Measurement always involves some estimating. A better instrument allows for better measurements, recorded as a greater number of significant figures (digits).
Recording - include EVERY digit that is absolutely certain...PLUS the ONE digit that is estimated. These are the SIGNIFICANT FIGURES certain estimated 3
Rules for Significant Figures
2. All zeroes between non-zero digits are significant (5 sig figs) (4 sig figs) 1. All non-zero digits are significant. 374 (3 sig figs) 8.1 (2 sig figs) 3. Leading zeroes are NOT significant (2 sig figs) (2 sig figs)
4. Trailing zeroes are significant ONLY if there is a decimal point (3 sig figs) (2 sig figs) (4 sig figs) (4 sig figs) Always LOOK FOR A DECIMAL
To avoid confusion, scientists commonly use SCIENTIFIC NOTATION. ALL digits in scientific notation are SIGNIFICANT 6.02 x Move the decimal so it is behind the first non-zero digit. 2.Count the number of places that you moved the decimal - to the left is +, right is -
x x x x , ,236, x x x x x 10 -4
0-4: round down 5 -9: round up Rounding Rules (2 sig figs) (3 sig figs) (1 sig fig) (2 sig figs) 0.030
Addition and Subtraction Multiplication and Division Rules for
You can only give an answer that is as accurate as your least accurate number.
Add or subtract Count digits to the right of the decimal. Round the answer to match the value with the LEAST number of decimal places. Answer = least number of decimal places =
Multiply or divide Answer is rounded to contain the same number of sig figs as the value with the LEAST × = The answer, with significant figures, is 705.
DO NOT round for each calculation. When performing multiple calculations, use the rule of the final calculation to round the answer. ( )(3.6) = ? (0.5)(3.6) = 1.8 = 2 (0.5012)(3.6) = = 1.8