Significant Figures

1. Significant Figures

2. Rules: • #1 – Nonzero digits are significant • 19 • 311 • 7862 • 1,237,983 • #2 – Zeros between significant figures are significant • 109 • 5002 • 6507 • 1,000,341

3. Rules • #3 – Final zeros after a decimal are significant • 10.0 • 234.00 • 2986.000 • 10000.00 • #4 – Zeros that are placeholders are NOT significant • 10 • 0.0003 • 350,000 • 0.099

4. Rounding • When rounding to a specific amount of significant figures: • In scientific notation, all numbers preceding “x10” are significant • 5-9 as next digit: round up • 1-4 as next digit: round down • If you end up with zeros that need to be significant, but are not: • Add a decimal at the end of the number • All previous digits are then significant • 100 rounded to 3 significant digits = 100. • Add a bar over the final significant zero • 100 rounded to 2 significant digits = 100

5. The Quick Method: • If there is a decimal, count all digits to the right of the first nonzero digit as significant. • 0.00150 • 0.0005 • 10.010 • 10,120.0 • If there is NOT a decimal, count all digits to the left of the first nonzero digit. • 10,000 • 230,450 • 250 • 1,205,375,000