Converting Decimals to Fractions Worksheet - Free Printable
Educational worksheet: Converting Decimals to Fractions Worksheet. Download and print for classroom or home learning activities.
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Step-by-step solution for: Converting Decimals to Fractions Worksheet
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Show Answer Key & Explanations
Step-by-step solution for: Converting Decimals to Fractions Worksheet
Let’s go step by step to convert each decimal into a decimal fraction (that means writing it as a fraction over 10, 100, 1000, etc., based on how many decimal places) and then simplify it to its simplest form.
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- Count the number of digits after the decimal point.
- Write the number without the decimal as the numerator.
- Use 10, 100, 1000, etc. as the denominator — same number of zeros as decimal places.
- Then reduce the fraction by dividing top and bottom by their greatest common factor (GCF).
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Let’s do them one by one:
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2) 0.05
→ Decimal fraction: 5/100
→ Simplify: GCF of 5 and 100 is 5 → 5÷5=1, 100÷5=20 → 1/20
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3) 0.14
→ Decimal fraction: 14/100
→ Simplify: GCF of 14 and 100 is 2 → 14÷2=7, 100÷2=50 → 7/50
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4) 0.125
→ Decimal fraction: 125/1000
→ Simplify: GCF of 125 and 1000 is 125 → 125÷125=1, 1000÷125=8 → 1/8
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5) 0.64
→ Decimal fraction: 64/100
→ Simplify: GCF of 64 and 100 is 4 → 64÷4=16, 100÷4=25 → 16/25
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6) 0.27
→ Decimal fraction: 27/100
→ Simplify: 27 and 100 have no common factors except 1 → already simplest → 27/100
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7) 0.216
→ Decimal fraction: 216/1000
→ Simplify: GCF of 216 and 1000? Let’s see: both divisible by 8 → 216÷8=27, 1000÷8=125 → 27/125
*(Check: 27 = 3³, 125 = 5³ → no more common factors)*
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8) 0.89
→ Decimal fraction: 89/100
→ 89 is prime, doesn’t divide 100 → 89/100
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9) 0.625
→ Decimal fraction: 625/1000
→ Simplify: GCF is 125 → 625÷125=5, 1000÷125=8 → 5/8
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10) 0.428
→ Decimal fraction: 428/1000
→ Simplify: GCF of 428 and 1000? Both even → divide by 2 → 214/500 → again by 2 → 107/250
→ 107 is prime, doesn’t divide 250 → 107/250
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11) 0.08
→ Decimal fraction: 8/100
→ Simplify: GCF is 4 → 8÷4=2, 100÷4=25 → 2/25
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12) 0.546
→ Decimal fraction: 546/1000
→ Simplify: Divide by 2 → 273/500
→ Check if 273 and 500 share any factors: 273 ÷ 3 = 91, but 500 not divisible by 3 → so 273/500
*(Double-check: 273 = 3×7×13; 500 = 2²×5³ → no overlap → correct)*
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13) 0.35
→ Decimal fraction: 35/100
→ Simplify: GCF is 5 → 35÷5=7, 100÷5=20 → 7/20
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14) 0.864
→ Decimal fraction: 864/1000
→ Simplify: Divide by 8 → 864÷8=108, 1000÷8=125 → now check 108 and 125
→ 108 = 2²×3³, 125 = 5³ → no common factors → 108/125
Wait — let me double-check that division:
864 ÷ 8 = 108? Yes.
1000 ÷ 8 = 125? Yes.
And 108 and 125 share no common factors → yes, 108/125
But wait — can we simplify earlier? Maybe divide by 4 first?
864 ÷ 4 = 216, 1000 ÷ 4 = 250 → then 216/250 → divide by 2 → 108/125 → same result. Correct.
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Now let’s write all answers in order:
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Final Answer:
2) 0.05 = 5/100 = 1/20
3) 0.14 = 14/100 = 7/50
4) 0.125 = 125/1000 = 1/8
5) 0.64 = 64/100 = 16/25
6) 0.27 = 27/100 = 27/100
7) 0.216 = 216/1000 = 27/125
8) 0.89 = 89/100 = 89/100
9) 0.625 = 625/1000 = 5/8
10) 0.428 = 428/1000 = 107/250
11) 0.08 = 8/100 = 2/25
12) 0.546 = 546/1000 = 273/500
13) 0.35 = 35/100 = 7/20
14) 0.864 = 864/1000 = 108/125
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Rule:
- Count the number of digits after the decimal point.
