Significant figures (often called sig figs) are the digits in a number that carry real meaning about its precision. They include all the certain digits in a measurement plus the first uncertain (or estimated) digit. In simpler words, significant figures show how accurate and trustworthy a number is.
There are a few important rules to follow when determining the number of significant figures in a number, especially after performing basic operations like addition, subtraction, multiplication, or division (check summary at the bottom of the page). The following significant figures examples (practice problems with solutions) are designed to test your understanding of these rules. They are organized into categories, which you can browse using the table of contents. Each answer is hidden under a content toggle—click to reveal and check if you got it right. Enjoy exploring and practicing!
Number of Significant Numbers
1. Identify the number of significant digits/figures in the following given numbers.
I. 45
II. 0.076
III. 8.6220
IV. 5002
V. 3900
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I. Answer: 2 Significant numbers. Explanation: Both digits are non-zero, so they’re always counted.
II. Answer: 2 Significant numbers. Explanation: Leading zeros never count; only the “7” and “6” are significant.
III. Answer: 5 Significant numbers. Explanation: All non-zeros count, and the trailing zero after the decimal point also count.
IV. Answer: 4 Significant numbers. Explanation: Zeros between non-zero digits always count.
V. Answer: 2 Significant numbers. Explanation: The trailing zeros are not significant.
2. How many significant figures are in the number following numbers:
- 0.01030
- 70.010
- 2000
- 0.004560
- 5.0900
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I. Answer: 4 significant figures
Explanation: Leading zeros never count. The digits 1, 0, 3, 0 are significant because the trailing zero after the 3 is to the right of a decimal, so it counts.
II. Answer: 5 significant figures
Explanation: All non-zero digits are significant. The zeros between 7 and 1 count, and the final zero after the decimal also counts.
III. 2000
III. Answer: 1 significant figure
Explanation: With no decimal shown, only the 2 is significant; the trailing zeros are placeholders.
IV. Answer: 4 significant figures
Explanation: Leading zeros don’t count. The digits 4, 5, 6, 0 are significant because the final zero after the 6 is to the right of a decimal.
V. Answer: 5 significant figures
Explanation: Non-zero digits count, and zeros between them or after the decimal are significant. So 5, 0, 9, 0, 0 are all significant.
Rounding off
3. Write the following numbers as specified:
I. 12.378162 (correct to 4 significant digits).
II. 0.0045623 (correct to 3 significant digits)
III. 98765 (correct to 2 significant digits)
IV. 1.00987 (correct to 5 significant digits)
V. 45000 (correct to 2 significant digits)
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I. Answer: 12.38
Explanation: The first four significant digits are 1, 2, 3, 7. The next digit is 8, which rounds the 7 up to 8.
II. Answer: 0.00456
Explanation: Leading zeros don’t count. The first three significant digits are 4, 5, 6. The next digit is 2, so we keep 456.
III. Answer: 99000
Explanation: The first two significant digits are 9 and 8. The next digit is 7, which rounds the 8 up to 9. The remaining digits are replaced with zeros to keep the value in the right scale.
IV. Answer: 1.0099
Explanation: All non-zero digits and zeros between them count. The first five significant digits are 1, 0, 0, 9, 8. The next digit 7 rounds the 8 up to 9.
V. Answer: 45
Explanation: Without a decimal, the trailing zeros are placeholders.
4. Round off the list of numbers to two significant figures.
I. 34.05
II. 21.3
III. 76.9
IV. 44.7
V. 0.008562
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I. Answer: 34
Explanation: The first two digits are 3 and 4. Since the next digit (0) is less than 5, we keep it as 34.
Answer: 21
Explanation: The first two digits are 2 and 1. The next digit (3) is less than 5, so it stays 21.
III. Answer: 77
Explanation: The first two digits are 7 and 6. The next digit (9) is greater than 5, so we round up, making it 77.
