1. M ODULE 1 Lesson 5 Objective: Name decimal fractions in expanded, unit, and word forms by applying place value reasoning.

2. MULTIPLY AND DIVIDE BY EXPONENTS Write 54 tenths as a decimal. Say the decimal. Multiply it by 10². Say the product. 5.4 x 10² = 540

3. MULTIPLY AND DIVIDE BY EXPONENTS Write 6 tenths as a decimal. Say the decimal. Multiply it by 10². Say the product. 0.6 x 10² = 60

4. MULTIPLY AND DIVIDE BY EXPONENTS Write 6 tenths as a decimal. Say the decimal. Divide it by 10². Say the quotient. 0.6 ÷10² = 0.006

5. MULTIPLY AND DIVIDE BY EXPONENTS Write 2 and seven hundred eighty-four thousandths as a decimal. 2.784 Multiply it by 10³. Say the product. 2.784 x 10³ = 2784 Write six thousand five hundred eighty three. 6583 Divide it by 10³. Say the quotient. 6583 ÷ 10³ = 6.583

6. MULTIPLYING METRIC UNITS 3 m = ____ cm Show 3 in your place value chart. How many centimeters are in 1 meter? Show how many centimeters are in 3 meters on your place value chart. 3 m = 300 cm 3 300

7. MULTIPLYING METRIC UNITS 7 kg = ____ g Show 7 in your place value chart. How many grams are in 1 kilogram? Show how many grams are in 7 kilograms on your place value chart. 7 kg = 7000 g 7 0007

8. MULTIPLYING METRIC UNITS 7000 ml = ____ l Show 7000 in your place value chart. How many milliliters are in 1 liter? Show how many liters are in 7000 milliliters on your place value chart. 7000 ml = 7 l 0 0 0 7 7

9. MULTIPLYING METRIC UNITS 7500 m = ____ km ____ m Show 7500 in your place value chart. How many meters are in 1 km? Show how many kilometers are in 7500 meters on your place value chart. 7500 m = 7 km 500 m 5 0 0 7 7 7 5 0 0

10. MULTIPLYING METRIC UNITS 8350 g = ____ kg ____ g Show 8350 in your place value chart. How many grams are in 1 kilogram? Show how many kilograms are in 8350 grams on your place value chart. 8350 g = 8 kg 350 g 7

11. APPLICATION PROBLEM Jordan measures a desk at 200 cm. James measures the same desk in millimeters, and Amy measures the same desk in meters. What is James’ measurement in millimeters? What is Amy’s measurement in meters? Show your thinking using a place value mat or an equation with exponents. Include a statement of solution. James: 200 cm = ____ mm 2000 mm Amy: 200 cm = ____ m 2 m 7

12. CONCEPT DEVELOPMENT Three thousand forty seven Write this number in standard form, expanded form, and unit form. Standard form: 3,047 Expanded form: 3,000 + 40 + 7 Unit form: 3 thousand, 4 tens, 7 ones Explain to your partner the purpose of writing this number in these different forms. 7

13. CONCEPT DEVELOPMENT – P ROBLEM 1 Write one thousandth using digits on your place value chart. How many ones, tenths, hundredths, thousandths? This is the standard form of the decimal for 1 thousandth. 7 000 1

14. CONCEPT DEVELOPMENT – P ROBLEM 1 7

15. 7

16. CONCEPT DEVELOPMENT – P ROBLEM 2 7

17. 7

18. 7

19. CONCEPT DEVELOPMENT – P ROBLEM 3 Write 25.413 in word form. Twenty-five and four hundred thirteen thousandths  Now write this decimal in unit form. 2 tens 5 ones 4 tenths 1 hundredth 3 thousandths What are other unit forms of this number? 25 ones 413 thousandths 254 tenths 13 hundredths 25,413 thousandths  Write it as a mixed number, then in expanded form. 7

20. CONCEPT DEVELOPMENT – P ROBLEM 3 Write 12.04 in word form. Twelve and four hundredths  Now write this decimal in unit form. 1 ten 2 ones 4 hundredths What are other unit forms of this number? 12 ones 4 hundredths 1, 204 hundredths  Write it as a mixed number, then in expanded form. 7

21. CONCEPT DEVELOPMENT – P ROBLEM 3 Write 9.495 in word form. Nine and four hundred ninety-five thousandths  Now write this decimal in unit form. 9 ones 4 tenths 9 hundredths 5 thousandths  Write it as a mixed number, then in expanded form. 7

22. CONCEPT DEVELOPMENT – P ROBLEM 4 Write four hundred four thousandths in standard form. 0.404  Now write four hundred and four thousandths in standard form. 400.004  Tell the digits you used to write four hundred four thousandths.  How did you know where to write the decimal in each of the standard forms?  Now write the expanded and unit forms for each of these numbers. 7

23. CONCEPT DEVELOPMENT – P ROBLEM 4 Write two hundred two thousandths in standard form. 0.202  Now write nine hundred nine tenths in standard form. 900.9  How did you know where to write the decimal in each of the standard forms?  Now write the expanded and unit forms for each of these numbers. 7