4.5678 600 0.5008 Significant Figures 1.004 8 32.000 9.99999 7 2.45

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 Recording - include EVERY digit that is absolutely certain...PLUS the ONE digit that is estimated. These are the SIGNIFICANT FIGURES. 3.2 3 estimated certain

Rules for Significant Figures

1. All non-zero digits are significant. 374 (3 sig figs) 8.1 (2 sig figs) 2. All zeroes between non-zero digits are significant. 50407 (5 sig figs) 8.001 (4 sig figs) 3. Leading zeroes are NOT significant. 0.54 (2 sig figs) 0.0098 (2 sig figs)

Always LOOK FOR A DECIMAL 4. Trailing zeroes are significant ONLY if there is a decimal point. 2370 (3 sig figs) 16000 (2 sig figs) 160.0 (4 sig figs) 000.1800 (4 sig figs)

6.02 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 SIGNIFICANT 6.02 x 10 23 Move the decimal so it is behind the first non-zero digit. Count the number of places that you moved the decimal - to the left is +, right is -

238000 2.38 x 10 5 0.0052 5.2 x 10 -3 1.5 x 10 4 15 000 6.35 x 10 -4 0.000635 103,000 1,236,000 42.0 0.00000021 5. 0.000238 1.03 x 10 5 1.236 x 10 6 4.20 x 10 1 2.1 x 10 -7 2.38 x 10 -4

0-4: round down 5 -9: round up 0.00533 (2 sig figs) 0.0053 Rounding Rules 0-4: round down 5 -9: round up 0.00533 (2 sig figs) 0.0053 426.3 (3 sig figs) 426 1890 (1 sig fig) 2000 0.0296 (2 sig figs) 0.030

Rules for Addition and Subtraction Multiplication and Division

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. 12.0 + 131.59 + 0.2798 = 143.8698 Answer = 143.9 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. 51.3 × 13.75 = 705.375 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. (0.3012 + 0.2)(3.6) = ? (0.5)(3.6) = 1.8 = 2 (0.5012)(3.6) = 1.80432 = 1.8