Name:

Block:

Chemistry

Math with Significant Figures

Directions: Use a calculator, record the answer the calculator shows, then round this answer to the correct number of significant figures & circle the rounded answer. Answers can be written in scientific notation or decimal notation.

Addition & Subtraction: Round your answer so has the same number of decimal places, as far to the right as all measurements have in common
Problem	Answer shown on Calculator	Answer rounded to the correct # of significant figures.
1) 9 + 2 =	11	11 (Both measurements to the ones place so the answer is rounded to the ones place.)
2) 23.1 + 4.77 + 125.39 + 3.581 =	156.841	156.8 (The tenths place is the furthest to the right that all the measurements have in common, Do not round the 8 up since 4 is less than 5.)
3) 22.101 - 0.9307 =	21.1703	21.170 (The thousandths place is the last digit to the right that all the measurements have in common, Trailing zeros count so you end at the thousands place),
4) 10,005 - .028 =	10004.972	10,005 ( The first measurement goes to the ones place the second goes to the thousandths place, so the answer is rounded to the ones place.)
5) 564,321 - 264,321=	300,000.	300,000. (You must include the decimal point to show the trailing zeros are significant. Both measurements go to the ones place so the answer must be rounded to the ones place.
Multiplication and Division: Round the answer so it contains the same number of significant figures as the least precise factor
1) (3.4617 x 10^7) ÷ (5.61 x 10^¯4) =	6.170588235 E10	6.17 E10 (5 sig fig x 3 sig fig means you round your answer to 3 sig fig.
2) 14 x 187.6 =	2626.4	2600 (2 sig fig x 4 sig fig means you round your answer to 2 sig fig.
3) (4.7620 x 10^¯15) ÷ [(3.8529 x 10^12) (2.813 x 10^¯7) (9.50)] =	5.95969882 E-22	5.96 E-22 ( 5 sig fig/(5 sig fig x 4 sig fig x 3 sig fig means you have 3 sig fig in your final answer.)
4) [(561.0) (34,908) (23.0)] ÷ [(21.888) (75.2) (120.00)] =	2280.397194	2280 (4 sig fig x 5 sig fig x 3 sig fig/5 sig fig x 3 sig fig x 5 sig fig means you have 3 sig fig in you answer. NO DECIMAL PT!!!)
Mixed Operations
1) (2 + 15) x 18.3 =	311.1	310 ( 1 sig fig + 2 sig fig gives an answer with 2 sig fig then this answer with 2 sig fig x 3 sig fig gives a final answer with 2 sig fig.
2) (47.5 x 8.98) – 8.98 =	427. –8.98 = 418.02	418 (3 sig fig x 3 sig fig gives an answer with three sig fig so 426.55 is rounded to 427. Then the 427 is used for the subtraction of 8.98 so the final answer is rounded to the ones place.
3) 1111 x (333333 – 8)=	370324075	370300000 or 3.703 E 8 ( Complete the subtraction first the answer is rounded to the ones place, then the answer with 6 sig fig is multiplied by 4 sig fig so the final answer has 4 sig fig.
4) (11.789 x 4 ) – 22 =	28	30 (5 sig fig x 1 sig fig gives an answer with 1 sig fig so 47.156 is rounded to 50 then 50 –22 is 28 on the calculator which must be rounded to the tens place.)