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Rules for Significant Figures

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

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Rules for Significant Figures

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  1. 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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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 =

  11. 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

  12. 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 cm² Since 3.2 has 2 sig figs and 2.11 has 3 sig figs the answer has 2 sig figs Answer: 6.8 cm²

  13. 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 =

  14. 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

  15. 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 millimetre 4) Repeat Step 2

  16. 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

  17. 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

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