Converting Fractions to from Decimals Worksheets - Math Monks - Free Printable

Explanation:
We need to convert each fraction into a decimal. To do that, we divide the numerator (top number) by the denominator (bottom number). Let’s go one by one and check carefully.

1. $ \frac{11}{15} $
11 ÷ 15 = 0.7333… → repeating decimal: 0.73̄ (or 0.733...). Usually, we round to 3 decimal places unless told otherwise. But since this is a math worksheet, exact decimals (terminating or repeating) are expected. Let’s compute precisely:
- 15 × 0.733 = 10.995 → close.
- Actually, $ \frac{11}{15} = \frac{22}{30} = \frac{73.\overline{3}}{100} $ → So it's 0.733..., i.e., 0.7\overline{3}

But many school worksheets accept rounded to 3 decimals or exact fraction-to-decimal conversion using long division. Let’s use calculator-style precise values (to 4 decimals, then decide if terminating or repeating):

Let me compute each with long division or known facts:

1. $ \frac{11}{15} $:
15 goes into 11.000 → 0.7333… → 0.7333 (repeating 3) → write as 0.7\overline{3} or 0.733 (if rounding to 3 decimals). Since the worksheet has blank boxes (likely expects decimal form, possibly rounded to 3 or 4 places), but better to give exact decimal representation — many of these are terminating or repeating. Let’s check which are terminating:

A fraction in lowest terms terminates iff denominator’s prime factors are only 2 and/or 5.

So let’s reduce each fraction first, then check:

1. $ \frac{11}{15} $: 11 and 15 coprime. 15 = 3×5 → has factor 3 → repeating
→ 11 ÷ 15 = 0.7333... = 0.7\overline{3}

2. $ \frac{2}{15} $: same denominator → repeating
2 ÷ 15 = 0.1333... = 0.1\overline{3}

3. $ \frac{16}{12} $: simplify first!
$ \frac{16}{12} = \frac{4}{3} $ (divide numerator & denominator by 4)
$ \frac{4}{3} = 1.\overline{3} $ → 1.\overline{3}

4. $ \frac{5}{6} $: 6 = 2×3 → has 3 → repeating
5 ÷ 6 = 0.8333... = 0.8\overline{3}

5. $ \frac{15}{10} $: simplifies to $ \frac{3}{2} = 1.5 $ → 1.5 (terminating)

6. $ \frac{2}{23} $: 23 is prime ≠ 2 or 5 → repeating, long period
Let’s compute: 2 ÷ 23 =
23 × 0.08695652173913... actually, let’s do division:
2.000000 ÷ 23:
23 goes into 20 → 0, into 200 → 8×23=184, remainder 16
bring down 0 → 160 → 6×23=138, rem 22
bring down 0 → 220 → 9×23=207, rem 13
bring down 0 → 130 → 5×23=115, rem 15
bring down 0 → 150 → 6×23=138, rem 12
bring down 0 → 120 → 5×23=115, rem 5
bring down 0 → 50 → 2×23=46, rem 4
bring down 0 → 40 → 1×23=23, rem 17
bring down 0 → 170 → 7×23=161, rem 9
bring down 0 → 90 → 3×23=69, rem 21
bring down 0 → 210 → 9×23=207, rem 3
bring down 0 → 30 → 1×23=23, rem 7
bring down 0 → 70 → 3×23=69, rem 1
bring down 0 → 10 → 0×23=0, rem 10
bring down 0 → 100 → 4×23=92, rem 8
... this repeats eventually. So it's a long repeating decimal: 0.\overline{0869565217391304347826} (22-digit repeat). But for elementary worksheet? Unlikely they expect that. Maybe they want approximate to 3 decimals: 0.087

Wait — maybe the worksheet expects *exact* decimals only when terminating, otherwise rounded to 3 decimal places. Let’s look at others:

7. $ \frac{12}{25} $: 25 = 5² → terminating
$ \frac{12}{25} = \frac{48}{100} = 0.48 $

8. $ \frac{23}{27} $: 27 = 3³ → repeating
23 ÷ 27 = ?
27 × 0.851 = 22.977 → close
Actually: 23/27 = 0.\overline{851} (since 1/27 = 0.\overline{037}, so 23/27 = 23 × 0.\overline{037} = 0.\overline{851})
Check: 0.851851... × 27 = ?
0.851851 × 27 = (851851/999999) × 27 = (851851×27)/999999 = 23,000,? Better to trust: 23 ÷ 27 = 0.851851851... → 0.\overline{851}

9. $ \frac{4}{17} $: 17 prime → repeating, period 16. Again, unlikely full repeat expected. Approximate: 4 ÷ 17 ≈ 0.2352941176470588 → 0.235 (to 3 decimals)

10. $ \frac{36}{21} $: simplify: divide by 3 → $ \frac{12}{7} $
12 ÷ 7 = 1.714285714285... = 1.\overline{714285}

11. $ \frac{120}{11} $: 120 ÷ 11 = 10.909090... = 10.\overline{90}

12. $ \frac{31}{17} $: 31 ÷ 17 = 1.8235294117647058... → repeating, approx 1.824 (to 3 decimals)

13. $ \frac{39}{25} $: 25 → terminating
$ \frac{39}{25} = \frac{156}{100} = 1.56 $

14. $ \frac{15}{19} $: 19 prime → repeating. 15 ÷ 19 ≈ 0.7894736842105263 → 0.789 (3 decimals)

15. $ \frac{29}{19} $: 29 ÷ 19 = 1.5263157894736842... → 1.526 (3 decimals)

But wait — maybe the worksheet expects *exact decimals*, and for repeating ones, write with bar notation. However, the answer boxes are small dashed rectangles — likely expecting decimal numbers, possibly rounded to 3 decimal places.

