This Significant Figures Calculator solves mathematical operations and counts significant figures. It explains how to control sig figs in multiplication, division, addition, and subtraction
Logarithms: Round the result to the input's decimal places. Match its significant figures.
Antilogarithms: Use the decimal places for rounding.
Exponentiation: Rounding is based only on the accuracy of the base number.
Final Step: At the end round the answer to the accurate number of significant figures.
Each part of the expression highlights the least significant digits
What Are Significant Figures?
Significant Figures, or "Sig Figs" are the meaningful digits in a number or expression. They indicate its precision and accuracy. Significant figures give reliable results. They build confidence in a number, the first non-zero digits are important.
For Example:
- 23 has 2 Significant Figures
- 100 has 3 Significant Figures
- 2025 has 4 Significant Figures
Rules For Significant Figures
These are the following rules for determining significant figures:
Rule No. 1: “The first non-zero digit on the left side is significant.”
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Examples:
- 0.007890 in this first non-digit is 7 so it is the first significant digit and it has 4 sig figs (7, 8, 9, 0)
- 59.00 has 4 sig figs.
Rule No. 2: “Trailing zeros in a whole number with a decimal point are significant.”
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Examples:
- 45.00 has 4 figures.
- 1000.0 has 5 figures.
Rule No. 3: “Leading zeros before the non-zero digits are not significant.”
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Examples:
- 0.0083 has 2 significant digits.
- 0.0637 has 3 significant digits.
Rule No. 4: “All non-zero digits before and after the decimal point are significant.”
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Examples:
- 415.35 has five significant.
- 345 has 3 three significant.
Rule No. 5: “Accurate numbers have an unlimited number of significant figures.”
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Examples:
- π (pi) = 3.141592653589... so, pi has an infinite number of significant figures
- 10 dm = 1 m (unlimited sig. figs.)
Rule No. 6: “In scientific notation, we write any value as A × 10^x. The rules applied to A determine the number of significant figures. The x is exact, so it has unlimited significant figures.”
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Examples:
- 6.022 x 10^23 has 1 significant digit
- 1.789 * 10^-3 has 2 significant digit
How To Use Our Significant Figures Calculator?
Our Sig Fig Calculator is versatile and easy to use. It lets you work with many numbers at once, such as by performing operations like 7.76 ÷ 7.88 or rounding a number to your desired significant figures.
Our tool guarantees precision with its accurate, efficient calculations. Follow these steps to get accurate results for any measurement with significant figures.
Input Required Information:
- At first, you enter a number or expression that you want to write in the given field.
- Choose the operation if your expression contains any elements.
- Then select or input the rounded number that you want to use. (optional field)
- Tap the calculate button.
Output You Get:
- Round to Significant Figures: Adjust numbers to the specified count of significant figures.
- Count of Significant Figures: Count the significant figures in a number or expression.
- Decimal Precision Counter: Count the number of decimal places in a number.
- Convert to Scientific Notation: Express numbers with significant figures using scientific notation.
- Convert to Exponential Notation: Express numbers with sig figs using E-notation.
How Many Significant Figures Are There?
Here are some common examples showing Significant Figures, Decimals, Scientific Notation, and E-Notation.
