Decimal Place Value Worksheets - Math Monks - Free Printable

Absolutely! Let’s solve each part of this Decimal Place Value Worksheet step by step, with clear explanations.

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## ✔ 1) Write each number in expanded form.

Expanded form means writing the number as the sum of each digit multiplied by its place value.

a) 673.12

- 6 is in the hundreds place → 6 × 100 = 600
- 7 is in the tens place → 7 × 10 = 70
- 3 is in the ones place → 3 × 1 = 3
- 1 is in the tenths place → 1 × 0.1 = 0.1
- 2 is in the hundredths place → 2 × 0.01 = 0.02

✔ Answer: (6 × 100) + (7 × 10) + (3 × 1) + (1 × 0.1) + (2 × 0.01)

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b) 866.81

- 8 × 100 = 800
- 6 × 10 = 60
- 6 × 1 = 6
- 8 × 0.1 = 0.8
- 1 × 0.01 = 0.01

✔ Answer: (8 × 100) + (6 × 10) + (6 × 1) + (8 × 0.1) + (1 × 0.01)

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c) 244.37

- 2 × 100 = 200
- 4 × 10 = 40
- 4 × 1 = 4
- 3 × 0.1 = 0.3
- 7 × 0.01 = 0.07

✔ Answer: (2 × 100) + (4 × 10) + (4 × 1) + (3 × 0.1) + (7 × 0.01)

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d) 130.78

- 1 × 100 = 100
- 3 × 10 = 30
- 0 × 1 = 0 (still write it for completeness)
- 7 × 0.1 = 0.7
- 8 × 0.01 = 0.08

✔ Answer: (1 × 100) + (3 × 10) + (0 × 1) + (7 × 0.1) + (8 × 0.01)

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e) 145.69

- 1 × 100 = 100
- 4 × 10 = 40
- 5 × 1 = 5
- 6 × 0.1 = 0.6
- 9 × 0.01 = 0.09

✔ Answer: (1 × 100) + (4 × 10) + (5 × 1) + (6 × 0.1) + (9 × 0.01)

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f) 429.67

- 4 × 100 = 400
- 2 × 10 = 20
- 9 × 1 = 9
- 6 × 0.1 = 0.6
- 7 × 0.01 = 0.07

✔ Answer: (4 × 100) + (2 × 10) + (9 × 1) + (6 × 0.1) + (7 × 0.01)

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## ✔ 2) Write each number in standard form.

Standard form means combining all the parts into one number.

a) (7 × 1000) + (2 × 100) + (5 × 10) + (3 × 1) + (9 × 0.1) + (7 × 0.01)

- 7 × 1000 = 7000
- 2 × 100 = 200
- 5 × 10 = 50
- 3 × 1 = 3
- 9 × 0.1 = 0.9
- 7 × 0.01 = 0.07

Add them:
7000 + 200 = 7200
7200 + 50 = 7250
7250 + 3 = 7253
7253 + 0.9 = 7253.9
7253.9 + 0.07 = 7253.97

✔ Answer: 7253.97

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b) (4 × 1000) + (0 × 100) + (0 × 10) + (1 × 1) + (3 × 0.1) + (9 × 0.01)

- 4 × 1000 = 4000
- 0 × 100 = 0
- 0 × 10 = 0
- 1 × 1 = 1
- 3 × 0.1 = 0.3
- 9 × 0.01 = 0.09

Add:
4000 + 0 + 0 + 1 = 4001
4001 + 0.3 = 4001.3
4001.3 + 0.09 = 4001.39

✔ Answer: 4001.39

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c) (5 × 100) + (1 × 10) + (3 × 1) + (2 × 0.1) + (0 × 0.01) + (1 × 0.001)

- 5 × 100 = 500
- 1 × 10 = 10
- 3 × 1 = 3
- 2 × 0.1 = 0.2
- 0 × 0.01 = 0
- 1 × 0.001 = 0.001

Add:
500 + 10 = 510
510 + 3 = 513
513 + 0.2 = 513.2
513.2 + 0 = 513.2
513.2 + 0.001 = 513.201

✔ Answer: 513.201

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d) (3 × 1000) + (9 × 100) + (7 × 10) + (8 × 1) + (7 × 0.1) + (7 × 0.01)

- 3 × 1000 = 3000
- 9 × 100 = 900
- 7 × 10 = 70
- 8 × 1 = 8
- 7 × 0.1 = 0.7
- 7 × 0.01 = 0.07

Add:
3000 + 900 = 3900
3900 + 70 = 3970
3970 + 8 = 3978
3978 + 0.7 = 3978.7
3978.7 + 0.07 = 3978.77

✔ Answer: 3978.77

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## ✔ 3) Find the missing numbers.

These are simple addition/subtraction problems using decimal place values.

a) 0.3 + 0.008 = ______

Just add:
0.300
+0.008
= 0.308

✔ Answer: 0.308

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b) 4 + 0.067 + ______ = 4.167

First, add what we have:
4 + 0.067 = 4.067

Now, subtract from total:
4.167 - 4.067 = 0.100

✔ Answer: 0.1

*(Note: 0.100 = 0.1)*

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c) ______ + 8 + 0.8 = 8.87

First, add known numbers:
8 + 0.8 = 8.8

Subtract from total:
8.87 - 8.8 = 0.07

✔ Answer: 0.07

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d) ______ = 5 + 0.007

This is straightforward:
5 + 0.007 = 5.007

✔ Answer: 5.007

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e) 9.327 = ______ + 9 + 0.007

First, add the known parts:
9 + 0.007 = 9.007

Subtract from total:
9.327 - 9.007 = 0.320

✔ Answer: 0.32

*(0.320 = 0.32)*

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f) 8.392 = 8.002 + ______

Subtract:
8.392 - 8.002 = 0.390

✔ Answer: 0.39

*(0.390 = 0.39)*

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## 🎉 Final Answers Summary:

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1) Expanded Form:

a) (6 × 100) + (7 × 10) + (3 × 1) + (1 × 0.1) + (2 × 0.01)
b) (8 × 100) + (6 × 10) + (6 × 1) + (8 × 0.1) + (1 × 0.01)
c) (2 × 100) + (4 × 10) + (4 × 1) + (3 × 0.1) + (7 × 0.01)
d) (1 × 100) + (3 × 10) + (0 × 1) + (7 × 0.1) + (8 × 0.01)
e) (1 × 100) + (4 × 10) + (5 × 1) + (6 × 0.1) + (9 × 0.01)
f) (4 × 100) + (2 × 10) + (9 × 1) + (6 × 0.1) + (7 × 0.01)

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2) Standard Form:

a) 7253.97
b) 4001.39
c) 513.201
d) 3978.77

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3) Missing Numbers:

a) 0.308
b) 0.1
c) 0.07
d) 5.007
e) 0.32
f) 0.39

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