Comparing and Ordering Decimals Worksheets - Math Monks - Free Printable
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Step-by-step solution for: Comparing and Ordering Decimals Worksheets - Math Monks
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Show Answer Key & Explanations
Step-by-step solution for: Comparing and Ordering Decimals Worksheets - Math Monks
Sure! Let’s solve each row by ordering the decimals from least to greatest. The key is to compare digits from left to right, starting with the whole number part, then tenths, hundredths, thousandths, etc.
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- Compare whole parts: all are 0.
- Look at tenths place:
- 0.004 → 0
- 0.04 → 0
- 0.0404 → 0
- 0.42 → 4
- 0.46 → 4
- So smallest group: 0.004, 0.04, 0.0404
- Now compare hundredths:
- 0.004 → 0 (hundredths)
- 0.04 → 4 (hundredths) — same as 0.0404
- 0.0404 → 4 (hundredths), then 0 (thousandths), 4 (ten-thousandths)
- So: 0.004 < 0.04 < 0.0404
- Then 0.42 and 0.46 → 0.42 < 0.46
✔ Order: 0.004, 0.04, 0.0404, 0.42, 0.46
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- Whole numbers: 0.06 and 0.606 have whole part 0; others have 6 → so 0.06 and 0.606 come first.
- Compare 0.06 and 0.606:
- 0.06 = 0.060 → tenths: 0 vs 6 → so 0.06 < 0.606
- Now the 6.x numbers:
- 6.60, 6.66, 6.67 → compare hundredths: 0 < 6 < 7
- So: 6.60 < 6.66 < 6.67
✔ Order: 0.06, 0.606, 6.60, 6.66, 6.67
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- Whole numbers: 0.39 has 0 → smallest
- Others all start with 3 → compare decimal parts:
- 3.03, 3.09, 3.13, 3.39
- Tenths: 0, 0, 1, 3 → so 3.03 and 3.09 come before 3.13 and 3.39
- Among 3.03 and 3.09 → hundredths: 3 < 9 → 3.03 < 3.09
- 3.13 < 3.39
✔ Order: 0.39, 3.03, 3.09, 3.13, 3.39
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- Whole numbers: 0.155 (0), 1.500 & 1.505 (1), 15.05 & 15.5 (15)
- So smallest: 0.155
- Next: 1.500 and 1.505 → compare thousandths: 0 < 5 → 1.500 < 1.505
- Then 15.05 and 15.5 → 15.05 = 15.050, 15.5 = 15.500 → hundredths: 0 < 5 → 15.05 < 15.5
✔ Order: 0.155, 1.500, 1.505, 15.05, 15.5
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- Whole numbers: 3.003, 3.033, 3.33 (all 3); 30.33 (30); 33.33 (33)
- So 3.xxx group first → compare decimals:
- 3.003, 3.033, 3.33 → look at tenths: 0, 0, 3 → so 3.003 and 3.033 before 3.33
- Between 3.003 and 3.033 → hundredths: 0 vs 3 → 3.003 < 3.033
- Then 30.33, then 33.33
✔ Order: 3.003, 3.033, 3.33, 30.33, 33.33
---
- Whole numbers: 0.77 (0), 1.75 & 1.77 (1), 7.5 (7), 17.5 (17)
- So: 0.77 first
- Then 1.75 and 1.77 → compare hundredths: 5 < 7 → 1.75 < 1.77
- Then 7.5, then 17.5
✔ Order: 0.77, 1.75, 1.77, 7.5, 17.5
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- Whole numbers: 0.09 (0), 9.009 & 9.09 (9), 99.90 (99), 999.9 (999)
- So: 0.09 first
- Then 9.009 and 9.09 → compare thousandths: 9.009 = 9.009, 9.09 = 9.090 → 009 < 090 → 9.009 < 9.09
- Then 99.90, then 999.9
✔ Order: 0.09, 9.009, 9.09, 99.90, 999.9
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## ✔ Final Answers:
1. 0.004, 0.04, 0.0404, 0.42, 0.46
2. 0.06, 0.606, 6.60, 6.66, 6.67
3. 0.39, 3.03, 3.09, 3.13, 3.39
4. 0.155, 1.500, 1.505, 15.05, 15.5
5. 3.003, 3.033, 3.33, 30.33, 33.33
6. 0.77, 1.75, 1.77, 7.5, 17.5
7. 0.09, 9.009, 9.09, 99.90, 999.9
Let me know if you’d like a visual chart or step-by-step comparison for any row!
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Row 1: 0.42, 0.46, 0.04, 0.004, 0.0404
- Compare whole parts: all are 0.
