Significant Figures Sig Figs

Sig Figs Scientists use significant figures to show the precision of a measured quantity. When you use measurements in calculations, the answer is only as precise as the least precise measurement used in the calculation The measurement with the fewest significant figures.

Rules for Sig Figs Any non-zero number is ALWAYS significant. Any zero between non-zero numbers is significant. Any zero before a non-zero number is NOT significant. Any zero after a non-zero number is significant ONLY IF there is a decimal in the number.

Any non-zero number is ALWAYS significant 62 1219 2 sig figs 4 sig figs

Any zero between non-zero numbers is significant 803 3091 82,024 3 sig figs 4 sig figs 5 sig figs

Any zero before a non-zero number is NOT significant. 3 sig figs 0.000491 0.0132 0.00008914 These are called leading zeros 3 sig figs 4 sig figs

83,000 2 sig figs 83,000. 83.000 5 sig figs 5 sig figs Any zero after a non-zero number is significant ONLY IF there is a decimal in the number. 83,000 83,000. 83.000 These are called trailing zeros 2 sig figs (No Decimal) 5 sig figs (Decimal) 5 sig figs (Decimal)

5 sig figs 10082 70,000 0.0025 1 sig fig 0.000309 50010.000 2 sig figs Examples 10082 70,000 0.0025 0.000309 50010.000 0.0040030 5 sig figs 1 sig fig 2 sig figs 3 sig figs 8 sig figs 5 sig figs

Multiplying and Dividing (round to least number of sig figs) Identify the sig figs for each number Round answer to the least number of sig figs. Look at the number next to last sig fig to determine rounding 62 ÷ 41 = 1.512195122 Answer: 1.5 (2 sig figs)

Adding and Subtracting (Round to least precise) Stack the numbers you are adding or subtracting. (line up the decimals) Identify the sig figs for each number. Round answer to the same number of decimal places as the number with the fewest decimal places.

13.019 +1.2 14.2198 Answer: 14.2 Answer: 292 Example 94.00 15 +182.713 291.713 Answer: 14.2 Answer: 292

Examples 62,881 ÷ 97 5,621 x 893 218 ÷ 26 59,411 x 2 307 x 32,000 8.00 ÷ 532 6 x 6 59.21 - 18.8722 8.679 + 0.3 + 5.88 123.6 + 16.23 63.1 – 0.02 – 0.0057 36.45 + 1.467 1.7 – 0.1357 6 + 6