IV. Answer: 45
Explanation: The first two digits are 4 and 4. The next digit (7) is greater than 5, so we round the last kept digit up to get 45.
V. Answer: 0.0086
Explanation: Leading zeros are not significant. The first two significant digits are 8 and 5. Since the next digit (6) is greater than 5, the 5 rounds up, giving 0.0086.
5. Round each of the following numbers to three significant figures:
- 542.79573
- 7,845.8749
- 0.000048389
- 2.45755567
- 76.89
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I. Answer: 543
Explanation: The first three significant digits are 5, 4, and 2. The next digit is 7, which is greater than 5, so the 2 rounds up to 3, giving 543.
II. Answer: 7,850
Explanation: The first three significant digits are 7, 8, and 4. The next digit is 5, so the 4 rounds up to 5. Since we’re rounding, the remaining digits become zeros, giving 7,850.
III. Answer: 0.0000484
Explanation: Leading zeros don’t count. The first three significant digits are 4, 8, and 3. The next digit is 8, so the 3 rounds up to 4, giving 0.0000484.
IV. Answer: 2.46
Explanation: The first three significant digits are 2, 4, and 5. The next digit is 7, so the 5 rounds up to 6, giving 2.46.
V. Answer: 76.9
Explanation: The first three significant digits are 7, 6, and 8. The next digit is 9, which rounds the 8 up to 9, giving 76.9.
6. Round off the following decimal numbers as specified:
- 0.0801 (1 significant figure)
- 7.0887 (2 significant figure)
- 9.02430 (3 significant figure)
- 24.03 (5 significant figure)
- 0.00098765 (2 significant figures)
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I. Answer: 0.08
Explanation: Ignore leading zeros. The first significant digit is 8. No need to keep more digits, so the answer is 0.08.
II. Answer: 7.1
Explanation: The first two significant digits are 7 and 0. The next digit is 8, so the 0 rounds up to 1, giving 7.1.
III. Answer: 9.02
Explanation: The first three significant digits are 9, 0, and 2. The next digit is 4, which is less than 5, so no rounding up. Final answer is 9.02.
IV. Answer: 24.030
Explanation: The number already has 4 significant figures (2, 4, 0, 3). To make it 5 significant figures, we add a trailing zero after the 3, giving 24.030.
V. Answer: 0.00099
Explanation: Ignore leading zeros. The first two significant digits are 9 and 8. The next digit is 7, so the 8 rounds up to 9, giving 0.00099.
Addition and Subtraction
7. Perform the following calculations to the correct number of significant figures:
I. 12.0550 + 9.05
II. 257.2 – 19.789
III. 105.64 + 23.1
IV. 0.00456 + 0.0001223
V. 674.89 – 23.1
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I. Answer: 21.11
Explanation:
12.0550 has 4 decimal places.; 9.05 has 2 decimal places;
→ Result must have 2 decimal places.
12.0550 + 9.05 = 21.105 → 21.11
II. Answer: 237.4
Explanation:
257.2 has 1 decimal place; 19.789 has 3 decimal places.
→ Result must have 1 decimal place.
257.2 – 19.789 = 237.411 → 237.4
III. Answer: 128.7
Explanation:
105.64 has 2 decimal places; 23.1 has 1 decimal place.
→ Result must have 1 decimal place.
105.64 + 23.1 = 128.74 → 128.7
IV. Answer: 0.00468
Explanation:
0.00456 has 5 decimal places; 0.0001223 has 7 decimal places.
→ Result must have 5 decimal places.
0.00456 + 0.0001223 = 0.0046823 → 0.00468
V. V. 674.89 – 23.1
Answer: 651.8
Explanation:
674.89 has 2 decimal places; 23.1 has 1 decimal place.
→ Result must have 1 decimal place.
