significant digit
- Noun:
- A digit in a number that contributes to its precision: A significant digit is any digit of a number that is known with certainty or reliably, used to express the precision of a measurement or calculation.
- A digit from the first non-zero digit to the last digit (including trailing zeros when they denote precision): In a numerical value, significant digits begin with the first non-zero digit on the left and end with the last digit that is reliably known, which can be a non-zero digit or a zero that is considered exact.
- Noun:
- The measurement 0.05060 has four significant digits: 5, 0, 6, and the final 0.
- When reporting the result, ensure you use the correct number of significant digits to reflect the instrument's accuracy.
- The constant π is often approximated as 3.14, which has three significant digits.
"Significant figures": A synonymous term often used interchangeably with "significant digits" to denote the meaningful digits in a number.
- The rule for multiplication is that the answer should have the same number of significant figures as the measurement with the fewest significant figures.
Leading and trailing zeros: The role of zeros in determining significant digits.
- In the number 0.0045, the zeros are not significant; they only locate the decimal point. The significant digits are 4 and 5.
- In the number 4500, if the zeros are not measured (they are placeholders), it has two significant digits (4 and 5). If they are measured, it could have four.
Significant figure (n): A term used identically to "significant digit" to express precision in a numerical value.
- Rounding to three significant figures, 12.345 becomes 12.3.
Precision (n): The degree to which repeated measurements show the same result, closely related to the concept of significant digits.
- Accuracy (n): The closeness of a measurement to the true value, a concept distinct from but often discussed alongside precision and significant digits.
- Meaningful digit: A digit that carries meaning contributing to a number's precision.
- Reliable digit: A digit that is known with certainty.
To round to [number] significant digits/figures: To adjust a number to contain a specified count of meaningful digits.
- Round the calculated density to two significant digits.
To lose a significant digit: To reduce the number of reliable digits in a calculation, often due to subtraction of similar numbers.
- Subtracting 5.247 from 5.251 can cause you to lose significant digits in the result.
Scientific notation: A method of writing numbers that explicitly shows all significant digits.
- Expressing 4500 with two significant digits as 4.5 × 10³ clearly indicates the precision.
Uncertainty: The estimated amount by which a measured or calculated value may differ from the true value; significant digits are a simplified way of representing this uncertainty.
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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)
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he calculated the answer to four significant figures
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