 Download Download Presentation Mathematical Operations with Significant Figures

Mathematical Operations with Significant Figures

Download Presentation Mathematical Operations with Significant Figures

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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