Ordering fractions and decimals worksheet with four sets of numbers to arrange in ascending order.

You're given a worksheet that asks you to order sets of five fractions and decimals from smallest to largest. The hint suggests converting all numbers to decimals using division — this is the best approach because comparing decimals is straightforward.

Let’s solve each set one by one.

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🔢 SET 1:

Numbers:
0.2, 3/10, 1/10, 0.25, 11/100

✔ Convert all to decimals:

- 0.2 → already decimal = 0.2
- 3/10 = 3 ÷ 10 = 0.3
- 1/10 = 1 ÷ 10 = 0.1
- 0.25 → already decimal = 0.25
- 11/100 = 11 ÷ 100 = 0.11

Now list them in order (smallest to largest):

→ 0.1, 0.11, 0.2, 0.25, 0.3

Which correspond to:

→ 1/10, 11/100, 0.2, 0.25, 3/10

✔ Answer for Set 1:
1/10 11/100 0.2 0.25 3/10

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🔢 SET 2:

Numbers:
0.3, 3/5, 4/5, 0.7, 85/100

✔ Convert all to decimals:

- 0.3 → 0.3
- 3/5 = 3 ÷ 5 = 0.6
- 4/5 = 4 ÷ 5 = 0.8
- 0.7 → 0.7
- 85/100 = 85 ÷ 100 = 0.85

Order from smallest to largest:

→ 0.3, 0.6, 0.7, 0.8, 0.85

Which correspond to:

→ 0.3, 3/5, 0.7, 4/5, 85/100

✔ Answer for Set 2:
0.3 3/5 0.7 4/5 85/100

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🔢 SET 3:

Numbers:
3/4, 3/8, 0.77, 0.61, 8/12

✔ Convert all to decimals:

- 3/4 = 3 ÷ 4 = 0.75
- 3/8 = 3 ÷ 8 = 0.375
- 0.77 → 0.77
- 0.61 → 0.61
- 8/12 = 8 ÷ 12 = 0.666... (≈ 0.667)

Order from smallest to largest:

→ 0.375, 0.61, 0.667, 0.75, 0.77

Which correspond to:

→ 3/8, 0.61, 8/12, 3/4, 0.77

✔ Answer for Set 3:
3/8 0.61 8/12 3/4 0.77

*(Note: 8/12 can be simplified to 2/3, but since the original problem uses 8/12, we keep it as is.)*

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🔢 SET 4:

Numbers:
7/5, 11/8, 1.12, 1.02, 13/10

✔ Convert all to decimals:

- 7/5 = 7 ÷ 5 = 1.4
- 11/8 = 11 ÷ 8 = 1.375
- 1.12 → 1.12
- 1.02 → 1.02
- 13/10 = 13 ÷ 10 = 1.3

Order from smallest to largest:

→ 1.02, 1.12, 1.3, 1.375, 1.4

Which correspond to:

→ 1.02, 1.12, 13/10, 11/8, 7/5

✔ Answer for Set 4:
1.02 1.12 13/10 11/8 7/5

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## ✔ FINAL ANSWERS:

Set 1:

1/10 11/100 0.2 0.25 3/10

Set 2:

0.3 3/5 0.7 4/5 85/100

Set 3:

3/8 0.61 8/12 3/4 0.77

Set 4:

1.02 1.12 13/10 11/8 7/5

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💡 Tip: Always convert fractions to decimals by dividing numerator by denominator. Then compare the decimal values — it’s much easier than trying to find common denominators for mixed sets!

Let me know if you’d like to see these on a number line or need help with simplifying fractions too!