Lesson 5
Objective: Name decimal fractions in expanded, unit,
and word forms by applying place value reasoning.




Write 54 tenths as a decimal.
Say the decimal.
Multiply it by 10².
Say the product.
◦ 5.4 x 10² = 540




Write 6 tenths as a decimal.
Say the decimal.
Multiply it by 10².
Say the product.
◦ 0.6 x 10² = 60




Write 6 tenths as a decimal.
Say the decimal.
Divide it by 10².
Say the quotient.
◦ 0.6 ÷10² = 0.006

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
3
0
3
0
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
7
0
0
0
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
0
0
0
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
7
5
0
0
7
5
0
0
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
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
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
 2m
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.
0



0
0
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.
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
𝟏
expanded form using a fraction like this, 1 x ( 𝟏𝟎𝟎𝟎) or using a decimal
like this 1 x 0.001.
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 = 0.001 =
𝟏
𝟏𝟎𝟎𝟎
=1x(
𝟏
𝟏𝟎𝟎𝟎
)
0.001 = 1 x 0.001
1 thousandth
𝟏
𝟏𝟎𝟎𝟎

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 = 0.003 =
𝟑
𝟏𝟎𝟎𝟎
=3x(
𝟏
𝟏𝟎𝟎𝟎
)
0.003 = 3 x 0.001
3 thousandths
𝟑
𝟏𝟎𝟎𝟎

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:
1x(
𝟏
𝟏𝟎𝟎
)+3x(
𝟏
𝟏𝟎𝟎𝟎
)
1 x 0.01 + 3 x 0.001

Now write this decimal in unit form.

1 hundredth 3 thousandths = 13 thousandths
Thirteen thousandths = 0.013 =
𝟏𝟑
𝟏𝟎𝟎𝟎
𝟏𝟑
𝟏𝟎𝟎𝟎
= 0.013 = 1 x 0.01 + 3 x 0.001
1 hundredth 3 thousandths
13 thousandths

Write two hundred seventy-three thousandths in standard form, and
expanded form using fractions and then using decimals.

Standard form: 0.273

Expanded forms:
2x(
𝟏
𝟏𝟎
)+7x(
𝟏
𝟏𝟎𝟎
)+3x(
𝟏
𝟏𝟎𝟎𝟎
)
2 x 0.1 + 7 x 0.01 + 3 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 =
0.273 =
𝟐𝟕𝟑
𝟏𝟎𝟎𝟎
𝟐𝟕𝟑
𝟏𝟎𝟎𝟎
= 0.273 = 2 x 0.1 + 7 x 0.01 + 3 x 0.001
2 tenths 7 hundredths 3 thousandths
273 thousandths

Write one and six hundred eight thousandths in standard form, and
expanded form using fractions and then using decimals.

Standard form: 1.608

Expanded forms:
1+6x(
𝟏
𝟏𝟎
)+8x(
𝟏
𝟏𝟎𝟎𝟎
)
1 + 6 x 0.1 + 8 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 =
1
1
𝟔𝟎𝟖
𝟏𝟎𝟎𝟎
𝟔𝟎𝟖
𝟏𝟎𝟎𝟎
= 1.608 = 1 + 6 x 0.1 + 8 x 0.001
1 one 6 tenths 8 thousandths = 1 one 60 hundredths 8
thousandths = 1 one 608 thousandths

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.
Twenty-five and four hundred thirteen thousandths= 25.413 =
25
25
𝟒𝟏𝟑
=
𝟏𝟎𝟎𝟎
𝟒𝟏𝟑
𝟏𝟎𝟎𝟎
𝟏
𝟏
𝟏
2 x 10 + 5 x 1 + 4 x 𝟏𝟎 + 1 x 𝟏𝟎𝟎 + 3 x 𝟏𝟎𝟎𝟎
25.413 = 2 x 10 + 5 x 1 + 4 x 0.1 + 1 x 0.01 + 3 x 0.001
2 tens 5 ones 4 tenths 1 hundredths 3 thousandths
25 ones 413 thousandths

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.
𝟒
Twelve and four hundredths= 12.04 = 12 𝟏𝟎𝟎
𝟒
𝟏
12 𝟏𝟎𝟎 = 1 x 10 + 2 x 1 + 4 x 𝟏𝟎𝟎
12.04 = 1 x 10 + 2 x 1 + 4 x 0.01
1 ten 2 ones 4 hundredths = 12 ones 4 hundredths =
1,204 hundredths

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.
Nine and four hundred ninety-five thousandths = 9.495 =
𝟒𝟗𝟓
9 𝟏𝟎𝟎𝟎
𝟒𝟗𝟓
𝟏
𝟏
𝟏
9 𝟏𝟎𝟎𝟎 = 9 x 1 + 4 x 𝟏𝟎 + 9 𝟏𝟎𝟎 + 5 𝟏𝟎𝟎𝟎
9.495 = 9 x 1 + 4 x 0.1 + 9 x 0.01 + 5 x 0.001
9 ones 4 tenths 9 hundredths 5 thousandths = 9,495 thousandths





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.
Four hundred four thousandths = 0.404 =
𝟒𝟎𝟒
𝟏𝟎𝟎𝟎
𝟏
𝟏
= 4 x (𝟏𝟎 ) + 4 (𝟏𝟎𝟎𝟎)
0.404= 4 x 0.1 + 4 x 0.001
4 tenths 4 thousandths
𝟒
𝟏
Four hundred and four thousandths = 400 𝟏𝟎𝟎𝟎 = 4 x 100 + 4 (𝟏𝟎𝟎𝟎) =
400.004 = 4 x 100 + 4 x 0.001
4 hundreds and 4 thousandths




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 = 0.202 =
𝟏
𝟐𝟎𝟐
𝟏𝟎𝟎𝟎
=
𝟏
2 x (𝟏𝟎) + 2 (𝟏𝟎𝟎𝟎)
0.202= 2 x 0.1 + 2 x 0.001
2 tenths 2 thousandths
𝟗
𝟏
Nine hundred and nine tenths = 900 𝟏𝟎𝟎𝟎 = 9 x 100 + 9 (𝟏𝟎) =
900.9 = 9 x 100 + 9 x 0.1
9 hundred and 9 tenths