674.89 – 23.1 = 651.79 → 651.8
Multiplication and Division
8. Perform the following calculations to the correct number of significant figures:
I. (4.23 x 103 ) (0.250)
II. 0.07927 ÷ 0.753
III. 56.5 x 1.82 ÷ 100.03
IV. (3.390 x 106 ) ÷ (4.7 x 201 )
V. [(24.7 x 305 ) ÷ 68.433] + 354.99
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I. Answer: 109
Step 1: Multiply inside the parentheses: 4.23×103=435.69
Step 2: Multiply by 0.250: 435.69×0.250=108.9225
Step 3: Apply significant figures: All values has 3 significant figures, so the final answer should have 3 sig figs as well.
So, final answer: 108.9225≈109
II. Answer: 0.105
0.07927 has 4 sig figs; 0.753 has 3 sig figs; So, final answer should have 3 sig figs.
Final Answer: 0.1053… which when rounded to 3 sig figs becomes: 0.105
III. Answer: 1.03
56.5 has 3 sig figs; 1.82 has 3 sig figs; 100.03 has 5 sig figs. It follows that the final answer should have 3 sig figs.
Next, we start calculating:
Step 1: 56.5×1.82=102.93
Step 2: 102.93÷100.03=1.029
1.029 rounded to 3 sig figs = 1.03
IV. Answer: 0.38
Step 1: Multiply out numerator: 3.390×106=359.34
Step 2: Multiply out denominator: 4.7×201=944.7
Step 3: Divide: 359.34÷944.7=0.3803…
Step 4: Apply significant figures. The least significant figure is 2 (i. e 4.7). So, our final answer should be in 2 sig figs
0.3803≈0.38
V. Answer: 465
Step 1: 24.7×305=7523.5
Step 2: 7523.5÷68.433=109.91
Step 3: 110+354.99=464.99.
Sig figs rule for addition: Must match decimal places → 110 has no decimal places, so final must have no decimals.
Scientific Notation
9. Identify the number of significant figures in the following numbers (in scientific notation):
I. 3.800 × 10³
II. 5.20 × 10⁻²
III. 7.06 × 10⁴
IV. 9.000 × 10⁻⁷
V. 1.0040 × 10²
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I. Answer: 4 significant figures. Explanation: All digits are significant because the zeros come after the decimal point and after non-zero digits.
II. Answer: 3 significant figures. Explanation: The trailing zero after the 2 is significant because it comes after a decimal.
III. Answer: 3 significant figures. Explanation: The zero in the middle is significant because it’s between non-zero digits.
IV. Answer: 4 significant figures. Explanation: All zeros are significant because they come after the decimal and after a non-zero digit.
V. Answer: 5 significant figures. Explanation: Both zeros between 1 and 4 are significant, and the trailing zero after the 4 is also significant because of the decimal.
Summary of Significant Figures Rules
The rules below explain which digits count as significant and which do not.
1. Nonzero digits are always significant.
- Every nonzero digit counts as a significant figure.
- Example: 3874 has 4 significant figures.
2. Zeros between nonzero digits are significant.
- If a zero is “trapped” between two nonzero digits, it always counts.
- Example: 708 has 3 significant figures.
3. Trailing zeros without a decimal are not significant.
- Zeros at the end of a whole number (with no decimal point) do not count.
- Example: 500 has 1 significant figure.
4. Trailing zeros with a decimal are significant.
- If a decimal point is shown, zeros at the end of the number are significant.
- Example: 500. has 3 significant figures.
- Example: 500.0 has 4 significant figures.
5. Leading zeros are never significant.
- Zeros that appear before the first nonzero digit are simply placeholders and do not count.
- Example: 0.0843 has 3 significant figures.
- Example: 0.0074 has 2 significant figures.
6. Exact numbers and measured zeros.
- If zeros appear at the end of a measurement, they can be significant if they were intentionally recorded.
- Example: 1090 m may have 4 significant figures if all digits were measured.
7. Numbers in scientific notation.
- All digits written in scientific notation are significant. The power of 10 does not affect the count.
- Example: 4.300 × 10⁻⁴ has 4 significant figures.