Significant Figures and Rounding August 18, 2014

Sig Fig Rules Non Zero digits are significant Zeros between two non zero digits are significant Trailing zeros before the tenths place are not significant Leading zeros after the decimal point are not significant Trailing zeros after the decimal point are significant

Non Zero digits are significant How many significant figures are in the following? 72.3 327 1,465 9 123,987

Zeros between two non zero digits are significant How many significant figures are in the following? 101 2,302 500,078 1.009 78.02

Trailing zeros before the tenths place are not significant How many significant figures are in the following? 190 80 100,000,000 4,520 67,070

Leading zeros after the decimal point are not significant How many significant figures are in the following? 0.0019 0.0435 0.00007 0.045609 0.0780095

Trailing zeros after the decimal point are significant How many significant figures are in the following? 1.90 80.09870 0.09800 23.960 456,789.040

How Many Sig Figs? 3.7745 205 1.700 350.0 307.080 0.000400 4,000,000,001 2.89 x 104

Rounding Rules Don’t do anything for 4 or less If greater than five round up If 5 followed by a nonzero digit round up If 5 followed by a zero, if last sig fig is even stay, if last sig fig is odd round up

Greater or less than 5 Round to three sig figs 2.546  2.55 2.543  2.54

Rounding 5’s Round to 3 sig figs Followed by a non zero digit 2.5551  2.56 2.5557  2.56 Followed by a zero 2.5550  2.56 (if odd round up) 2.5450  2.54 (if even stay the same)

Round the following to 4 sig figs 84,791 38.5432 256.75 4.9356 0.00054818 136,758 308,659,000 2.0145