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Count sig figs and understand which digits are significant
Significant figures (sig figs) represent the meaningful digits in a number that contribute to its precision. Understanding sig figs is essential in science, engineering, and mathematics for expressing measurement accuracy and performing calculations correctly.
All non-zero digits (1-9) are always significant. Example: 345 has 3 sig figs.
Zeros between non-zero digits are significant. Example: 1002 has 4 sig figs.
Leading zeros (zeros before the first non-zero digit) are NOT significant. Example: 0.0045 has 2 sig figs.
Trailing zeros after a decimal point are significant. Example: 12.00 has 4 sig figs.
Addition and Subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places.
Multiplication and Division: The result should have the same number of significant figures as the measurement with the fewest sig figs.
Significant figures prevent overstating the precision of calculated results. They ensure that measurements and calculations accurately reflect the limitations of the measuring instruments and methods used. In scientific work, proper use of sig figs maintains data integrity and prevents false precision.
This number has 3 significant figures. The leading zeros are not significant, but the trailing zeros after the decimal point are significant, indicating precision to five decimal places.
Trailing zeros in whole numbers without a decimal point are ambiguous. For example, 1500 could have 2, 3, or 4 sig figs. Use scientific notation (1.5 × 10³) to clarify the intended precision.
Multiply the numbers normally, then round the result to match the number with the fewest significant figures. For example: 12.5 (3 sig figs) × 3.7 (2 sig figs) = 46.25 → 46 (2 sig figs).
Precision refers to how many significant figures a measurement has (detail level), while accuracy refers to how close a measurement is to the true value. A number can be precise (many sig figs) but not accurate.
Yes, exact numbers (like counted items or defined conversions like 12 inches = 1 foot) have infinite significant figures and don't limit the precision of calculations.
For logarithms, the number of decimal places in the log equals the number of sig figs in the original number. For example, log(123) = 2.090 has 3 decimal places corresponding to 3 sig figs in 123.