1. Engage NY Module 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 UNITS3 3
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

7. MULTIPLYING METRIC UNITS7 7
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 = g

8. MULTIPLYING METRIC UNITS7 7
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

9. MULTIPLYING METRIC UNITS7 5 7 5
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 7

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,
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 – Problem 11
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

14. CONCEPT DEVELOPMENT – Problem 1
We write 1 thousandth as a fraction like this.
𝟏 𝟏𝟎𝟎𝟎
1 thousandth is a single copy of a thousandth. I can write the expanded form using a fraction like this, 1 x ( 𝟏 𝟏𝟎𝟎𝟎 ) or using a decimal like this 1 x
The unit form of this decimal looks like this 1 thousandth. We use a numeral (1) and the unit (thousandth) written as a word for the unit form.
One thousandth = = 𝟏 𝟏𝟎𝟎𝟎
𝟏 𝟏𝟎𝟎𝟎 = 1 x ( 𝟏 𝟏𝟎𝟎𝟎 )
0.001 = 1 x 0.001
1 thousandth 7

15. CONCEPT DEVELOPMENT – Problem 1
Imagine 3 copies of 1 thousandths. How many thousandths is that?
Write in standard form and as a fraction.
Standard form: 0.003
Fraction form: 𝟑 𝟏𝟎𝟎𝟎
3 thousandths is 3 copies of 1 thousandth, turn and talk to your partner about how this would be written in expanded form using a fraction and using a decimal.
Three thousandths = = 𝟑 𝟏𝟎𝟎𝟎
𝟑 𝟏𝟎𝟎𝟎 = 3 x ( 𝟏 𝟏𝟎𝟎𝟎 )
0.003 = 3 x 0.001
3 thousandths 7

16. CONCEPT DEVELOPMENT – Problem 2
Write thirteen thousandths in standard form, and expanded form using fractions and then using decimals.
Turn and share with your partner.
Standard form: 0.013
Expanded forms: 1 x ( 𝟏 𝟏𝟎𝟎 ) + 3 x ( 𝟏 𝟏𝟎𝟎𝟎 )
1 x x 0.001
Now write this decimal in unit form.
1 hundredth 3 thousandths = 13 thousandths
Thirteen thousandths = = 𝟏𝟑 𝟏𝟎𝟎𝟎
𝟏𝟑 𝟏𝟎𝟎𝟎 = = 1 x x 0.001
1 hundredth 3 thousandths
13 thousandths 7

17. CONCEPT DEVELOPMENT – Problem 2
Write two hundred seventy-three thousandths in standard form, and expanded form using fractions and then using decimals.
Standard form: 0.273
Expanded forms: 2 x ( 𝟏 𝟏𝟎 ) + 7 x ( 𝟏 𝟏𝟎𝟎 ) + 3 x ( 𝟏 𝟏𝟎𝟎𝟎 )
2 x x x 0.001
Now write this decimal in unit form.
2 tenths 7 hundredths 3 thousandths = 2 tenths 73 thousandths = 27 hundredths 3 thousandths = 273 thousandths
Two hundred seventy three thousandths = = 𝟐𝟕𝟑 𝟏𝟎𝟎𝟎
𝟐𝟕𝟑 𝟏𝟎𝟎𝟎 = = 2 x x x 0.001
2 tenths 7 hundredths 3 thousandths
273 thousandths 7

18. CONCEPT DEVELOPMENT – Problem 2
Write one and six hundred eight thousandths in standard form, and expanded form using fractions and then using decimals.
Standard form:
Expanded forms: x ( 𝟏 𝟏𝟎 ) + 8 x ( 𝟏 𝟏𝟎𝟎𝟎 )
1 + 6 x x 0.001
Now write this decimal in unit form.
1 one 6 tenths 8 thousandths = 1 one 60 hundredths 8 thousandths = 1 one 608 thousandths
One and six hundred eight thousandths= =
1 𝟔𝟎𝟖 𝟏𝟎𝟎𝟎
1 𝟔𝟎𝟖 𝟏𝟎𝟎𝟎 = = x x 0.001
1 one 6 tenths 8 thousandths = 1 one 60 hundredths 8 thousandths = 1 one 608 thousandths 7

19. CONCEPT DEVELOPMENT – Problem 3
Write 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.
Twenty-five and four hundred thirteen thousandths= = 𝟒𝟏𝟑 𝟏𝟎𝟎𝟎
25 𝟒𝟏𝟑 𝟏𝟎𝟎𝟎 = 2 x x x 𝟏 𝟏𝟎 + 1 x 𝟏 𝟏𝟎𝟎 + 3 x 𝟏 𝟏𝟎𝟎𝟎
= 2 x x x x x 0.001
2 tens 5 ones 4 tenths 1 hundredths 3 thousandths
25 ones 413 thousandths 7

20. CONCEPT DEVELOPMENT – Problem 3
Write 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.
Twelve and four hundredths= = 12 𝟒 𝟏𝟎𝟎
12 𝟒 𝟏𝟎𝟎 = 1 x x x 𝟏 𝟏𝟎𝟎
12.04 = 1 x x x 0.01
1 ten 2 ones 4 hundredths = 12 ones 4 hundredths =
1,204 hundredths 7

21. CONCEPT DEVELOPMENT – Problem 3
Write 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.
Nine and four hundred ninety-five thousandths = =
9 𝟒𝟗𝟓 𝟏𝟎𝟎𝟎
9 𝟒𝟗𝟓 𝟏𝟎𝟎𝟎 = 9 x x 𝟏 𝟏𝟎 𝟏 𝟏𝟎𝟎 𝟏 𝟏𝟎𝟎𝟎
9.495 = 9 x x x x 0.001
9 ones 4 tenths 9 hundredths 5 thousandths = 9,495 thousandths 7

22. CONCEPT DEVELOPMENT – Problem 4
Write four hundred four thousandths in standard form.
0.404
Now write four hundred and four thousandths in standard form.
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.
Four hundred four thousandths = = 𝟒𝟎𝟒 𝟏𝟎𝟎𝟎 = 4 x ( 𝟏 𝟏𝟎 ) + 4 ( 𝟏 𝟏𝟎𝟎𝟎 )
0.404= 4 x x 0.001
4 tenths 4 thousandths
Four hundred and four thousandths = 400 𝟒 𝟏𝟎𝟎𝟎 = 4 x ( 𝟏 𝟏𝟎𝟎𝟎 ) =
= 4 x x 0.001
4 hundreds and 4 thousandths 7

23. CONCEPT DEVELOPMENT – Problem 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.
Two hundred two thousandths = = 𝟐𝟎𝟐 𝟏𝟎𝟎𝟎 =
2 x ( 𝟏 𝟏𝟎 ) + 2 ( 𝟏 𝟏𝟎𝟎𝟎 )
0.202= 2 x x 0.001
2 tenths 2 thousandths
Nine hundred and nine tenths = 900 𝟗 𝟏𝟎𝟎𝟎 = 9 x ( 𝟏 𝟏𝟎 ) =
900.9 = 9 x x 0.1
9 hundred and 9 tenths 7