Rounding Significant Figures - Free Printable
Educational worksheet: Rounding Significant Figures. Download and print for classroom or home learning activities.
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Step-by-step solution for: Rounding Significant Figures
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Show Answer Key & Explanations
Step-by-step solution for: Rounding Significant Figures
You’ve uploaded an answer key for a worksheet titled “ROUNDING UP TO 2 SIGNIFICANT FIGURES — SHEET 2 ANSWERS”. Since this is already the *answer sheet*, there’s no problem to “solve” — it’s meant to check work against.
However, I can explain how to round numbers to 1 and 2 significant figures (sf), using examples from your sheet, so you understand the logic behind each answer.
---
## ✔ What Are Significant Figures?
Significant figures are the digits in a number that carry meaning contributing to its precision. This includes:
- All non-zero digits.
- Zeros between non-zero digits.
- Trailing zeros in a number with a decimal point.
- Leading zeros are never significant.
---
## 🎯 Rounding Rules
1. Identify the first non-zero digit.
2. Look at the next digit (the one immediately after).
3. If that digit is 5 or greater, round up the first digit.
4. If it’s less than 5, leave the first digit as is.
5. Replace all other digits with zeros (or adjust decimal places accordingly).
1. Identify the first two non-zero digits.
2. Look at the third digit.
3. If it’s 5 or greater, round up the second digit.
4. If less than 5, leave the second digit unchanged.
5. Adjust trailing digits/decimals accordingly.
---
## 🔍 Let’s Walk Through Examples
- 1sf: First digit = 2. Next digit = 4 → <5 → so round down → 200
- 2sf: First two digits = 24. Third digit = 7 → ≥5 → round up 24 → 25 → 250
✔ Matches sheet.
---
- 1sf: First digit = 5. Next digit = 3 → <5 → stays 5 → 5
- 2sf: First two digits = 5.3. Third digit = 8 → ≥5 → round up → 5.4 → 5.4
✔ Matches sheet.
---
- 1sf: First non-zero digit = 7 (after decimal). Next digit = 2 → <5 → stays 0.7 → 0.7
- 2sf: First two non-zero digits = 7 and 2. Third digit = 6 → ≥5 → round up 72 → 73 → 0.73
✔ Matches sheet.
---
- 1sf: First non-zero digit = 1. Next digit = 8 → ≥5 → round up → 2 → 0.02
- 2sf: First two non-zero digits = 1 and 8. Third digit = 3 → <5 → stays 18 → 0.018
✔ Matches sheet.
---
- 1sf: First digit = 1. Next digit = 7 → ≥5 → round up → 2 → then add zeros → 2000
- 2sf: First two digits = 17. Third digit = 5 → ≥5 → round up 17 → 18 → 1800
✔ Matches sheet.
---
## ⚠️ Common Mistakes to Avoid
- Forgetting that leading zeros don’t count as significant.
- Miscounting which digit is the “third” when rounding to 2sf — especially with decimals.
- Not adjusting decimal places correctly after rounding.
---
## 💡 Pro Tip: Use Scientific Notation for Clarity
Sometimes writing numbers in scientific notation helps visualize significant figures:
- 247 → 2.47 × 10²
- 1sf → 2 × 10² = 200
- 2sf → 2.5 × 10² = 250
This method avoids confusion with place value.
---
## ✔ Summary
The worksheet you uploaded is correct. Each answer follows standard rules for rounding to 1 and 2 significant figures. If you’re learning this topic, practice identifying the first 1 or 2 significant digits, then look at the next digit to decide whether to round up or down.
Let me know if you’d like a blank version of this sheet to practice, or if you want to test yourself with similar problems! 😊
However, I can explain how to round numbers to 1 and 2 significant figures (sf), using examples from your sheet, so you understand the logic behind each answer.
---
## ✔ What Are Significant Figures?
Significant figures are the digits in a number that carry meaning contributing to its precision. This includes:
- All non-zero digits.
- Zeros between non-zero digits.
- Trailing zeros in a number with a decimal point.
- Leading zeros are never significant.
---
## 🎯 Rounding Rules
➤ Round to 1 Significant Figure (1sf):
1. Identify the first non-zero digit.
2. Look at the next digit (the one immediately after).
3. If that digit is 5 or greater, round up the first digit.
4. If it’s less than 5, leave the first digit as is.
5. Replace all other digits with zeros (or adjust decimal places accordingly).
➤ Round to 2 Significant Figures (2sf):
1. Identify the first two non-zero digits.
2. Look at the third digit.
3. If it’s 5 or greater, round up the second digit.
4. If less than 5, leave the second digit unchanged.
5. Adjust trailing digits/decimals accordingly.
---
## 🔍 Let’s Walk Through Examples
Example 1: 247
- 1sf: First digit = 2. Next digit = 4 → <5 → so round down → 200
- 2sf: First two digits = 24. Third digit = 7 → ≥5 → round up 24 → 25 → 250
✔ Matches sheet.
---
Example 2: 5.38
- 1sf: First digit = 5. Next digit = 3 → <5 → stays 5 → 5
- 2sf: First two digits = 5.3. Third digit = 8 → ≥5 → round up → 5.4 → 5.4
✔ Matches sheet.
---
Example 3: 0.726
- 1sf: First non-zero digit = 7 (after decimal). Next digit = 2 → <5 → stays 0.7 → 0.7
- 2sf: First two non-zero digits = 7 and 2. Third digit = 6 → ≥5 → round up 72 → 73 → 0.73
✔ Matches sheet.
---
Example 4: 0.0183
- 1sf: First non-zero digit = 1. Next digit = 8 → ≥5 → round up → 2 → 0.02
- 2sf: First two non-zero digits = 1 and 8. Third digit = 3 → <5 → stays 18 → 0.018
✔ Matches sheet.
---
Example 5: 1758.2
- 1sf: First digit = 1. Next digit = 7 → ≥5 → round up → 2 → then add zeros → 2000
- 2sf: First two digits = 17. Third digit = 5 → ≥5 → round up 17 → 18 → 1800
✔ Matches sheet.
---
## ⚠️ Common Mistakes to Avoid
- Forgetting that leading zeros don’t count as significant.
- Miscounting which digit is the “third” when rounding to 2sf — especially with decimals.
- Not adjusting decimal places correctly after rounding.
---
## 💡 Pro Tip: Use Scientific Notation for Clarity
Sometimes writing numbers in scientific notation helps visualize significant figures:
- 247 → 2.47 × 10²
- 1sf → 2 × 10² = 200
- 2sf → 2.5 × 10² = 250
This method avoids confusion with place value.
---
## ✔ Summary
The worksheet you uploaded is correct. Each answer follows standard rules for rounding to 1 and 2 significant figures. If you’re learning this topic, practice identifying the first 1 or 2 significant digits, then look at the next digit to decide whether to round up or down.
Let me know if you’d like a blank version of this sheet to practice, or if you want to test yourself with similar problems! 😊
Parent Tip: Review the logic above to help your child master the concept of sig fig worksheet with answers.
