Significant Figures Sig Figs Sig Figs Scientists use

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 1. Any non-zero number is ALWAYS significant. 2. Any zero between non-zero numbers is significant. 3. Any zero before a non-zero number is NOT significant. 4. 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 2 sig figs • 1219 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 3 sig figs • 0. 0132 • 0. 00008914 4 sig figs v. These are called leading zeros

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

Examples 5 sig figs • 10082 • 70, 000 • 0. 0025 • 0. 000309 • 50010. 000 • 0. 0040030 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) • Answer: 1. 5 (2 sig figs)

Adding and Subtracting (Round to least precise) 1. Stack the numbers you are adding or subtracting. (line up the decimals) 2. Identify the sig figs for each number. 3. Round answer to the same number of decimal places as the number with the fewest decimal places.

Example 13. 019 +1. 2 14. 2198 Answer: 14. 2 94. 00 15 +182. 713 291. 713 Answer: 292

Examples • 1. 2. 3. 4. 5. 6. 7. 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