Significant figures

Significant figures refer to the digits in a number that carry meaning contributing to its measurement accuracy. This concept is crucial in science, engineering, mathematics, and medicine, where precise measurements are essential. Significant figures include all non-zero digits, zeros between significant digits, and trailing zeros in a decimal portion.

Definition and Rules

The rules for determining significant figures are as follows:

1. All non-zero digits (1-9) are always significant.
2. Any zeros between significant digits are significant.
3. Leading zeros (zeros before the first non-zero digit) are not significant.
4. Trailing zeros in a number containing a decimal point are significant.
5. In a whole number with no decimal point, trailing zeros may or may not be significant, depending on whether they are measured or estimated.

Application in Measurements

In measurements, the significant figures of a number are digits that are known with certainty plus one last digit, which is somewhat uncertain or estimated. The number of significant figures in a measurement reflects the precision of the measurement. For example, if a length is measured as 3.20 cm, the measurement has three significant figures, indicating a higher precision than a measurement of 3.2 cm, which has only two significant figures.

Rounding

Rounding to a certain number of significant figures is a common practice when it is necessary to limit the number of digits in a result. The general rule for rounding is:

• If the digit to the right of the last significant figure is less than 5, do not change the last significant figure.
• If the digit is 5 or greater, increase the last significant figure by one.

Significant Figures in Calculations

When performing calculations, the number of significant figures in the result is determined by the original numbers involved in the calculation. The rules are:

• For addition and subtraction, the result should have as many decimal places as the number in the operation with the fewest decimal places.
• For multiplication and division, the result should have the same number of significant figures as the number with the fewest significant figures used in the calculation.

Importance

Understanding and correctly applying the concept of significant figures is essential for accurate scientific communication. It ensures that measurements and calculations are reported with a precision that reflects the limitations of the measuring process, preventing overinterpretation of data.

See Also

• Measurement
• Accuracy and precision
• Rounding
• Decimal