Significant Figures Worksheets - Math Monks - Free Printable
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Step-by-step solution for: Significant Figures Worksheets - Math Monks
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Show Answer Key & Explanations
Step-by-step solution for: Significant Figures Worksheets - Math Monks
Absolutely! Let’s solve each problem and round to the correct number of significant figures, following the rules for significant figures in arithmetic operations.
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## 📌 RULES REVIEW:
- The answer should have the same number of decimal places as the number with the fewest decimal places.
- The answer should have the same number of significant figures as the number with the fewest significant figures.
- Follow order of operations (PEMDAS), applying sig fig rules at each step or at the final result — but best practice is to keep extra digits during intermediate steps and round only at the end based on the least precise measurement.
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# ✔ A) Addition and Subtraction
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- 6.2 → 1 decimal place
- 4.114 → 3 decimal places
→ Answer must have 1 decimal place
Calculation:
6.2 + 4.114 = 10.314 → Round to 1 decimal place → 10.3
✔ Answer: 10.3
---
- 19.6 → 1 decimal place
- 8.77 → 2 decimal places
→ Answer must have 1 decimal place
Calculation:
19.6 - 8.77 = 10.83 → Round to 1 decimal place → 10.8
✔ Answer: 10.8
---
- 3.4 → 1 decimal place
- 8.2252 → 4 decimal places
→ Answer must have 1 decimal place
Calculation:
3.4 + 8.2252 = 11.6252 → Round to 1 decimal place → 11.6
✔ Answer: 11.6
---
- 7.8948 → 4 decimal places
- 4.1 → 1 decimal place
→ Answer must have 1 decimal place
Calculation:
7.8948 - 4.1 = 3.7948 → Round to 1 decimal place → 3.8
✔ Answer: 3.8
---
- 101.12 → 2 decimal places
- 98.7 → 1 decimal place
→ Answer must have 1 decimal place
Calculation:
101.12 - 98.7 = 2.42 → Round to 1 decimal place → 2.4
✔ Answer: 2.4
---
- 23 → no decimal places (exact? But treated as having uncertainty in ones place)
- 16.4 → 1 decimal place
- 22.0 → 1 decimal place
→ The least precise is 23 (no decimal places), so answer must have no decimal places.
Calculation:
23 + 16.4 + 22.0 = 61.4 → Round to nearest whole number → 61
✔ Answer: 61
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# ✔ B) Multiplication and Division
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- 1000 → ambiguous, but often treated as 1 significant figure unless specified otherwise (e.g., if it were 1000., it would be 4). In this context, likely 1 sig fig.
- 8.2 → 2 sig figs
→ Answer must have 1 sig fig
Calculation:
1000 ÷ 8.2 ≈ 121.95 → Round to 1 sig fig → 100
✔ Answer: 100
> Note: Some may argue 1000 has 4 sig figs if trailing zeros are significant — but without a decimal point, it’s conventionally considered to have 1 sig fig unless stated otherwise.
