Significant Figures
1. Solve for the correct number of significant figures.
a. 9.25 ÷ 4.970
b. 1.54 x 0.03078 x 0.8
c. (2.687 x 108) x (6.022 x 1023)
d. 723 x 1024
e. (6.7 x 104) ÷ (5.93 x 106)
2. Solve for the correct number of significant figures.
a. 45.7 – 2.981
b. 62.89 + 7.3 + 9.86
c. 27.1 + 55.88 + 425
d. 623 + 7.3 – 320
3. Solve for the correct number of significant figures
a. (568.98 -436.1) ÷ 9.7
b. (3.14 x 4.594) – 2.65
c. (9334 + 23 -9.7) x (8.1 x 105)
d. [(1.8 x 106) ÷ (2.64 x 105)] +7.43
Rules for Significant Figures
All non-zero digits are counted as significant digits
Zero may or may not be significant
When do I count zero as significant?
A leading zero is never counted
0.00567
A zero “inside” the number is always counted 8006
A zero at the end of the number is counted IF the decimal point is shown 650.
If the decimal point is not shown, do not count the trailing zero(s) 700
When adding or subtracting quantities, round off the answer to the same number of decimal
places as the quantity with the fewest decimal places
When multiplying or dividing quantities, round off the answer to the same number of significant
digits as the quantity with the fewest significant digits
For a series of calculations
If the operations are all the same kind (all add/subtract or all multiply/divide), then don’t round
off intermediate results. Just carry them in your calculator and round off at the end.
If the operations are not the same kind (some are add/subtract and some are multiply/divide), then
round off when you finish one type of operation, and carry those significant digits into the next
operation.
Exact numbers
Some quantities are exact numbers, with no uncertainty
Defined values are exact numbers
10 mm = 1 cm or 12 inches = 1 foot
Counted values are exact numbers
9 students in class or 200 pills in the bottle
Ignore exact numbers when counting significant digits