Sig Figs

Significant figure a digit that is reliably known. Ex: 6.2 has 2 sig figs. The hundredth place is not reliably known and, thus, not reported.

The easiest way to determine sig figs in a number is to write the number in scientific notation. 0.00620 = 6.20 x 10-3 The trailing zero is reliably known, so it is SIGNIFICANT. The number of significant figures is the number of digits when written in sci notation.

Some Rules for Sig Figs The number of sig figs does not equal the number of decimal places. In whole numbers, trailing zeroes are not sig figs. Ex: 320,000 is 3.2 x 105 It has 2 sig figs. Changing units may shift the decimal points but it doesn’t change the number of sig figs.

When multiplying/dividing (or taking roots), the number of sig figs in the answer should match the number of sig figs of the least precise number in the calculation. When adding/subtracting, the number of sig figs in the answer should match the smallest amount of decimal places of any number in the calculation.

It’s fine to keep extra numbers around in the intermediate steps, but your final answer MUST be accurate in terms of significant figures. Otherwise, you’ve performed magic and have something more accurate that we can verify.

Example The volume of a piece of Al is 4.44 x 10-4 m3. Given a density of 2.7 x103 kg/m3, what is the total mass of the piece of Al? (mass = density x volume)

m= 4.44 x 10-4 m3 (2.7 x103 kg/m3) m= 1.199 kg m= 1.2 kg

If we have a second mass of Al, measured to be 6 If we have a second mass of Al, measured to be 6.47 kg, how much total Al do we have?

` 6.47 kg + 1.2 kg = 7.7 kg