2Measurement always involves some estimating. A better instrument allows for better measurements, recorded as a greater number of significant figures (digits).
3Recording - include EVERY digit that is absolutely certain Recording - include EVERY digit that is absolutely certain...PLUS the ONE digit that is estimated.These are the SIGNIFICANT FIGURES.3.23estimatedcertain
51. All non-zero digits are significant. 374 (3 sig figs) (2 sig figs)2. All zeroes between non-zero digits are significant.50407 (5 sig figs) (4 sig figs)3. Leading zeroes are NOT significant.0.54 (2 sig figs) (2 sig figs)
6Always LOOK FOR A DECIMAL 4. Trailing zeroes are significant ONLY if there is adecimal point.2370 (3 sig figs) (2 sig figs)160.0 (4 sig figs) (4 sig figs)
76.02 x 10 23 Move the decimal so it is behind the first To avoid confusion, scientists commonly use SCIENTIFIC NOTATION.ALL digits in scientific notation are SIGNIFICANT6.02 x 10 23Move the decimal so it is behind the firstnon-zero digit.Count the number of places that you moved thedecimal - to the left is +, right is -
8x 10 5x 10 -31.5 x6.35 x103,0001,236,00042.01.03 x 10 51.236 x 10 64.20 x 10 12.1 x 10 -72.38 x 10 -4
90-4: round down 5 -9: round up 0.00533 (2 sig figs) 0.0053 Rounding Rules0-4: round down5 -9: round up(2 sig figs)(3 sig figs) 4261890 (1 sig fig) 2000(2 sig figs) 0.030
10RulesforAddition and SubtractionMultiplication and Division
11You can only give an answer that is as accurate as your least accurate number.
12Add or subtractCount digits to the right of the decimal.Round the answer to match the value with the LEAST number of decimal places.=Answer = 143.9least number of decimal places
13Multiply or divideAnswer is rounded to contain the same number of sig figs as the value with the LEAST.51.3 × =The answer, with significant figures, is 705.
14DO 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