- Write the number without the decimal as the numerator.
- Use 10, 100, 1000, etc. as the denominator — same number of zeros as decimal places.
- Then reduce the fraction by dividing top and bottom by their greatest common factor (GCF).
---
Let’s do them one by one:
---
2) 0.05
→ Decimal fraction: 5/100
→ Simplify: GCF of 5 and 100 is 5 → 5÷5=1, 100÷5=20 → 1/20
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3) 0.14
→ Decimal fraction: 14/100
→ Simplify: GCF of 14 and 100 is 2 → 14÷2=7, 100÷2=50 → 7/50
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4) 0.125
→ Decimal fraction: 125/1000
→ Simplify: GCF of 125 and 1000 is 125 → 125÷125=1, 1000÷125=8 → 1/8
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5) 0.64
→ Decimal fraction: 64/100
→ Simplify: GCF of 64 and 100 is 4 → 64÷4=16, 100÷4=25 → 16/25
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6) 0.27
→ Decimal fraction: 27/100
→ Simplify: 27 and 100 have no common factors except 1 → already simplest → 27/100
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7) 0.216
→ Decimal fraction: 216/1000
→ Simplify: GCF of 216 and 1000? Let’s see: both divisible by 8 → 216÷8=27, 1000÷8=125 → 27/125
*(Check: 27 = 3³, 125 = 5³ → no more common factors)*
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8) 0.89
→ Decimal fraction: 89/100
→ 89 is prime, doesn’t divide 100 → 89/100
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9) 0.625
→ Decimal fraction: 625/1000
→ Simplify: GCF is 125 → 625÷125=5, 1000÷125=8 → 5/8
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10) 0.428
→ Decimal fraction: 428/1000
→ Simplify: GCF of 428 and 1000? Both even → divide by 2 → 214/500 → again by 2 → 107/250
→ 107 is prime, doesn’t divide 250 → 107/250
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11) 0.08
→ Decimal fraction: 8/100
→ Simplify: GCF is 4 → 8÷4=2, 100÷4=25 → 2/25
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12) 0.546
→ Decimal fraction: 546/1000
→ Simplify: Divide by 2 → 273/500
→ Check if 273 and 500 share any factors: 273 ÷ 3 = 91, but 500 not divisible by 3 → so 273/500
*(Double-check: 273 = 3×7×13; 500 = 2²×5³ → no overlap → correct)*
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13) 0.35
→ Decimal fraction: 35/100
→ Simplify: GCF is 5 → 35÷5=7, 100÷5=20 → 7/20
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14) 0.864
→ Decimal fraction: 864/1000
→ Simplify: Divide by 8 → 864÷8=108, 1000÷8=125 → now check 108 and 125
→ 108 = 2²×3³, 125 = 5³ → no common factors → 108/125
Wait — let me double-check that division:
864 ÷ 8 = 108? Yes.
1000 ÷ 8 = 125? Yes.
And 108 and 125 share no common factors → yes, 108/125
But wait — can we simplify earlier? Maybe divide by 4 first?
864 ÷ 4 = 216, 1000 ÷ 4 = 250 → then 216/250 → divide by 2 → 108/125 → same result. Correct.
---
Now let’s write all answers in order:
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Final Answer:
2) 0.05 = 5/100 = 1/20
3) 0.14 = 14/100 = 7/50
4) 0.125 = 125/1000 = 1/8
5) 0.64 = 64/100 = 16/25
6) 0.27 = 27/100 = 27/100
7) 0.216 = 216/1000 = 27/125
8) 0.89 = 89/100 = 89/100
9) 0.625 = 625/1000 = 5/8
10) 0.428 = 428/1000 = 107/250
11) 0.08 = 8/100 = 2/25
12) 0.546 = 546/1000 = 273/500
13) 0.35 = 35/100 = 7/20
14) 0.864 = 864/1000 = 108/125
Parent Tip: Review the logic above to help your child master the concept of fraction to decimal worksheet grade 4.
