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 through each problem step by step. We’re converting decimals to fractions, then simplifying them.
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1) 3.25
- Decimal fraction: The “25” is in the hundredths place → so it’s 25/100.
- So, 3.25 = 3 and 25/100.
- Simplify 25/100: divide numerator and denominator by 25 → 1/4.
- Final: 3 1/4
✔ Matches answer key.
---
2) 1.72
- “72” is in hundredths → 72/100.
- So, 1.72 = 1 and 72/100.
- Simplify 72/100: divide by 4 → 18/25.
- Final: 1 18/25
✔ Matches.
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3) 8.66
- “66” is hundredths → 66/100.
- So, 8.66 = 8 and 66/100.
- Simplify 66/100: divide by 2 → 33/50.
- Final: 8 33/50
✔ Matches.
---
4) 0.321
- “321” is thousandths → 321/1000.
- No whole number part.
- Can we simplify 321/1000? Let’s check GCF of 321 and 1000.
- 321 ÷ 3 = 107 → 3×107=321
- 1000 not divisible by 3 or 107 → no common factors.
- So, stays as 321/1000
✔ Matches.
---
5) 4.32
- “32” is hundredths → 32/100.
- So, 4.32 = 4 and 32/100.
- Simplify 32/100: divide by 4 → 8/25.
- Final: 4 8/25
✔ Matches.
---
6) 2.625
- “625” is thousandths → 625/1000.
- So, 2.625 = 2 and 625/1000.
- Simplify 625/1000: divide by 125 → 5/8.
- Final: 2 5/8
✔ Matches.
---
7) 1.348
- “348” is thousandths → 348/1000.
- So, 1.348 = 1 and 348/1000.
- Simplify 348/1000: divide by 4 → 87/250.
- Check: 87 and 250 — 87=3×29, 250=2×5³ → no common factors.
- Final: 1 87/250
✔ Matches.
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8) 9.072
- “072” is thousandths → 72/1000 (leading zero doesn’t count).
- So, 9.072 = 9 and 72/1000.
- Simplify 72/1000: divide by 8 → 9/125.
- Final: 9 9/125
✔ Matches.
---
9) 0.84
- “84” is hundredths → 84/100.
- Simplify: divide by 4 → 21/25.
- Final: 21/25
✔ Matches.
---
10) 5.682
- “682” is thousandths → 682/1000.
- So, 5.682 = 5 and 682/1000.
- Simplify 682/1000: divide by 2 → 341/500.
- Check: 341 and 500 — 341=11×31, 500=2²×5³ → no common factors.
- Final: 5 341/500
✔ Matches.
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11) 1.927
- “927” is thousandths → 927/1000.
- So, 1.927 = 1 and 927/1000.
- Can we simplify? 927 ÷ 3 = 309 → 3×309=927; 1000 not divisible by 3 → no.
- Actually, 927 ÷ 3 = 309, but 1000 isn’t divisible by 3 → so fraction is already simplified? Wait — let’s double-check GCF(927,1000).
Actually, 927 = 3 × 309 = 3 × 3 × 103 → 9×103
1000 = 2³×5³ → no common factors with 927 → so yes, 927/1000 is simplest.
But wait — the answer key says 1 927/1000, which matches.
✔ Correct.
---
12) 8.8
- “8” is tenths → 8/10.
- So, 8.8 = 8 and 8/10.
- Simplify 8/10: divide by 2 → 4/5.
- Final: 8 4/5
✔ Matches.
---
13) 3.256
- “256” is thousandths → 256/1000.
- So, 3.256 = 3 and 256/1000.
- Simplify 256/1000: divide by 8 → 32/125.
- Check: 32=2⁵, 125=5³ → no common factors.
- Final: 3 32/125
✔ Matches.
---
14) 6.875
- “875” is thousandths → 875/1000.
- So, 6.875 = 6 and 875/1000.
- Simplify 875/1000: divide by 125 → 7/8.
- Because 875 ÷ 125 = 7, 1000 ÷ 125 = 8.
- Final: 6 7/8
✔ Matches.
---
All answers match the provided answer key. Since this is an answer sheet, and you asked me to solve the problems accurately — I’ve verified every single one.
Final Answer:
The completed table with correct conversions and simplified fractions is as shown in the original image. All 14 problems are correctly solved:
1) 3 1/4
2) 1 18/25
3) 8 33/50
4) 321/1000
5) 4 8/25
6) 2 5/8
7) 1 87/250
8) 9 9/125
9) 21/25
10) 5 341/500
11) 1 927/1000
12) 8 4/5
13) 3 32/125
14) 6 7/8
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1) 3.25
- Decimal fraction: The “25” is in the hundredths place → so it’s 25/100.
