Significant Figures

Why Significant FiguresIt enables us to have a clear idea

of the extent of the precision of the measuring instrument being used or the measuring method being employed.

Which figures are significant?Rule #1: Non-zero

digits are always significant

Rule #2: All zeroes between significant digits are significant

Rule #3: A final zero or trailing zeroes can only be significant if there is a decimal point or a bar.

Let’s practice!1234 kg56, 789 ft101 hr134.001 kW1230909 cm10.0 s100. s$ 2050.007000 kW0.0204000

Which figures are NOT significant?Zeroes are usually not significant in the following instances:Leading zeroes: zeroes before any significant figure are never significant.Ex. 0056, 0.00108

Trailing zeroes: zeroes after any significant figure are not significant when there are no decimal points or barsEx. 76 000, 76 000., 76 00.0,

0.076000, 76 000

Infinite Number of Significant FiguresCounted Numbers

12 eggs in a dozenThere are 16 students in a class

Physical ConstantsThe value of π (3.14)Avogadros’ Constant 6.02 x 1023

Seatwork: How many significant figures?

1. 600.2. 2.09003. 30454. 0.00105. 0.05606. 0.00997. 1001.0

8. 0.03009. 0.008010.10 00611.0.0033

012.0.070013.2 90014.690

Seatwork: How many significant figures?

• 20.005• 5.0900• 5 000• 3.006• 7.0809• 0.0350• 31.670

• 0.04004• 123.450• 103.05• 60.00• 200.0• 0.00700• 20.300

How many significant figures are in the following measurements?

1. 30.02. 2393. 0.8904. 43.205. 10006. 34.427. 90.08. 0.002

1

9. 5.40010.0.002311.14.6012.2 05013.200.6014.3515.136.0416.980.00

0

17.3.18.570.019.0.70020.12.04021.460.1322.15.01023.19.8024.0.0400

1

Adding and SubtractingThe result must

be rounded off to have the same number of decimal places as the quantity with the least number of decimal places.

Examples:0.0836 + 195.2 =2.67 + 7.3333 =3.5212 – 3.12 = 6 – 0.384 =

195.310.00

0.40

6

Multiplying and DividingThe result must

be rounded off to have the same number of significant figures as the quantity with the least number of significant figures.

Examples:0.0620 × 105.30 =3.000 × 0.0130 =1000. / 2.0 = 9 / 0.765 =

6.530.0390

50010

Practice Work.1.    37.76 + 3.907 + 226.4 = ?2.    319.15 - 32.614 = ?3.    104.630 + 27.08362 + 0.61 = ?4.    125 - 0.23 + 4.109 = ?5.    2.02 × 2.5 = ?6.    600.0 / 5.2302 = ?7.    0.0032 × 273 = ?8.    (5.5)3 = ?

Practice Work.1.    37.76 + 3.907 + 226.4 = 268.12.    319.15 - 32.614 = 286.543.    104.630 + 27.08362 + 0.61 = 132.324.    125 - 0.23 + 4.109 = 128.879 ~ 1295.    2.02 × 2.5 = 5.05 ~ 5.16.    600.0 / 5.2302 = 114.7183364 ~

114.77.    0.0032 × 273 = 0.8736 ~ 0.878.    (5.5)3 = 166.375 ~ 170

Practice Work. 9.    0.556 × (40 - 32.5) = ?10.    45 × 3.00 = ?11.    What is the average of 0.1707,

0.1713, 0.1720, 0.1704, and 0.1715?12.    3.00 x 105 - 1.5 x 102 = ? (Give

the exact numerical result, and then express that result to the correct number of significant figures).