---
- 10.0 → 3 sig figs
- 0.02 → 1 sig fig (leading zeros don’t count)
→ Answer must have 1 sig fig
Calculation:
10.0 × 0.02 = 0.20 → Round to 1 sig fig → 0.2
✔ Answer: 0.2
---
- 9.66 → 3 sig figs
- 0.33 → 2 sig figs
→ Answer must have 2 sig figs
Calculation:
9.66 ÷ 0.33 ≈ 29.2727 → Round to 2 sig figs → 29
✔ Answer: 29
---
- 8000 → ambiguous; likely 1 sig fig (unless written as 8.000×10³)
- 9.7 → 2 sig figs
→ Answer must have 1 sig fig
Calculation:
8000 ÷ 9.7 ≈ 824.74 → Round to 1 sig fig → 800
✔ Answer: 800
---
- 0.004 → 1 sig fig
- 33.511 → 5 sig figs
→ Answer must have 1 sig fig
Calculation:
0.004 × 33.511 = 0.134044 → Round to 1 sig fig → 0.1
✔ Answer: 0.1
---
- 0.005 → 1 sig fig
- 60 → 1 sig fig (if not written as 60. or 6.0×10¹)
→ Answer must have 1 sig fig
Calculation:
0.005 × 60 = 0.3 → Already 1 sig fig → 0.3
✔ Answer: 0.3
---
# ✔ C) Mixed Operation
---
Step 1: Addition inside parentheses
- 12.3 → 1 decimal place
- 0.06 → 2 decimal places
→ Sum must have 1 decimal place
12.3 + 0.06 = 12.36 → Round to 1 decimal place → 12.4
Step 2: Multiply by 53.44
- 12.4 → 3 sig figs
- 53.44 → 4 sig figs
→ Product must have 3 sig figs
12.4 × 53.44 = 662.656 → Round to 3 sig figs → 663
✔ Answer: 663
---
Step 1: Division first
- 14.021 → 5 sig figs
- 18.9 → 3 sig figs
→ Quotient must have 3 sig figs
14.021 ÷ 18.9 ≈ 0.74185 → Round to 3 sig figs → 0.742
Step 2: Subtract from 68.7
- 68.7 → 1 decimal place
- 0.742 → 3 decimal places
→ Difference must have 1 decimal place
68.7 - 0.742 = 67.958 → Round to 1 decimal place → 68.0
✔ Answer: 68.0
---
# 🧾 FINAL ANSWERS:
## A) Addition and Subtraction
1) 10.3
2) 10.8
3) 11.6
4) 3.8
5) 2.4
6) 61
## B) Multiplication and Division
1) 100
2) 0.2
3) 29
4) 800
5) 0.1
6) 0.3
## C) Mixed Operation
1) 663
2) 68.0
---
Let me know if you’d like explanations for any specific rule or want to check your own work! 😊
---
## 📌 RULES REVIEW:
For Addition & Subtraction:
- The answer should have the same number of decimal places as the number with the fewest decimal places.
For Multiplication & Division:
- The answer should have the same number of significant figures as the number with the fewest significant figures.
For Mixed Operations:
- Follow order of operations (PEMDAS), applying sig fig rules at each step or at the final result — but best practice is to keep extra digits during intermediate steps and round only at the end based on the least precise measurement.
---
# ✔ A) Addition and Subtraction
---
1) 6.2 + 4.114
- 6.2 → 1 decimal place
- 4.114 → 3 decimal places
→ Answer must have 1 decimal place
Calculation:
6.2 + 4.114 = 10.314 → Round to 1 decimal place → 10.3
✔ Answer: 10.3
---
2) 19.6 - 8.77
- 19.6 → 1 decimal place
- 8.77 → 2 decimal places
→ Answer must have 1 decimal place
Calculation:
19.6 - 8.77 = 10.83 → Round to 1 decimal place → 10.8
✔ Answer: 10.8
---
3) 3.4 + 8.2252
- 3.4 → 1 decimal place
- 8.2252 → 4 decimal places
→ Answer must have 1 decimal place
Calculation:
3.4 + 8.2252 = 11.6252 → Round to 1 decimal place → 11.6
✔ Answer: 11.6
---
4) 7.8948 - 4.1
- 7.8948 → 4 decimal places
- 4.1 → 1 decimal place
→ Answer must have 1 decimal place
Calculation:
7.8948 - 4.1 = 3.7948 → Round to 1 decimal place → 3.8
✔ Answer: 3.8
---
5) 101.12 - 98.7
- 101.12 → 2 decimal places
- 98.7 → 1 decimal place
→ Answer must have 1 decimal place
Calculation:
101.12 - 98.7 = 2.42 → Round to 1 decimal place → 2.4
✔ Answer: 2.4
---
6) 23 + 16.4 + 22.0
- 23 → no decimal places (exact? But treated as having uncertainty in ones place)
- 16.4 → 1 decimal place
- 22.0 → 1 decimal place
→ The least precise is 23 (no decimal places), so answer must have no decimal places.
