Comparing and Ordering Decimals Worksheets - Math Monks - Free Printable

Let’s solve each problem step by step. We need to order the decimals from largest to smallest.

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Problem ①: 4.677, 3.867, 2.7, 3.67, 3.90, 4.17

Compare whole numbers first:
- 4.677 and 4.17 → both start with 4
- 3.867, 3.67, 3.90 → all start with 3
- 2.7 → starts with 2 (smallest)

Now compare within groups:

Group starting with 4:
- 4.677 vs 4.17 → 4.677 is bigger (since 6 > 1 in tenths place)

Group starting with 3:
- 3.90, 3.867, 3.67
→ 3.90 is biggest (9 in tenths)
→ then 3.867 (8 in tenths)
→ then 3.67 (6 in tenths)

So full order largest to smallest:
4.677, 4.17, 3.90, 3.867, 3.67, 2.7

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Problem ②: 0.839, 0.642, 0.2, 8.39, 83.9, 0.711

Look at whole number parts:
- 83.9 → biggest (whole number 83)
- 8.39 → next (whole number 8)
- Then decimals less than 1: 0.839, 0.711, 0.642, 0.2

Order the small ones:
- 0.839 (8 tenths)
- 0.711 (7 tenths)
- 0.642 (6 tenths)
- 0.2 (2 tenths)

Full order:
83.9, 8.39, 0.839, 0.711, 0.642, 0.2

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Problem ③: 6.6, 6.02, 6.67, 66.7, 0.67, 0.067

Whole numbers:
- 66.7 → biggest (66)
- Then 6.6, 6.02, 6.67 → all start with 6
- Then 0.67, 0.067 → less than 1

Compare the 6.x group:
- 6.67 (6 and 67 hundredths)
- 6.6 = 6.60 → so 6.67 > 6.60
- 6.02 → smallest of this group

Compare the <1 group:
- 0.67 > 0.067

Full order:
66.7, 6.67, 6.6, 6.02, 0.67, 0.067

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Problem ④: 7.38, 0.738, 73.8, 69.3, 693.7, 738.7

Whole numbers:
- 738.7 → biggest
- 693.7 → next
- 73.8 → next
- 69.3 → next
- 7.38 → next
- 0.738 → smallest

No tricky comparisons needed — just look at whole number size.

Full order:
738.7, 693.7, 73.8, 69.3, 7.38, 0.738

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Problem ⑤: 0.09, 0.9, 0.99, 9.9, 9.1, 99.1

Whole numbers:
- 99.1 → biggest
- 9.9 and 9.1 → both start with 9
- 0.99, 0.9, 0.09 → less than 1

Compare 9.9 vs 9.1 → 9.9 > 9.1

Compare <1:
- 0.99 (99 hundredths)
- 0.9 = 0.90 → so 0.99 > 0.90
- 0.09 → smallest

Full order:
99.1, 9.9, 9.1, 0.99, 0.9, 0.09

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Problem ⑥: 11.7, 1.7, 117.7, 0.117, 0.017, 0.0017

Whole numbers:
- 117.7 → biggest
- 11.7 → next
- 1.7 → next
- Then decimals: 0.117, 0.017, 0.0017

Compare decimals:
- 0.117 (117 thousandths)
- 0.017 (17 thousandths)
- 0.0017 (1.7 thousandths) → smallest

Full order:
117.7, 11.7, 1.7, 0.117, 0.017, 0.0017

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Problem ⑦: 102.9, 10.2, 9.2, 102.7, 0.102, 0.01

Whole numbers:
- 102.9 and 102.7 → both start with 102
- 10.2 → next
- 9.2 → next
- 0.102 and 0.01 → less than 1

Compare 102.9 vs 102.7 → 102.9 > 102.7

Compare 0.102 vs 0.01 → 0.102 > 0.01

Full order:
102.9, 102.7, 10.2, 9.2, 0.102, 0.01

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Final Answer:

① 4.677, 4.17, 3.90, 3.867, 3.67, 2.7
② 83.9, 8.39, 0.839, 0.711, 0.642, 0.2
③ 66.7, 6.67, 6.6, 6.02, 0.67, 0.067
④ 738.7, 693.7, 73.8, 69.3, 7.38, 0.738
⑤ 99.1, 9.9, 9.1, 0.99, 0.9, 0.09
⑥ 117.7, 11.7, 1.7, 0.117, 0.017, 0.0017
⑦ 102.9, 102.7, 10.2, 9.2, 0.102, 0.01