Significant Figures All the digits that can be known precisely in a measurement, plus a last estimated digit.

1. Every non-zero digit is assumed to be significant m = 3 significant digits = 4 significant digits

2. Zeros between non-zero digits are significant m = 4 significant digits cm = 7 significant digits

3. Zeros left of nonzero digits are not significant m = 2 significant digits cm = 3 significant digits

4. Zeros at the end of a number, to the right of a decimal point are always significant m = 4 significant digits cm = 6 significant digits

5. Zeros at the rightmost end of a measurement that lie to the left of an assumed decimal point are not significant. They are place holders. 300 m = 1 significant digit 7000 cm = 1 significant digit

6. Two situations have an unlimited number of significant digits. Ex. 1: Counting – if you count 25 people in your room, there is exactly that number of people. Ex. 2: Defined quantities – 60 min = 1 hour or 100 cm = 1m. These are defined numbers.

How many significant figures in each? g ________ g _______ 146 cm ________ cm ________ kg _________ g _________ km _________ 99.9 mL _________ g ________ 144 lbs ________

Rounding To round you need to figure out how many significant figures the number should have – If the number after the last significant digit is less than 5, it is dropped – If the number is greater than 5, the last significant digit is raised by one. “Naked 5 Rule” – Only use when number to be rounded is followed by a ‘5’ & nothing else – If number before ‘5’ is odd, round it up – If number before ‘5’ is even, leave it

Round to 2 significant figures m m m g g g mL mL mL km

Addition and Subtraction Round to the same number of decimal places as the measurement with the least number of decimal places.

Addition

Subtraction

Multiplication and Division Round the answer to the least number of significant digits present in the problem.

Multiplication x 45.1 =

Division 89.2 / 5.5 =

Complete the calculations 1.12 cm cm cm = ________________ cm cm cm = _______________ g g g g = _____________ g g g g = _______________ cm cm = _______________________ cm – cm = _____________________ g – 43.7 g = _______________________ cm x 4.01 cm = ____________________ cm x 6.2 cm = _____________________ m x 1.2 m = ____________________ mm x mm = __________________ dm x dm = ____________________ cm2 / cm = ___________________ m2/ m = __________________