Calculation:
23 + 16.4 + 22.0 = 61.4 → Round to nearest whole number → 61
✔ Answer: 61
---
# ✔ B) Multiplication and Division
---
1) 1000 ÷ 8.2
- 1000 → ambiguous, but often treated as 1 significant figure unless specified otherwise (e.g., if it were 1000., it would be 4). In this context, likely 1 sig fig.
- 8.2 → 2 sig figs
→ Answer must have 1 sig fig
Calculation:
1000 ÷ 8.2 ≈ 121.95 → Round to 1 sig fig → 100
✔ Answer: 100
> Note: Some may argue 1000 has 4 sig figs if trailing zeros are significant — but without a decimal point, it’s conventionally considered to have 1 sig fig unless stated otherwise.
---
2) 10.0 × 0.02
- 10.0 → 3 sig figs
- 0.02 → 1 sig fig (leading zeros don’t count)
→ Answer must have 1 sig fig
Calculation:
10.0 × 0.02 = 0.20 → Round to 1 sig fig → 0.2
✔ Answer: 0.2
---
3) 9.66 ÷ 0.33
- 9.66 → 3 sig figs
- 0.33 → 2 sig figs
→ Answer must have 2 sig figs
Calculation:
9.66 ÷ 0.33 ≈ 29.2727 → Round to 2 sig figs → 29
✔ Answer: 29
---
4) 8000 ÷ 9.7
- 8000 → ambiguous; likely 1 sig fig (unless written as 8.000×10³)
- 9.7 → 2 sig figs
→ Answer must have 1 sig fig
Calculation:
8000 ÷ 9.7 ≈ 824.74 → Round to 1 sig fig → 800
✔ Answer: 800
---
5) 0.004 × 33.511
- 0.004 → 1 sig fig
- 33.511 → 5 sig figs
→ Answer must have 1 sig fig
Calculation:
0.004 × 33.511 = 0.134044 → Round to 1 sig fig → 0.1
✔ Answer: 0.1
---
6) 0.005 × 60
- 0.005 → 1 sig fig
- 60 → 1 sig fig (if not written as 60. or 6.0×10¹)
→ Answer must have 1 sig fig
Calculation:
0.005 × 60 = 0.3 → Already 1 sig fig → 0.3
✔ Answer: 0.3
---
# ✔ C) Mixed Operation
---
1) (12.3 + 0.06) × 53.44
Step 1: Addition inside parentheses
- 12.3 → 1 decimal place
- 0.06 → 2 decimal places
→ Sum must have 1 decimal place
12.3 + 0.06 = 12.36 → Round to 1 decimal place → 12.4
Step 2: Multiply by 53.44
- 12.4 → 3 sig figs
- 53.44 → 4 sig figs
→ Product must have 3 sig figs
12.4 × 53.44 = 662.656 → Round to 3 sig figs → 663
✔ Answer: 663
---
2) 68.7 - 14.021 ÷ 18.9
Step 1: Division first
- 14.021 → 5 sig figs
- 18.9 → 3 sig figs
→ Quotient must have 3 sig figs
14.021 ÷ 18.9 ≈ 0.74185 → Round to 3 sig figs → 0.742
Step 2: Subtract from 68.7
- 68.7 → 1 decimal place
- 0.742 → 3 decimal places
→ Difference must have 1 decimal place
68.7 - 0.742 = 67.958 → Round to 1 decimal place → 68.0
✔ Answer: 68.0
---
# 🧾 FINAL ANSWERS:
## A) Addition and Subtraction
1) 10.3
2) 10.8
3) 11.6
4) 3.8
5) 2.4
6) 61
## B) Multiplication and Division
1) 100
2) 0.2
3) 29
4) 800
5) 0.1
6) 0.3
## C) Mixed Operation
1) 663
2) 68.0
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Let me know if you’d like explanations for any specific rule or want to check your own work! 😊
Parent Tip: Review the logic above to help your child master the concept of sig fig worksheet with answers.
