Definition

1. Noun:
   • A meaningful digit in a number: A "significant figure" is any digit in a numerical value that contributes to its precision. This includes all digits from the first non-zero digit on the left to the last digit on the right, whether that last digit is non-zero or a trailing zero that is known to be exact.

Usage

• Scientific and Mathematical Context: The concept of significant figures is primarily used to indicate the precision of a measurement or calculation. The number of significant figures reflects how precisely a value is known.
• Reporting Results: When reporting numerical results, especially in science and engineering, it is standard practice to use the correct number of significant figures to avoid overstating precision.

Examples

• Noun:
  • The measurement 0.00560 has three significant figures (5, 6, and the final 0).
  • He reported the mass as 12.0 grams, which is to three significant figures.
  • When multiplying, the answer should have the same number of significant figures as the factor with the fewest significant figures.

Advanced Usage

• Leading Zeros: Leading zeros (zeros before the first non-zero digit) are not considered significant figures. They only serve to position the decimal point.
  • In the number 0.0025, only the '2' and '5' are significant figures.
• Trailing Zeros with a Decimal Point: Trailing zeros (zeros after non-zero digits) are considered significant if the number contains a decimal point.
  • The value 150.0 has four significant figures.
• Exact Numbers and Counts: Numbers that are exact counts or definitions (e.g., there are 100 centimeters in a meter) have an infinite number of significant figures and do not limit the precision of a calculation.

Variants and Related Words

• Significant Digit: A synonym for "significant figure."
• Precision (n): The degree to which repeated measurements show the same results, closely related to the concept of significant figures.
• Accuracy (n): The closeness of a measurement to the true value, a related but distinct concept from precision.

Synonyms

• Meaningful digit
• Significant digit

Related Phrases

• To a certain number of significant figures: A phrase used to specify the precision of a reported value.
  • Express your final answer to two significant figures.
• Round to significant figures: The process of adjusting a number to contain a specified number of meaningful digits.
  • You need to round the result to three significant figures.

Noun

1. any digit of a number that is known with certainty; any digit of a number beginning with the leftmost non-zero digit and ending with the rightmost non-zero digit (or a zero considered to be the exact value)
   • he calculated the answer to four significant figures