Scientific Figures Calculator

Scientific Figures Calculator

Use this calculator to perform basic arithmetic operations and determine the result with the correct number of significant figures or decimal places.

Understanding Significant Figures

Significant figures (often called "sig figs") are crucial in scientific and engineering fields because they indicate the precision of a measurement. When you record a measurement, the number of significant figures tells you how many digits are known with certainty, plus one estimated digit. Using significant figures correctly ensures that calculations do not imply a greater precision than the original measurements allow.

Rules for Counting Significant Figures:

1. Non-zero digits: All non-zero digits are significant. (e.g., 123.45 has 5 sig figs)
2. Zeros between non-zero digits: Zeros located between non-zero digits are significant. (e.g., 1002 has 4 sig figs)
3. Leading zeros: Zeros that precede all non-zero digits are NOT significant. They merely indicate the position of the decimal point. (e.g., 0.00123 has 3 sig figs)
4. Trailing zeros (with a decimal point): Trailing zeros are significant if the number contains a decimal point. (e.g., 12.00 has 4 sig figs, 120. has 3 sig figs)
5. Trailing zeros (without a decimal point): Trailing zeros in a number without a decimal point are generally considered NOT significant unless explicitly stated (e.g., by using scientific notation or a decimal point at the end). For example, 1200 typically has 2 sig figs, while 1200. has 4 sig figs.
6. Exact numbers: Numbers that are counted or defined (e.g., 12 eggs in a dozen, 100 cm in 1 meter) have an infinite number of significant figures and do not limit the precision of a calculation.

Rules for Arithmetic Operations:

1. Multiplication and Division:

When multiplying or dividing measurements, the result should be rounded to the same number of significant figures as the measurement with the fewest significant figures.

Example:

• 12.34 (4 sig figs) × 5.6 (2 sig figs) = 69.104
• The measurement with the fewest sig figs is 5.6 (2 sig figs).
• Therefore, the result should be rounded to 2 significant figures: 69.

2. Addition and Subtraction:

When adding or subtracting measurements, the result should be rounded to the same number of decimal places as the measurement with the fewest decimal places.

Example:

• 12.34 (2 decimal places) + 5.6 (1 decimal place) = 17.94
• The measurement with the fewest decimal places is 5.6 (1 decimal place).
• Therefore, the result should be rounded to 1 decimal place: 17.9.

How to Use the Calculator:

Enter your first and second numerical values into the respective input fields. Select the desired arithmetic operation (+, -, *, /) from the dropdown menu. Click "Calculate" to see the raw result, the result rounded to the correct number of significant figures or decimal places, and an explanation of the rounding rule applied.