| Number | Sig Figs | Decimals | Scientific Notation | E-Notation |
|---|---|---|---|---|
| 0.0010 | 2 | 4 | 1 × 10^-3 | 1e-3 |
| 200 | 1 | 0 | 2 × 10^2 | 2e+2 |
| 8000 | 1 | 0 | 8 × 10^3 | 8e+3 |
| 980 | 2 | 0 | 9.8 × 10^2 | 9.8e+2 |
| 3800 | 2 | 0 | 3.8 × 10^3 | 3.8e+3 |
| 3251.424 | 7 | 3 | 3.251424 × 10^3 | 3.251424e+3 |
| 80.095 | 5 | 3 | 8.0095 × 10^1 | 8.0095e+1 |
| 13.107 | 5 | 3 | 1.3107 × 10^1 | 1.3107e+1 |
| 0.00007 | 1 | 5 | 7 × 10-5 | 7e-5 |
| 833.000 | 6 | 3 | 8.33 × 10^2 | 8.33e+2 |
| 801 | 3 | 0 | 8.01 × 10^2 | 8.01e+2 |
| 825000 | 3 | 0 | 8.25 × 10^5 | 8.25e+5 |
| 1.20 | 3 | 2 | 1.2 × 10^0 | 1.2e+0 |
| 2.5 | 2 | 1 | 2.5 × 10^0 | 2.5e+0 |
| 0.0001 | 1 | 4 | 1 × 10^-4 | 1e-4 |
| 0.00580 | 3 | 5 | 5.8 × 10^-3 | 5.8e-3 |
| 2900 | 2 | 0 | 2.9 × 10^3 | 2.9e+3 |
| 14.600 | 5 | 3 | 1.46 × 10^1 | 1.46e+1 |
| 8.070 | 4 | 3 | 8.07 × 10^0 | 8.07e+0 |
| 0.00169 | 3 | 5 | 1.69 × 10^-3 | 1.69e-3 |
| 102 / 2 | 1 | 0 | 5 × 10^1 | 5e+1 |
| 14.010 | 5 | 3 | 1.401 × 10^1 | 1.401e+1 |
| 16.58 | 4 | 2 | 1.658 × 10^1 | 1.658e+1 |
| 0.01986 | 4 | 5 | 1.986 × 10^-2 | 1.986e-2 |
| 0.0198 | 3 | 4 | 1.98 × 10^-2 | 1.98e-2 |
| 3457.1 | 5 | 1 | 3.4571 × 10^3 | 3.4571e+3 |
| 4.51 - 2.1395 | 3 | 2 | 2.37 × 10^0 | 2.37e+0 |
| 0.000236 | 3 | 6 | 2.36 × 10^-4 | 2.36e-4 |
| 0.169 | 3 | 3 | 1.69 × 10^-1 | 1.69e-1 |
| 18.96 | 4 | 2 | 1.896 × 10^1 | 1.896e+1 |
| 0.0432 | 3 | 4 | 4.32 × 10^-2 | 4.32e-2 |
| 363.75 | 5 | 2 | 3.6375 × 10^2 | 3.6375e+2 |
| 0.00798516 | 6 | 8 | 7.98516 × 10^-3 | 7.98516e-3 |
| 0.024561 | 5 | 6 | 2.4561 × 10^-2 | 2.4561e-2 |
| 82.00756 | 7 | 5 | 8.200756 × 10^1 | 8.200756e+1 |
| 1000 | 1 | 0 | 1 × 10^3 | 1e+3 |
| 0.06900 | 4 | 5 | 6.9 × 10^-2 | 6.9e-2 |
| 0.0025 | 2 | 4 | 2.5 × 10^-3 | 2.5e-3 |
| 3 | 1 | 0 | 3 × 10^0 | 3e+0 |
| 0.00104 | 3 | 5 | 1.04 × 10^-3 | 1.04e-3 |
| 0.046 | 2 | 3 | 4.6 × 10^-2 | 4.6e-2 |
| 3000 | 1 | 0 | 3 × 10^3 | 3e+3 |
| 23.95 | 4 | 2 | 2.395 × 10^1 | 2.395e+1 |
| 0.00097 | 2 | 5 | 9.7 × 10^-4 | 9.7e-4 |
| 35.2 | 3 | 1 | 3.52 × 10^1 | 3.52e+1 |
| 3.00 | 3 | 2 | 3 × 10^0 | 3e+0 |
| 1.0000 | 5 | 4 | 1 × 10^0 | 1e+0 |
| 0.9976 | 4 | 4 | 9.976 × 10^-1 | 9.976e-1 |
| 0.026 | 2 | 3 | 2.6 × 10^-2 | 2.6e-2 |
| 0.037 | 2 | 3 | 3.7 × 10^-2 | 3.7e-2 |
