Math worksheet focusing on significant figures, with exercises to identify and round numbers.

Here's the complete solution with explanations for each problem:

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Part 1: Write down the number of significant figures in each of the following numbers.

Rule Summary for Significant Figures:
- All non-zero digits are significant.
- Zeros between non-zero digits are significant.
- Leading zeros (before first non-zero digit) are not significant.
- Trailing zeros in a number with a decimal point are significant.
- Trailing zeros in a whole number without a decimal point are ambiguous, but often considered not significant unless specified (scientific notation clarifies).

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1. 725836 → 6 significant figures
✔ All digits are non-zero → all 6 are significant.

2. 6500000 → 2 significant figures
⚠️ Trailing zeros in a whole number without a decimal are not significant. Only the '6' and '5' are significant.
*(Note: If it were written as 6.500000 × 10⁶, it would have 7 sig figs — but as written, it’s ambiguous; standard convention is to count only non-trailing-zero digits unless otherwise noted.)*

3. 3.680150 → 7 significant figures
✔ All digits are significant:
- Non-zeros: 3,6,8,1,5 → 5 sig figs
- Zero between non-zeros: 0 (between 8 and 1) → significant
- Trailing zero after decimal: 0 at end → significant
→ Total = 7

4. 470.00 → 5 significant figures
✔ The decimal point makes trailing zeros significant.
- 4,7 → non-zero → significant
- 0 between 7 and decimal? No — but the two trailing zeros after decimal are significant.
Actually: 4,7,0,0,0 → all 5 are significant because the decimal point indicates precision.
→ 5 sig figs.

5. 0.00360725 → 6 significant figures
✔ Leading zeros are NOT significant. First non-zero digit is ‘3’.
Digits after that: 3,6,0,7,2,5 → all are significant.
The zero between 6 and 7 is sandwiched → significant.
→ Total = 6 sig figs.

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Part 2: Round the following numbers to 3 significant figures.

Rounding Rules:
- Identify the first 3 significant digits.
- Look at the 4th significant digit:
- If ≥5 → round up the 3rd digit.
- If <5 → leave the 3rd digit unchanged.
- Keep trailing zeros if needed to preserve place value or decimal precision.

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6. 260647 → 261000
✔ First 3 sig figs: 2,6,0 → 260
Next digit is 6 (≥5) → round up the 0 to 1 → becomes 261
→ 261000 (trailing zeros are placeholders)

7. 8.0275201 → 8.03
✔ First 3 sig figs: 8.02
Next digit is 7 (≥5) → round up 2 to 3 → 8.03

8. 0.00472351 → 0.00472
✔ Leading zeros don’t count. First 3 sig figs: 4,7,2 → 0.00472
Next digit is 3 (<5) → no rounding up → remains 0.00472

9. 600.90005 → 601
✔ First 3 sig figs: 6,0,0 → 600
Next digit is 9 (≥5) → round up → 600 → 601
→ 601 (the decimal part is gone since we’re rounding to 3 sig figs and 601 has 3 sig figs)

10. (3.25 × 5.75) / 5.25 → ? (first calculate, then round to 3 sig figs)

Step 1: Calculate numerator:
3.25 × 5.75 = ?

Let’s compute:
3.25 × 5.75
= (3 + 0.25) × (5 + 0.75)
Or better:
3.25 × 5.75 = 3.25 × (5 + 0.75) = 3.25×5 + 3.25×0.75
= 16.25 + 2.4375 = 18.6875

Step 2: Divide by 5.25:
18.6875 ÷ 5.25

Let’s do the division:
18.6875 ÷ 5.25 = ?

Multiply numerator and denominator by 100 to eliminate decimals:
1868.75 ÷ 525

Divide:
525 × 3 = 1575
1868.75 - 1575 = 293.75
525 × 0.5 = 262.5
293.75 - 262.5 = 31.25
525 × 0.06 = 31.5 → too big
525 × 0.0595 ≈ 31.2375 → close

Better to use calculator-style:

18.6875 ÷ 5.25 = 3.5595238...

Now round to 3 significant figures:

First 3 sig figs: 3.55 (since 3.559... → 3,5,5)
Next digit is 9 (≥5) → round up the last 5 → becomes 3.56

✔ Final answer: 3.56

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## ✔ Final Answers:

Significant Figures Count:
1. 6
2. 2
3. 7
4. 5
5. 6

Rounded to 3 Significant Figures:
6. 261000
7. 8.03
8. 0.00472
9. 601
10. 3.56

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Note on #2 (6500000):
In some contexts, especially if this is from a textbook or curriculum that assumes trailing zeros in whole numbers are not significant, 2 is correct. If scientific notation were used (e.g., 6.5 × 10⁶), it would be unambiguously 2 sig figs. If it were 6.500000 × 10⁶, it would be 7. But as written, 2 is the expected answer.

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