Mathematical Operations with Significant Figures

1. Mathematical Operations with Significant Figures Ms. McGrath Science 10

2. Rounding rules 1.If the rounding number is less than 5, there is no change example: 2.634 • if we want to round this value to contain only 2 sig figs we keep the 2 and 6 and drop the 3 and 4 • because the 3 is less than 5, we don’t make any changes • 2.634 rounded to 2 sig figs becomes 2.6

3. Rounding rules 2. If the rounding number is greater than 5, we increase by one example: 2.463 • if we want to round this value to contain only 2 sig figs we keep the 2 and 4 and drop the 6 and 3 • because the 6 is greater than 5, we increase the 4 by one • 2.463 rounded to 2 sig figs becomes 2.5

4. Rounding rules 3. If the rounding number is exactly 5, examine the number that precedes (in front of) the 5: • we don’t change the number if the digit that precedes it is even • we round up, by one if the digit that precedes it is odd • if the value is exactly 5, and is followed by other digits, we refer back to rounding rule 1

5. Rounding rules example: 2.65 • round to two sig figs • the last digit is 5 • because the digit in front of the 5 is even, we keep it 2.65 rounded to two sig figs becomes 2.6

6. Rounding rules example: 2.750 • round to two sig figs • the last digit is 5 • the 7 that precedes the 5 is odd, so we increase by one 2.750 rounded to two sig figs becomes 2.8

7. Rounding practice Round each value to two sig figs: a) 36.4 f) 6.022 x 10 b) 729 g) 0.002 34 c) 0.145 h) 497 d) 8.357 i) 507 e) 0.00107 j) 88 304

8. Rounding practice Round each value to three sig figs: a) 6.3505 f) 10.01250 k) 3 055 b) 1 751 550 g) 17 515 501 l) 3 065 000 c) 105 650 h) 597 m) 0.015 450 d) 0.7845 i) 106 554.0 n) 0.02154 e) 1.00508 j) 25 070 o) 3 065

9. Calculations using sig figs • When calculating using measurements, we cannot increase our “precision” just by calculating • We need to keep the appropriate measurement by keeping the appropriate number of sig figs

10. Adding and Subtracting • When adding and subtracting, your final answer has the least amount of decimal places.

11. Adding and Subtracting Example: 11.002 mm + 17.2 mm 28.202 mm The correct answer is 28.2 mm

12. Multiplying and dividing • When multiplying and dividing, your final answer can only contain the same amount of significant figures as your LEAST precise measurement.

13. Multiplying and dividing Example: 67.34 contains 4 sig figs and 2345.5 contains 5 sig figs. 67.34 is the LEAST precise measurement, so we keep 4 sig figs in our final calculation 2345.5 m x 67.34 = 157 945.97 m2

14. Tutorial on the Use of Significant Figures 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 = ...

15. Tutorial on the Use of Significant Figures 1.    37.76 + 3.907 + 226.4 = 268.1 2.    319.15 - 32.614 = 286.54 3.    104.630 + 27.08362 + 0.61 = 132.32 4.    125 - 0.23 + 4.109 = 129 5.    2.02 × 2.5 = 5.0 6.    600.0 / 5.2302 = 114.7 7.    0.0032 × 273 = 0.87