| 0.749 | 3 | 3 | 7.49 × 10^-1 | 7.49e-1 |
| 0.82 | 2 | 2 | 8.2 × 10^-1 | 8.2e-1 |
| 3.5897 | 5 | 4 | 3.5897 × 10^0 | 3.5897e+0 |
| 0.0405 | 3 | 4 | 4.05 × 10^-2 | 4.05e-2 |
| 0.00230 | 3 | 5 | 2.3 × 10^-3 | 2.3e-3 |
| 0.0023080 | 5 | 7 | 2.308 × 10^-3 | 2.308e-3 |
| 0.0340 | 3 | 4 | 3.4 × 10^-2 | 3.4e-2 |
| 2.00120 | 6 | 5 | 2.0012 × 10^0 | 2.0012e+0 |
| 23.023 | 5 | 3 | 2.3023 × 10^1 | 2.3023e+1 |
| 0.0003 | 1 | 4 | 3 × 10^-4 | 3e-4 |
| 0.00340 | 3 | 5 | 3.4 × 10^-3 | 3.4e-3 |
| 0.030 | 2 | 3 | 3 × 10^-2 | 3e-2 |
| 0.001 | 1 | 3 | 1 × 10^-3 | 1e-3 |
| .00020 | 2 | 5 | 2 × 10^-4 | 2e-4 |
| .100 | 3 | 3 | 1 × 10^-1 | 1e-1 |
| .010 | 2 | 3 | 1 × 10^-2 | 1e-2 |
| 2.0034 | 5 | 4 | 2.0034 × 10^0 | 2.0034e+0 |
| 3.4 x 10^4 | 1 | 0 | 3 × 10^4 | 3e+4 |
| 9.0 x 10^-3 | 1 | 3 | 9.0 × 10^-3 | 9e-3 |
| 4.02 x 10^-9 | 1 | 9 | 4.02 × 10^-9 | 4e-9 |
| 0.00010 | 2 | 5 | 1 × 10^-4 | 1e-4 |
| 1.12500 x 10^4 | 1 | 0 | 1.12500 × 10^4 | 1e+4 |
| 1.0200 x 10^5 | 1 | 0 | 1.0200 × 10^5 | 1e+5 |
| 6.02 x 10^23 | 1 | 0 | 6.02 × 10^23 | 6e+23 |
| 6.07 x 10^-15 | 1 | 15 | 6 × 10^-15 | 6e-15 |
| 500 | 1 | 0 | 5 × 10^2 | 5e+2 |
| 6000 | 1 | 0 | 6 × 10^3 | 6e+3 |
| 11.090 | 5 | 3 | 1.109 × 10^1 | 1.109e+1 |
| 0.01249 | 4 | 5 | 1.249 × 10^-2 | 1.249e-2 |
| 1.21 × 10^-3 | 1 | 3 | 1 × 10^-3 | 1e-3 |
| 1.625 × 10^-3 | 2 | 0 | 1.3 × 10^1 | 1.3e+1 |
| 0.000000043 | 2 | 9 | 4.3 × 10^-8 | 4.3e-8 |
| 4.5e7 | 2 | 0 | 4.5 × 10^7 | 4.5e+7 |
| 14468.98263 | 10 | 5 | 1.446898263 × 10^4 | 1.446898263e+4 |
FAQ’s
How many significant figures are present in 1,000?
1000 has 1 significant figure. The leading zeros and the trailing zeros without a decimal point are not significant.
How many significant figures are present in the measurement 0.0082 L?
There are five digits provided in the question: three zero digits and two non-zero digits. Follow the significant figure's rules. Leading zeros before a decimal and after it are not significant figures. There are no non-zero digits between the zeros. So, only two significant figures exist in this measurement.
References:
Wikipedia − Determine Significant Figures
Britannica − Significant Figures Rules
Columbia University − Understanding Significant Figures