Converting decimals to fractions worksheet - Free Printable

Let’s go through each problem one by one. We’re converting decimals to fractions. The key is to write the decimal as a fraction over 10, 100, 1000, etc., depending on how many digits are after the decimal point — then simplify if possible.

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1) 0.167
This has 3 decimal places → write as 167/1000
Check if it simplifies: 167 is prime? Yes, and doesn’t divide 1000 → 167/1000

2) 0.083
3 decimal places → 83/1000
83 is prime → doesn’t simplify → 83/1000

3) 0.2
1 decimal place → 2/10 = 1/5 (divide numerator and denominator by 2)

4) 0.75
2 decimal places → 75/100 = 3/4 (divide by 25)

5) 0.2
Same as #3 → 1/5

6) 0.833
3 decimal places → 833/1000
Check: 833 ÷ 7 = 119, 1000 not divisible by 7 → no common factors? Let’s check GCD(833,1000).
833 = 7×119 = 7×7×17 → 1000 = 2³×5³ → no common factors → 833/1000

Wait — actually, 0.833 is often used for 5/6 ≈ 0.8333... but here it’s written as 0.833 exactly → so we treat it as exact decimal → 833/1000

But let me double-check: sometimes in worksheets, they mean repeating or rounded values. But since it says “convert”, and gives 0.833, we take it literally.

Actually, looking at problems 6 and 10 both say 0.833 — maybe they expect 5/6? But 5/6 = 0.8333... not 0.833. Since it’s written with 3 digits, we’ll stick with 833/1000 unless told otherwise.

BUT — wait! In many school contexts, 0.833 is meant to represent 5/6. Let me verify:

5 ÷ 6 = 0.833333... → so if they wrote 0.833, it might be rounded. But the instruction is to convert the given decimal — so strictly speaking, 0.833 = 833/1000.

However, looking at other numbers like 0.333 (problems 14 and 19), which is clearly meant to be 1/3, even though 1/3 = 0.333..., same with 0.167 likely meaning 1/6.

Ah — this is important. In educational materials, when they write 0.167, 0.333, 0.833, they usually mean the repeating decimals that approximate common fractions.

Let me re-evaluate based on common fraction equivalents:

- 0.167 → approximately 1/6 (since 1÷6=0.1666...)
- 0.083 → approximately 1/12 (1÷12=0.08333...)
- 0.2 → 1/5
- 0.75 → 3/4
- 0.833 → 5/6 (5÷6=0.8333...)
- 0.25 → 1/4
- 0.333 → 1/3
- 0.4 → 2/5
- 0.375 → 3/8
- 0.6 → 3/5
- 0.917 → ? 11/12 = 0.91666... → close to 0.917
- 0.125 → 1/8

Given that, I think the worksheet expects us to recognize these as common fractions, even if the decimal is truncated.

So let’s do it properly with that understanding:

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Revised approach: Match to closest simple fraction

1) 0.167 → 1/6 (because 1÷6 = 0.1666... ≈ 0.167)

2) 0.083 → 1/12 (1÷12 = 0.08333...)

3) 0.2 → 1/5

4) 0.75 → 3/4

5) 0.2 → 1/5

6) 0.833 → 5/6 (5÷6 = 0.8333...)

7) 0.25 → 1/4

8) 0.75 → 3/4

9) 0.25 → 1/4

10) 0.833 → 5/6

11) 0.7 → 7/10

12) 0.6 → 3/5

13) 0.625 → 5/8 (because 5÷8=0.625 exactly)

14) 0.333 → 1/3

15) 0.4 → 2/5

16) 0.375 → 3/8 (3÷8=0.375)

17) 0.6 → 3/5

18) 0.917 → 11/12 (11÷12=0.91666... ≈ 0.917)

19) 0.333 → 1/3

20) 0.125 → 1/8

Now let’s confirm each:

- 1/6 = 0.1666... → rounds to 0.167 → OK
- 1/12 = 0.08333... → rounds to 0.083 → OK
- 5/6 = 0.8333... → rounds to 0.833 → OK
- 11/12 = 0.91666... → rounds to 0.917 → OK
- Others are exact.

So final answers:

1) 1/6
2) 1/12
3) 1/5
4) 3/4
5) 1/5
6) 5/6
7) 1/4
8) 3/4
9) 1/4
10) 5/6
11) 7/10
12) 3/5
13) 5/8
14) 1/3
15) 2/5
16) 3/8
17) 3/5
18) 11/12
19) 1/3
20) 1/8

I think this is what the worksheet intends.

Final Answer:
1) 1/6
2) 1/12
3) 1/5
4) 3/4
5) 1/5
6) 5/6
7) 1/4
8) 3/4
9) 1/4
10) 5/6
11) 7/10
12) 3/5
13) 5/8
14) 1/3
15) 2/5
16) 3/8
17) 3/5
18) 11/12
19) 1/3
20) 1/8