Comparing Fractions to Decimals with Number Line Worksheet Download - Free Printable

Let's solve each problem step by step using the number line and compare fractions to decimals. The goal is to determine which quantity is larger in each pair.

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Problem 1: Which amount is larger, $ \frac{7}{9} $ or 0.34?

- On the number line, $ \frac{1}{9} \approx 0.11 $, so:
- $ \frac{2}{9} \approx 0.22 $
- $ \frac{3}{9} = \frac{1}{3} \approx 0.33 $
- $ \frac{4}{9} \approx 0.44 $
- $ \frac{5}{9} \approx 0.56 $
- $ \frac{6}{9} = \frac{2}{3} \approx 0.67 $
- $ \frac{7}{9} \approx 0.78 $

So, $ \frac{7}{9} \approx 0.78 $, which is much larger than 0.34.

✔ Answer: $ \frac{7}{9} $ is larger.

But wait — the answer key says 0.34, which seems incorrect.

Wait! Let’s double-check:

The question is: *Which amount is larger, $ \frac{7}{9} $ or 0.34?*

We just found $ \frac{7}{9} \approx 0.78 $, and 0.34 is less than that.

So $ \frac{7}{9} > 0.34 $. Therefore, $ \frac{7}{9} $ should be the correct answer.

But the answer key says 0.34, which is wrong unless there's a typo.

Wait — let’s look again at the image.

Ah! There’s a mistake in the answer key for #1.

But let’s check the number line: It shows $ \frac{1}{9}, \frac{2}{9}, ..., \frac{8}{9} $, with decimal equivalents below.

It labels $ \frac{1}{9} $ as 0.10 (which is approximate), but actually $ \frac{1}{9} = 0.\overline{1} \approx 0.11 $, so the labels are approximations.

But $ \frac{7}{9} \approx 0.777... $, so it's around 78% on the number line.

0.34 is about 34%, so clearly $ \frac{7}{9} $ is much larger.

✔ So the correct answer should be $ \frac{7}{9} $, not 0.34.

But the answer key says 0.34, which is incorrect.

Wait — perhaps the problem was misread?

No, problem 1 says: “Which amount is larger, $ \frac{7}{9} $ or 0.34?”

Yes — so $ \frac{7}{9} $ is larger.

But the answer key says 0.34, which is wrong.

This suggests either:
- A typo in the problem,
- Or the answer key is wrong.

Let’s check Problem 2.

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Problem 2: Which amount is larger, $ \frac{3}{6} $ or 0.68?

- $ \frac{3}{6} = \frac{1}{2} = 0.5 $
- 0.68 is greater than 0.5

So $ 0.68 > \frac{3}{6} $

✔ Answer: 0.68

Answer key says: 0.68 → ✔ Correct.

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Problem 3: Which amount is larger, $ \frac{6}{7} $ or 0.72?

- $ \frac{6}{7} \approx 0.857 $
- 0.72 < 0.857

So $ \frac{6}{7} > 0.72 $

✔ Answer: $ \frac{6}{7} $

Answer key says: $ \frac{6}{7} $ → ✔ Correct.

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Problem 4: Which amount is larger, $ \frac{4}{6} $ or 0.47?

- $ \frac{4}{6} = \frac{2}{3} \approx 0.666... $
- 0.47 < 0.666...

So $ \frac{4}{6} > 0.47 $

✔ Answer: $ \frac{4}{6} $

Answer key says: $ \frac{4}{6} $ → ✔ Correct.

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Problem 5: Which amount is larger, $ \frac{3}{7} $ or 0.54?

- $ \frac{3}{7} \approx 0.4286 $
- 0.54 > 0.4286

So $ 0.54 > \frac{3}{7} $

✔ Answer: 0.54

Answer key says: 0.54 → ✔ Correct.

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Problem 6: Which amount is larger, $ \frac{1}{3} $ or 0.51?

- $ \frac{1}{3} \approx 0.333 $
- 0.51 > 0.333

So $ 0.51 > \frac{1}{3} $

✔ Answer: 0.51

Answer key says: 0.51 → ✔ Correct.

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Problem 7: Which amount is larger, $ \frac{5}{7} $ or 0.54?

- $ \frac{5}{7} \approx 0.714 $
- 0.54 < 0.714

So $ \frac{5}{7} > 0.54 $

✔ Answer: $ \frac{5}{7} $

Answer key says: $ \frac{5}{7} $ → ✔ Correct.

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Problem 8: Which amount is larger, $ \frac{3}{4} $ or 0.89?

- $ \frac{3}{4} = 0.75 $
- 0.89 > 0.75

So $ 0.89 > \frac{3}{4} $

✔ Answer: 0.89

Answer key says: 0.89 → ✔ Correct.

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Problem 9: Which amount is larger, $ \frac{4}{5} $ or 0.6?

- $ \frac{4}{5} = 0.8 $
- 0.8 > 0.6

So $ \frac{4}{5} > 0.6 $

✔ Answer: $ \frac{4}{5} $

Answer key says: $ \frac{4}{5} $ → ✔ Correct.

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Problem 10: Which amount is larger, $ \frac{1}{2} $ or 0.34?

- $ \frac{1}{2} = 0.5 $
- 0.5 > 0.34

So $ \frac{1}{2} > 0.34 $

✔ Answer: $ \frac{1}{2} $

Answer key says: $ \frac{1}{2} $ → ✔ Correct.

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❗️Now back to Problem 1:

> Problem 1: Which amount is larger, $ \frac{7}{9} $ or 0.34?

- $ \frac{7}{9} \approx 0.777... $
- 0.34 < 0.777...

So $ \frac{7}{9} > 0.34 $

✔ Correct answer: $ \frac{7}{9} $

But the answer key says 0.34, which is wrong.

This is likely a typo in the answer key.

Possibility: Maybe the problem was supposed to be $ \frac{1}{9} $ or $ \frac{2}{9} $? But no — it clearly says $ \frac{7}{9} $.

Alternatively, maybe the student was supposed to pick the smaller one? But the instruction says "Which amount is larger?"

So unless the problem is misprinted, the answer key is incorrect for problem 1.

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✔ Final Summary of Answers:

| Problem | Question | Correct Answer |
|--------|---------|----------------|
| 1 | $ \frac{7}{9} $ vs 0.34 | $ \frac{7}{9} $ (Answer key says 0.34 → ✘ Incorrect) |
| 2 | $ \frac{3}{6} $ vs 0.68 | 0.68 ✔ |
| 3 | $ \frac{6}{7} $ vs 0.72 | $ \frac{6}{7} $ ✔ |
| 4 | $ \frac{4}{6} $ vs 0.47 | $ \frac{4}{6} $ ✔ |
| 5 | $ \frac{3}{7} $ vs 0.54 | 0.54 ✔ |
| 6 | $ \frac{1}{3} $ vs 0.51 | 0.51 ✔ |
| 7 | $ \frac{5}{7} $ vs 0.54 | $ \frac{5}{7} $ ✔ |
| 8 | $ \frac{3}{4} $ vs 0.89 | 0.89 ✔ |
| 9 | $ \frac{4}{5} $ vs 0.6 | $ \frac{4}{5} $ ✔ |
| 10 | $ \frac{1}{2} $ vs 0.34 | $ \frac{1}{2} $ ✔ |

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🟨 Conclusion:

All answers except #1 are correct in the answer key.

For Problem 1, the correct answer is $ \frac{7}{9} $, not 0.34.

There is a mistake in the answer key for problem 1.

✔ Final Answer:
- Problem 1: $ \frac{7}{9} $ is larger.
- All others match the key.

Let me know if you'd like a corrected version of the answer key!