Significant Figures When we take measurements or make calculations, we do so with a certain precision. This precision is determined by the instrument we use to take those measurements. So, when we do calculations based on our measurements, the calculations must be as precise as the measurements.

Rules: How to determine how many significant figures (ie. How precise?) All numbers between 1 and 9 (non-zero) are always significant. Zeros between 2 non-zero numbers are always significant. Example: significant figures sig. figs sig. figs sig. figs.

All numbers after (to the right) of the decimal are significant sig. figs sig. figs sig. figs sig. figs. Any zeros before the decimal are not significant sig. figs sig. figs.

Zeros that serve to indicate the position of the decimal are not significant sig. figs sig. fig. These 2 numbers indicate 23 hundred and 1 hundred. If there was a decimal at the end of these numbers, it would change the precision and therefore change the number of significant figures sig. figs sig. figs.

Problems: Indicate the number of significant figures ______ ______ ______ ______ ______ ______ ______ ______ ______ ______

Adding and subtracting with Sig. Figs. The last sig fig in a measurement is an estimate (not known with certainty). Measurements can only have one estimated digit. The answer, when you add or subtract, can not be better than your worst estimate. You have to round the answer to the place value of the measurement (in the problem) with the greatest uncertainty.

For example l First line up the decimal places Then do the adding Find the estimated numbers in the problem This answer must be rounded to the tenths place

Rules for addition and subtraction: 1.Determine which number has the least amount of significant figures after the decimal = answer = = answer = 22.3

Problems: addition and subtraction ______ ______ ______ ______ ______ ______ ______ ______ ______ ______

MULTIPLICATION and DIVISION

Multiplication and division 1.Determine which number has the least amount of significant figures in total. This is the number of significant figures your answer will have x 1.2 = ÷ 1.2 = answer = 3.1 answer = 2.2 ***sometimes you have to “round-off”!!

Rounding rules Look at the digit in the place value following the one you’re rounding. If the first digit to be cut is 0 to 4 don’t change it (round down) If the first digit to be cut is 6 to 9 make it one bigger (round up) If the first digit to be cut is exactly 5 (followed by nothing or zeros), round the number so that the preceding digit will be even. Round cm to: four sig figs to three sig figs to two sig figs to one sig fig cm 45.5 cm 46 cm 50 cm

Problems: multiplication & division x 2.61______ x 0.23______ ÷ 1.21______ ÷ 4.1______ x 42.1______ x 0.02______ ÷ 0.023______ x 23______ ÷ 0.12______ x 12 ÷ 12.5______