- Look at tenths place:
- 0.004 → 0
- 0.04 → 0
- 0.0404 → 0
- 0.42 → 4
- 0.46 → 4
- So smallest group: 0.004, 0.04, 0.0404
- Now compare hundredths:
- 0.004 → 0 (hundredths)
- 0.04 → 4 (hundredths) — same as 0.0404
- 0.0404 → 4 (hundredths), then 0 (thousandths), 4 (ten-thousandths)
- So: 0.004 < 0.04 < 0.0404
- Then 0.42 and 0.46 → 0.42 < 0.46
✔ Order: 0.004, 0.04, 0.0404, 0.42, 0.46
---
Row 2: 6.67, 6.66, 6.60, 0.06, 0.606
- Whole numbers: 0.06 and 0.606 have whole part 0; others have 6 → so 0.06 and 0.606 come first.
- Compare 0.06 and 0.606:
- 0.06 = 0.060 → tenths: 0 vs 6 → so 0.06 < 0.606
- Now the 6.x numbers:
- 6.60, 6.66, 6.67 → compare hundredths: 0 < 6 < 7
- So: 6.60 < 6.66 < 6.67
✔ Order: 0.06, 0.606, 6.60, 6.66, 6.67
---
Row 3: 3.39, 3.03, 3.09, 3.13, 0.39
- Whole numbers: 0.39 has 0 → smallest
- Others all start with 3 → compare decimal parts:
- 3.03, 3.09, 3.13, 3.39
- Tenths: 0, 0, 1, 3 → so 3.03 and 3.09 come before 3.13 and 3.39
- Among 3.03 and 3.09 → hundredths: 3 < 9 → 3.03 < 3.09
- 3.13 < 3.39
✔ Order: 0.39, 3.03, 3.09, 3.13, 3.39
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Row 4: 15.5, 15.05, 1.505, 0.155, 1.500
- Whole numbers: 0.155 (0), 1.500 & 1.505 (1), 15.05 & 15.5 (15)
- So smallest: 0.155
- Next: 1.500 and 1.505 → compare thousandths: 0 < 5 → 1.500 < 1.505
- Then 15.05 and 15.5 → 15.05 = 15.050, 15.5 = 15.500 → hundredths: 0 < 5 → 15.05 < 15.5
✔ Order: 0.155, 1.500, 1.505, 15.05, 15.5
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Row 5: 30.33, 3.33, 33.33, 3.033, 3.003
- Whole numbers: 3.003, 3.033, 3.33 (all 3); 30.33 (30); 33.33 (33)
- So 3.xxx group first → compare decimals:
- 3.003, 3.033, 3.33 → look at tenths: 0, 0, 3 → so 3.003 and 3.033 before 3.33
- Between 3.003 and 3.033 → hundredths: 0 vs 3 → 3.003 < 3.033
- Then 30.33, then 33.33
✔ Order: 3.003, 3.033, 3.33, 30.33, 33.33
---
Row 6: 1.77, 17.5, 1.75, 0.77, 7.5
- Whole numbers: 0.77 (0), 1.75 & 1.77 (1), 7.5 (7), 17.5 (17)
- So: 0.77 first
- Then 1.75 and 1.77 → compare hundredths: 5 < 7 → 1.75 < 1.77
- Then 7.5, then 17.5
✔ Order: 0.77, 1.75, 1.77, 7.5, 17.5
---
Row 7: 999.9, 99.90, 9.09, 0.09, 9.009
- Whole numbers: 0.09 (0), 9.009 & 9.09 (9), 99.90 (99), 999.9 (999)
- So: 0.09 first
- Then 9.009 and 9.09 → compare thousandths: 9.009 = 9.009, 9.09 = 9.090 → 009 < 090 → 9.009 < 9.09
- Then 99.90, then 999.9
✔ Order: 0.09, 9.009, 9.09, 99.90, 999.9
---
## ✔ Final Answers:
1. 0.004, 0.04, 0.0404, 0.42, 0.46
2. 0.06, 0.606, 6.60, 6.66, 6.67
3. 0.39, 3.03, 3.09, 3.13, 3.39
4. 0.155, 1.500, 1.505, 15.05, 15.5
5. 3.003, 3.033, 3.33, 30.33, 33.33
6. 0.77, 1.75, 1.77, 7.5, 17.5
7. 0.09, 9.009, 9.09, 99.90, 999.9
Let me know if you’d like a visual chart or step-by-step comparison for any row!
Parent Tip: Review the logic above to help your child master the concept of ordering decimals from least to greatest worksheet.
