Significant Figures and Rounding

1. Significant Figures and Rounding

2. Counting Sig. Figs. Pacific a.k.a.: Present Start with first non-zero, go in direction Atlantic a.k.a.: Absent Start with first non-zero, go in  direction • Steps to Count # of Sig. Figs. • See if decimal is present or not. • Go from correct direction. • Start counting at 1st Non-Zero # • Keep counting until you run out of #s

3. Examples • 300,150 • Decimal point absent – 5 sig figs • 300.0 • Decimal point present – 4 sig figs • 300 • Decimal point absent – 1 sig fig • 0.0000015 • Decimal point present – 2 sig figs • 631.10 • Decimal point present – 5 sig figs

4. Rounding Sig. Figs. • Always start from the LEFT • Start counting at the 1st non-zero # • Count to the correct # of Sig. Figs. • Round that # • If that # is a 0 before the ones position, then turn to sci. not. and then round. • For every # after the rounded position • If before decimal, turn to zero • If after decimal, drop

5. Example – Round 0.065930 to 2 S.F. • Always start from the LEFT • 0.065930 • Start counting at the 1st non-zero # • 0.065930 • Count to the correct # of Sig. Figs. • 0.065930 • Round that # • 0.065930 Final Answer: 0.066

6. Example – Round 0.065930 to 3S.F. • Always start from the LEFT • 0.065930 • Start counting at the 1st non-zero # • 0.065930 • Count to the correct # of Sig. Figs. • 0.065930 • Round that # • 0.065930 Final Answer: 0.0659

7. Examples: • 135.35 (4 S.F.) • 135.35 (2 S.F.) • 1.506 x 104 (3 S.F.) • 5.80354 (3 S.F.) • 100 (2 S.F.)

8. Determining the Number of Sig Figs in Calculations • Find out the # of sig. figs. for all numbers • Round to the lowest # of S. F. Ex: 3.8 x 4.50 = (Round to 2 S.F.)

9. Determining the Number of Sig Figs in Calculations • Round to the lowest place holding # that all of them have in common Ex: + 12.0 + 134.354 147.664 = 147.7