Printable worksheet for practicing significant figures, featuring 16 numbers to determine significant digit counts.

Let's solve each of these problems step by step using the rules for significant figures:

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🔢 Rules for Significant Figures:

1. All non-zero digits are significant.
2. Zeros between non-zero digits are significant.
3. Leading zeros (before the first non-zero digit) are NOT significant.
4. Trailing zeros (after the last non-zero digit) are significant ONLY if the number has a decimal point.
5. Trailing zeros in a whole number without a decimal point are NOT significant unless specified otherwise (e.g., with a bar or scientific notation).
6. In scientific notation, all digits in the coefficient are significant.

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Now let’s go through each number:

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1) 0.29060
- Leading zero → not significant.
- 2, 9, 0 (between non-zeros), 6, and trailing 0 after decimal → all significant.
- So: 2, 9, 0, 6, 0 → 5 significant digits ✔

2) 10203005
- All non-zero digits are significant.
- Zeros between non-zeros are significant.
- Trailing zeros? No decimal → so trailing zeros not significant.
- But here, the zeros are between non-zeros → they are significant.
- Digits: 1, 0, 2, 0, 3, 0, 0, 5 → all are significant because:
- 0s are between non-zeros → significant
- Last two zeros are after the 5 → but since no decimal, they’re not significant?
Wait: Let's check: 10203005 → this is a whole number ending in two zeros.
- The last two zeros are trailing, and there's no decimal point, so they are not significant.
- But wait: the zero before the 3 is between 2 and 3 → significant.
- The zero after 3 is between 3 and 0 → still part of the number.

Actually, all digits in 10203005 are significant because:
- There are no leading zeros.
- All zeros are in between non-zero digits → significant.
- The last two zeros: 005 → the two zeros are between 3 and 5? No! It's 10203005 → digits:
1, 0, 2, 0, 3, 0, 0, 5 → the last two zeros are before the 5 → actually, it's 10203005 → that’s:
- 1, 0, 2, 0, 3, 0, 0, 5 → so the last zero is before 5 → so it's not a trailing zero? Wait: 10203005 → the last digit is 5, so the zeros are before it.

Wait: 10203005 → positions:
- 1 (significant)
- 0 (between 1 and 2) → significant
- 2 (significant)
- 0 (between 2 and 3) → significant
- 3 (significant)
- 0 (between 3 and 0) → significant
- 0 (between 0 and 5) → significant
- 5 (significant)

So all 8 digits are significant because every zero is between non-zero digits.

✔ 8 significant digits

3) 1785
- All non-zero digits → all significant.
- No zeros → so 4 significant digits

4) 50
- No decimal point.
- Trailing zero → not significant.
- So only the 5 is significant.
- 1 significant digit

5) 0.02
- Leading zeros → not significant.
- Only the 2 is significant.
- 1 significant digit

6) 47.2950
- All digits: 4, 7, 2, 9, 5, 0
- Decimal present → trailing zero is significant.
- So all six digits are significant.
- 6 significant digits

7) 23.0
- Decimal present → trailing zero is significant.
- So 2, 3, and 0 → all significant.
- 3 significant digits

8) 0847020
- Leading zero → not significant.
- So we start from 8: 8, 4, 7, 0, 2, 0
- Now, the zeros:
- First zero (after 7) → between 7 and 2 → significant
- Last zero → trailing, but no decimal → not significant
- But wait: the number is written as 0847020 — this looks like a number with a leading zero, possibly indicating formatting.
- However, in standard rules, leading zeros are never significant.
- So: 8, 4, 7, 0, 2 → the zero between 7 and 2 is significant.
- Last zero is trailing and no decimal → not significant.
- So digits: 8, 4, 7, 0, 2 → 5 significant digits?

Wait: 0847020 → remove leading zero → 847020
- Now: 8, 4, 7, 0, 2, 0 → last zero is trailing, no decimal → not significant
- Middle zero (between 7 and 2) → significant
- So: 8, 4, 7, 0, 2 → 5 significant digits

But note: if it were 847020., then the last zero would be significant.

Here, no decimal → so 5 significant digits

✔ 5 significant digits

9) 0.91
- Leading zero → not significant.
- 9 and 1 → both significant.
- 2 significant digits

10) 1.234
- All digits non-zero → all significant.
- 4 significant digits

11) 007850
- Leading zeros → not significant.
- Remove them: 7850
- Now: 7, 8, 5, 0
- No decimal → trailing zero → not significant
- So only 7, 8, 5 → 3 significant digits

✔ 3 significant digits

12) 0660
- Leading zero → not significant.
- Remaining: 6, 6, 0
- No decimal → trailing zero → not significant
- So only the two 6s → 2 significant digits

13) 23.0561
- All digits: 2, 3, 0, 5, 6, 1
- Decimal present → all digits are significant.
- Even the zero between 3 and 5 → significant.
- 6 significant digits

14) 8.0
- Decimal present → trailing zero is significant.
- So 8 and 0 → both significant.
- 2 significant digits

15) 1.020000
- All digits: 1, 0, 2, 0, 0, 0, 0
- Decimal present → all trailing zeros are significant.
- So all digits are significant → 7 significant digits

16) 1000
- Whole number, no decimal point.
- Trailing zeros → not significant.
- Only the 1 is significant.
- 1 significant digit

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✔ Final Answers:

| Number | Significant Digits |
|---------------|--------------------|
| 1) 0.29060 | 5 |
| 2) 10203005 | 8 |
| 3) 1785 | 4 |
| 4) 50 | 1 |
| 5) 0.02 | 1 |
| 6) 47.2950 | 6 |
| 7) 23.0 | 3 |
| 8) 0847020 | 5 |
| 9) 0.91 | 2 |
|10) 1.234 | 4 |
|11) 007850 | 3 |
|12) 0660 | 2 |
|13) 23.0561 | 6 |
|14) 8.0 | 2 |
|15) 1.020000 | 7 |
|16) 1000 | 1 |

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📝 Summary:

Use the rules carefully:
- Decimal point matters for trailing zeros.
- Leading zeros never count.
- Zeros between non-zeros always count.
- Trailing zeros only count if decimal is present.

Let me know if you'd like this in a printable format or need explanations for any specific ones!