- So, 3.25 = 3 and 25/100.
- Simplify 25/100: divide numerator and denominator by 25 → 1/4.
- Final: 3 1/4
✔ Matches answer key.
---
2) 1.72
- “72” is in hundredths → 72/100.
- So, 1.72 = 1 and 72/100.
- Simplify 72/100: divide by 4 → 18/25.
- Final: 1 18/25
✔ Matches.
---
3) 8.66
- “66” is hundredths → 66/100.
- So, 8.66 = 8 and 66/100.
- Simplify 66/100: divide by 2 → 33/50.
- Final: 8 33/50
✔ Matches.
---
4) 0.321
- “321” is thousandths → 321/1000.
- No whole number part.
- Can we simplify 321/1000? Let’s check GCF of 321 and 1000.
- 321 ÷ 3 = 107 → 3×107=321
- 1000 not divisible by 3 or 107 → no common factors.
- So, stays as 321/1000
✔ Matches.
---
5) 4.32
- “32” is hundredths → 32/100.
- So, 4.32 = 4 and 32/100.
- Simplify 32/100: divide by 4 → 8/25.
- Final: 4 8/25
✔ Matches.
---
6) 2.625
- “625” is thousandths → 625/1000.
- So, 2.625 = 2 and 625/1000.
- Simplify 625/1000: divide by 125 → 5/8.
- Final: 2 5/8
✔ Matches.
---
7) 1.348
- “348” is thousandths → 348/1000.
- So, 1.348 = 1 and 348/1000.
- Simplify 348/1000: divide by 4 → 87/250.
- Check: 87 and 250 — 87=3×29, 250=2×5³ → no common factors.
- Final: 1 87/250
✔ Matches.
---
8) 9.072
- “072” is thousandths → 72/1000 (leading zero doesn’t count).
- So, 9.072 = 9 and 72/1000.
- Simplify 72/1000: divide by 8 → 9/125.
- Final: 9 9/125
✔ Matches.
---
9) 0.84
- “84” is hundredths → 84/100.
- Simplify: divide by 4 → 21/25.
- Final: 21/25
✔ Matches.
---
10) 5.682
- “682” is thousandths → 682/1000.
- So, 5.682 = 5 and 682/1000.
- Simplify 682/1000: divide by 2 → 341/500.
- Check: 341 and 500 — 341=11×31, 500=2²×5³ → no common factors.
- Final: 5 341/500
✔ Matches.
---
11) 1.927
- “927” is thousandths → 927/1000.
- So, 1.927 = 1 and 927/1000.
- Can we simplify? 927 ÷ 3 = 309 → 3×309=927; 1000 not divisible by 3 → no.
- Actually, 927 ÷ 3 = 309, but 1000 isn’t divisible by 3 → so fraction is already simplified? Wait — let’s double-check GCF(927,1000).
Actually, 927 = 3 × 309 = 3 × 3 × 103 → 9×103
1000 = 2³×5³ → no common factors with 927 → so yes, 927/1000 is simplest.
But wait — the answer key says 1 927/1000, which matches.
✔ Correct.
---
12) 8.8
- “8” is tenths → 8/10.
- So, 8.8 = 8 and 8/10.
- Simplify 8/10: divide by 2 → 4/5.
- Final: 8 4/5
✔ Matches.
---
13) 3.256
- “256” is thousandths → 256/1000.
- So, 3.256 = 3 and 256/1000.
- Simplify 256/1000: divide by 8 → 32/125.
- Check: 32=2⁵, 125=5³ → no common factors.
- Final: 3 32/125
✔ Matches.
---
14) 6.875
- “875” is thousandths → 875/1000.
- So, 6.875 = 6 and 875/1000.
- Simplify 875/1000: divide by 125 → 7/8.
- Because 875 ÷ 125 = 7, 1000 ÷ 125 = 8.
- Final: 6 7/8
✔ Matches.
---
All answers match the provided answer key. Since this is an answer sheet, and you asked me to solve the problems accurately — I’ve verified every single one.
Final Answer:
The completed table with correct conversions and simplified fractions is as shown in the original image. All 14 problems are correctly solved:
1) 3 1/4
2) 1 18/25
3) 8 33/50
4) 321/1000
5) 4 8/25
6) 2 5/8
7) 1 87/250
8) 9 9/125
9) 21/25
10) 5 341/500
11) 1 927/1000
12) 8 4/5
13) 3 32/125
14) 6 7/8
Parent Tip: Review the logic above to help your child master the concept of fraction decimal worksheet 1 answer.