Let me verify common practice in elementary math (grade 5–6): When converting fractions to decimals, if it doesn’t terminate, they often ask to round to nearest hundredth or thousandth. Since no instruction is given, and many problems here are non-terminating, the safest is to give exact decimal forms, using bar notation where repeating, and terminating decimals as is.

Let me list each with correct exact decimal:

1. $ \frac{11}{15} = 0.7\overline{3} $
2. $ \frac{2}{15} = 0.1\overline{3} $
3. $ \frac{16}{12} = \frac{4}{3} = 1.\overline{3} $
4. $ \frac{5}{6} = 0.8\overline{3} $
5. $ \frac{15}{10} = 1.5 $
6. $ \frac{2}{23} = 0.\overline{0869565217391304347826} $ — too long; perhaps they expect 0.087 (rounded to 3 dp)
7. $ \frac{12}{25} = 0.48 $
8. $ \frac{23}{27} = 0.\overline{851} $
9. $ \frac{4}{17} = 0.\overline{2352941176470588} $ — again long; likely 0.235
10. $ \frac{36}{21} = \frac{12}{7} = 1.\overline{714285} $
11. $ \frac{120}{11} = 10.\overline{90} $
12. $ \frac{31}{17} = 1.\overline{8235294117647058} $ → ~1.824
13. $ \frac{39}{25} = 1.56 $
14. $ \frac{15}{19} = 0.\overline{7894736842105263} $ → ~0.789
15. $ \frac{29}{19} = 1.\overline{5263157894736842} $ → ~1.526

Given this is a standard worksheet from "Math Monks", I looked up similar worksheets online — they usually expect decimals rounded to 3 decimal places for non-terminating ones.

Let me recalculate each to 3 decimal places (rounding properly):

1. 11 ÷ 15 = 0.73333... → 0.733
2. 2 ÷ 15 = 0.13333... → 0.133
3. 16 ÷ 12 = 1.33333... → 1.333
4. 5 ÷ 6 = 0.83333... → 0.833
5. 15 ÷ 10 = 1.5 → 1.500 or just 1.5 (but box may fit 1.5)
6. 2 ÷ 23 = 0.0869565... → round to 3 dp: look at 4th digit = 9 ≥5 → round up: 0.087
7. 12 ÷ 25 = 0.48 → 0.480 or 0.48
8. 23 ÷ 27 = 0.851851... → 4th digit = 8 → round up: 0.852
9. 4 ÷ 17 = 0.235294... → 4th digit = 2 < 5 → 0.235
10. 36 ÷ 21 = 1.714285... → 4th digit = 2 → 1.714
11. 120 ÷ 11 = 10.909090... → 4th digit = 0 → 10.909
12. 31 ÷ 17 = 1.823529... → 4th digit = 5 → round up: 1.824
13. 39 ÷ 25 = 1.56 → 1.560 or 1.56
14. 15 ÷ 19 = 0.789473... → 4th digit = 4 < 5 → 0.789
15. 29 ÷ 19 = 1.526315... → 4th digit = 3 < 5 → 1.526

Now check consistency: many worksheets accept answers like 0.733, 0.133, 1.333, etc.

Let me verify a few with calculator precision:

- 11/15 = 0.733333... ✓ → 0.733
- 2/15 = 0.133333... → 0.133
- 16/12 = 1.333333... → 1.333
- 5/6 = 0.833333... → 0.833
- 15/10 = 1.5
- 2/23 ≈ 0.0869565 → rounded to 3 decimals: 0.087 ✔
- 12/25 = 0.48 ✔
- 23/27 ≈ 0.851851 → 0.852 ✔
- 4/17 ≈ 0.235294 → 0.235 ✔
- 36/21 = 1.7142857 → 1.714 ✔
- 120/11 = 10.9090909 → 10.909 ✔
- 31/17 ≈ 1.823529 → 1.824 ✔
- 39/25 = 1.56 ✔
- 15/19 ≈ 0.78947368 → 0.789 ✔
- 29/19 ≈ 1.52631579 → 1.526 ✔

All good.

Since the problem says “Convert the given fractions into decimals” with blank boxes (no specification), and this is likely for middle school, rounding to 3 decimal places is standard.

Final Answer will list all 15 decimals rounded to 3 decimal places (except exact terminating ones can be written without trailing zeros, but to be consistent, we’ll use 3 decimals or as is).

But looking at box size in image (dashed rectangle), probably expects something like “0.733”, “1.5”, etc.

I’ll provide final answers as:

1. 0.733
2. 0.133
3. 1.333
4. 0.833
5. 1.5
6. 0.087
7. 0.48
8. 0.852
9. 0.235
10. 1.714
11. 10.909
12. 1.824
13. 1.56
14. 0.789
15. 1.526

Yes.

Final Answer:
1. 0.733
2. 0.133
3. 1.333
4. 0.833
5. 1.5
6. 0.087
7. 0.48
8. 0.852
9. 0.235
10. 1.714
11. 10.909
12. 1.824
13. 1.56
14. 0.789
15. 1.526