Rules for Significant Figures

All non zero digits are significant 1,2,3,4,5,6,7,8,9 All zeros between two non zero digits are

significant 5004 4 sig figs All zeros to the right of both a number and a

decimal in a decimal number are significant

3.4000 5 sig figs

Significant figures

Determine the number of sig figs in each of the following measurements:

23 cm 77m 1.498g 7007m 248.3s 700.7007m 1070 g 700.7000m 0.238km 7007000m 8.036m 000.7000m 0.005678 m 0.007000m 1200m 700000m

Significant figures (Answers)

Determine the number of sig figs in each of the following measurements:

23 cm 2 77m 2 1.498g 4 7007m 4 248.3s 4 700.7007m 7 1070 g 3 700.7000m 7 0.238km 3 7007000m 4 8.036m 4 000.7000m 4 0.005678 m 4 0.007000m 4 1200m 2 700000m 1

ROUNDING NUMBERS

ROUND THE FOLLOWING NUMBERS TO 2, 3 AND 4 SIG FIGS:

NUMBER 2 S.F. 3 S.F. 4 S.F. 5.64378 4.35150 2.05055 123456 26.065

ROUNDING NUMBERS (ANS) ROUND THE FOLLOWING NUMBERS TO 2, 3

AND 4 SIG FIGS: NUMBER 2 S.F. 3 S.F. 4 S.F. 5.64378 5.6 5.64 5.644 4.35150 4.4 4.35 4.352 2.05055 2.1 2.05 2.051 123456 120000 123000 123500 26.065 26 26.1 26.07

ROUNDING NUMBERS

Round each of the following to 2 s.f. and 1 s.f. NUMBER 2 S.F. 1 S.F. 16.97 0.173 197.67 2.52 17.99 1.0016 20.78 1.47

New Rule for Rounding

197.67 rounded to 2 sig figs

looks like this

200

The bar over the 0 indicates a number higher than 195 and makes the 0 significant

ROUNDING NUMBERS (ANS) Round each of the following to 2 s.f. and 1 s.f. NUMBER 2 S.F. 1 S.F. 16.97 17 20 0.173 0.17 0.2 197.67 200 200 2.52 2.5 3 17.99 18 20 1.0016 1.0 1 20.78 21 20 1.47 1.5 1

RULES FOR ADDING AND SUBTRACTING

Round your answer to the least precise measurement

Example

4.5 cm + 2.34 cm = 6.84 cm

Since your least precise measurement is 4.5 cm ( tenths), your answer will be rounded to the nearest tenth 6.8 cm

ADDING AND SUBTRACTING WITH SIG. FIGS.

12cm + 0.031cm + 7.979cm= 0.085cm + 0.062cm + 0.14cm = 3.419g + 3.912g + 7.0518g + 0.0013g = 30.5g + 16.82g + 41.07g +85.219g = 41.025g – 23.28g = 289kg – 43.7kg = 145.63ml – 28.9 ml = 40.008 ml – 29.0941ml =

ADDING AND SUBTRACTING WITH SIG. FIGS.(ANSWERS)

12cm + 0.031cm + 7.979 = 20.cm 0.085cm + 0.062cm + 0.14cm = 0.29cm 3.419g + 3.912g + 7.0518g + 0.0013g = 14.384g 30.5g + 16.82g + 41.07g +85.219g = 173.6g 41.025g – 23.28g = 17.75g 289kg – 43.7kg = 245kg 145.63ml – 28.9 ml = 116.7ml 40.008 ml – 29.0941ml = 10.914ml

RULES FOR MULTIPYING AND DIVIDING

The number of significant digits in the result is the same as that of the measure of the least number of significant digits

Example 3.2 cm X 2.11 cm = 6.752 cm²Since 3.2 has 2 sig figs and 2.11 has 3 sig figs the answer has 2 sig figs

Answer: 6.8 cm²

MULTIPLYING AND DIVIDING WITH SIG. FIGS.

17.3cm x 6.2cm = 5.00mm x 7.3216mm = 20.8cm x 123.1 cm = 109.3758 m ÷ 5.813m = 247.89 km ÷ 43.5 km =

MULTIPLYING AND DIVIDING WITH SIG. FIGS. (ANSWERS)

17.3cm x 6.2cm = 107.26 110cm² 5.00mm x 7.3216mm =36.608 36.6mm² 20.8cm x 123.1 cm =2560.48 2560cm² 109.3758 m ÷ 5.813m =18.81572338

18.82m2

247.89 km ÷ 43.5 km =5.69862069

5.70km2

It’s Your Turn

1)Measure the length and width of a piece of looseleaf to the nearest centimetre

2)Determine its perimeter and area using the appropriate number of significant figures

3) Measure the length and width again to the nearest millimetre4) Repeat Step 2

Chapter 1 Pre-assessment

3) Which of the following represents the most precise measurement?

a) The length of a wall measured with a cm ruler

b) The length of a wall measured with a meter stick

c) The length of a wall measured with a mm tape measure

Pre-assessment Quiz

4) The length of a piece of paper is given as 28cm. Which measurement is most accurate?

a) 28.5 cm

b) 27.6cm

c) 281.3mm