response

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Lesson 1

Lesson 3

## Lesson Map

Topic A: Place Value with Whole Numbers

Topic B: Place Value with Decimals

Topic C: Reading, Writing, Comparing, and Rounding Decimals