Decimal Place Value Worksheets - Math Monks - Free Printable

Let’s solve each part step by step.

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Part 1: Write in expanded form

Expanded form means breaking the number into its place values — ones, tens, hundreds, tenths, hundredths, etc.

We write each digit multiplied by its place value.

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a) 63.87

- 6 is in the tens place → 6 × 10
- 3 is in the ones place → 3 × 1
- 8 is in the tenths place → 8 × 1/10 or 0.1
- 7 is in the hundredths place → 7 × 1/100 or 0.01

So:
(6 × 10) + (3 × 1) + (8 × 1/10) + (7 × 1/100)

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b) 3.04

- 3 is in the ones place → 3 × 1
- 0 is in the tenths place → we can skip it (or write 0 × 1/10)
- 4 is in the hundredths place → 4 × 1/100

So:
(3 × 1) + (4 × 1/100)

*(Note: We usually omit zero terms unless asked to include them.)*

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c) 8.7

- 8 is in the ones place → 8 × 1
- 7 is in the tenths place → 7 × 1/10

So:
(8 × 1) + (7 × 1/10)

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d) 0.87

- 0 is in the ones place → skip
- 8 is in the tenths place → 8 × 1/10
- 7 is in the hundredths place → 7 × 1/100

So:
(8 × 1/10) + (7 × 1/100)

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e) 380.17

Break it down:

- 3 is in the hundreds place → 3 × 100
- 8 is in the tens place → 8 × 10
- 0 is in the ones place → skip
- 1 is in the tenths place → 1 × 1/10
- 7 is in the hundredths place → 7 × 1/100

So:
(3 × 100) + (8 × 10) + (1 × 1/10) + (7 × 1/100)

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Part 2: Write in standard form

Standard form means adding up all the parts to get one number.

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a) (2 × 100) + (9 × 10) + (3 × 1)

Calculate each:

- 2 × 100 = 200
- 9 × 10 = 90
- 3 × 1 = 3

Add: 200 + 90 + 3 = 293

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b) (8 × 1000) + (4 × 10) + (3 × 1) + (2 × 1/100)

Calculate:

- 8 × 1000 = 8000
- 4 × 10 = 40
- 3 × 1 = 3
- 2 × 1/100 = 0.02

Add: 8000 + 40 + 3 + 0.02 = 8043.02

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c) (6 × 100) + (7 × 10) + (4 × 1) + (6 × 1/1000)

Calculate:

- 6 × 100 = 600
- 7 × 10 = 70
- 4 × 1 = 4
- 6 × 1/1000 = 0.006

Add: 600 + 70 + 4 + 0.006 = 674.006

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d) (6 × 1000) + (3 × 1/10)

Calculate:

- 6 × 1000 = 6000
- 3 × 1/10 = 0.3

Add: 6000 + 0.3 = 6000.3

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e) (5 × 1000) + (9 × 100) + (3 × 1) + (3 × 1/10)

Calculate:

- 5 × 1000 = 5000
- 9 × 100 = 900
- 3 × 1 = 3
- 3 × 1/10 = 0.3

Add: 5000 + 900 + 3 + 0.3 = 5903.3

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Final Answer:

Write in expanded form:

a) (6 × 10) + (3 × 1) + (8 × 1/10) + (7 × 1/100)
b) (3 × 1) + (4 × 1/100)
c) (8 × 1) + (7 × 1/10)
d) (8 × 1/10) + (7 × 1/100)
e) (3 × 100) + (8 × 10) + (1 × 1/10) + (7 × 1/100)

Write in standard form:

a) 293
b) 8043.02
c) 674.006
d) 6000.3
e) 5903.3