Rounding to Significant Figures Worksheets - Free Printable

Sure! Let’s go through each problem step by step and round the given decimals to the specified number of significant figures (sig figs).

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🔢 Rules for Significant Figures:

- All non-zero digits are significant.
- Zeros between non-zero digits are significant.
- Leading zeros are not significant.
- Trailing zeros in a number with a decimal point are significant.
- When rounding, look at the digit immediately after the last desired sig fig:
- If it’s 5 or greater, round up.
- If it’s less than 5, leave the last digit unchanged.

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## ✔ Problem 1: `2.3609`

a) Round to 1 significant digit:

- First digit is 2
- Next digit is 3 → less than 5 → do not round up
- So, we keep 2 and replace everything else with zeros or adjust decimal place accordingly.

→ Answer: 2

b) Round to 2 significant digits:

- First two digits: 2.3
- Next digit is 6 → ≥5 → round up the last digit (3 → 4)

→ Answer: 2.4

c) Round to 3 significant digits:

- First three digits: 2.36
- Next digit is 0 → <5 → leave as is

→ Answer: 2.36

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## ✔ Problem 2: `578.2194`

a) Round to 2 significant digits:

- First two digits: 57 → but since this is a 3-digit number, we need to express it in scientific notation or adjust decimal place.

Actually, for numbers like this, we consider the first two non-zero digits: 5 and 7 → so we want 580? Wait — let’s be precise.

We want 2 sig figs:

- Look at 578.2194 → first two sig figs: 5 and 7
- The third digit is 8 → ≥5 → round up 57 → becomes 58
- But since original number is in hundreds, we write it as 580 (but that has 2 sig figs only if we write it as 5.8 × 10²)

✔ Correct way: 580 — but to show 2 sig figs clearly, we can write 5.8 × 10²

However, since the worksheet likely expects standard form, we’ll write 580 — implying 2 sig figs (the trailing zero is not significant).

But technically, 580 has 2 sig figs only if written as 5.8 × 10².

To avoid confusion, we’ll follow common practice for such worksheets:

→ Answer: 580

*(Note: In strict terms, 580 without a decimal point may be ambiguous, but in context of rounding, it’s accepted.)*

b) Round to 5 significant digits:

- First five digits: 578.21
- Next digit is 9 → ≥5 → round up the last digit (1 → 2)

→ Answer: 578.22

c) Round to 1 significant digit:

- First digit: 5
- Next digit: 7 → ≥5 → round up → 5 → 6
- Since it's in the hundreds, result is 600

→ Answer: 600

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## ✔ Problem 3: `7.3482`

a) Round to 2 significant digits:

- First two digits: 7.3
- Next digit: 4 → <5 → leave as is

→ Answer: 7.3

b) Round to 3 significant digits:

- First three digits: 7.34
- Next digit: 8 → ≥5 → round up → 7.34 → 7.35

→ Answer: 7.35

c) Round to 4 significant digits:

- First four digits: 7.348
- Next digit: 2 → <5 → leave as is

→ Answer: 7.348

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## ✔ Problem 4: `41.095`

a) Round to 2 significant digits:

- First two digits: 41
- Next digit: 0 → <5 → leave as is → 41

→ Answer: 41

b) Round to 3 significant digits:

- First three digits: 41.0
- Next digit: 9 → ≥5 → round up → 41.0 → 41.1

→ Answer: 41.1

c) Round to 1 significant digit:

- First digit: 4
- Next digit: 1 → <5 → leave as is → but since it's tens place, result is 40

→ Answer: 40

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## ✔ Problem 5: `1254.33`

a) Round to 4 significant digits:

- First four digits: 1254
- Next digit: 3 → <5 → leave as is

→ Answer: 1254

b) Round to 1 significant digit:

- First digit: 1
- Next digit: 2 → <5 → leave as is → but since it's in thousands, result is 1000

→ Answer: 1000

c) Round to 3 significant digits:

- First three digits: 125
- Next digit: 4 → <5 → leave as is → so 1250

→ Answer: 1250

*(Note: 1250 has 3 sig figs — the trailing zero is not significant unless specified with a decimal or scientific notation. In this context, it’s acceptable.)*

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## 📝 Final Answers:

1) 2.3609

a) 2
b) 2.4
c) 2.36

2) 578.2194

a) 580
b) 578.22
c) 600

3) 7.3482

a) 7.3
b) 7.35
c) 7.348

4) 41.095

a) 41
b) 41.1
c) 40

5) 1254.33

a) 1254
b) 1000
c) 1250

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Let me know if you’d like these answers formatted into a printable sheet or explained further! 😊