Rules for deciding the number of significant figures in a measured quantity:
1. All nonzero digits are significant: 1.254 m has 4 significant figures, 1.2 m has 2 significant figures.
2. Zeroes between nonzero digits are significant: 1007 kg has 4 significant figures, 8.07 mL has 3 significant figures.
3. Zeroes to the left of the first nonzero digits are not significant; such zeroes merely indicate the position of the decimal point: 0.001 ft has only 1 significant figure, 0.092 ft has 2 significant figures.
4. Zeroes to the right of a decimal point in a number are significant: 0.083 km has 2 significant figures, 0.2000 mi has 4 significant figures.
5. When a number ends in zeroes that are not to the right of a decimal point, the zeroes are not necessarily significant: 170 miles may be 2 or 3 significant figures, 70,600 L may be 3, 4, or 5 significant figures. For our clas we will consider them as not significant unless there is a decimal point at the end. The potential ambiguity in the last rule can be avoided by the use of scientific notation. For example, depending on whether 3, 4, or 5 significant figures is correct, we could write 50 600 L as: 5.06 × 10^4 L (3 significant figures) 5.060 × 10^4 L (4 significant figures), or
5.0600 × 10^4 L (5 significant figures).
6. $1.569 per gallon has an infinite number of sig. figs. because it is exact. Most conversion factors are exact.
Number |
Significant figures |
Scientific notation |
Calculator sci. not. |
120 |
2 |
1.2 x 10^2 |
1.2 E2 |
120. |
3 |
1.20 x 10^2 |
1.2 E2 |
550 000 |
2 |
5.5 x 10^5 |
5.5 E5 |
550 001 |
6 |
5.500 01 x 10^5 |
5.50001 E5 |
0.000 024 5 |
3 |
2.45 x 10^ -5 |
2.45 E-5 |
33.000 11 |
7 |
3.300 011 x 10^1 |
3.300011 E1 |
Assignment:
Problem |
Answer using sig. fig. |
Answer in Sci. Notation |
1. (70.50)(0.0600) |
. | . |
2. 563 / 1.41999 |
. | . |
3. 35.33+48.7- 0.0600 |
. | . |
4. 1500. - 290.5 |
. | . |
5. 18 x 10^6 / (3.884 x 58293) |
. | . |
6. (8.95 x 10^5)(1.25 x 10^ -2) |
. | . |
7. 2500 / 6275 |
. | . |
8. (13.77 x 0.992)/(10.0 x 166) |
. | . |
9. The number of donuts in a dozen |
. | . |
10. Find the result of in two ways: (1.00 + 0.56258)/(1.00 - 0.56258)
a) Work as is and round off the answer to 1 decimal place.
b) round off each number to 1 decimal place first, and then calculate to 1 decimal place.
