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## Mathematical Operations with Significant Figures

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**Mathematical Operations with Significant Figures**Ms. McGrath Science 10**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**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**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**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**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**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**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**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**Adding and Subtracting**• When adding and subtracting, your final answer has the least amount of decimal places.**Adding and Subtracting**Example: 11.002 mm + 17.2 mm 28.202 mm The correct answer is 28.2 mm**Multiplying and dividing**• When multiplying and dividing, your final answer can only contain the same amount of significant figures as your LEAST precise measurement.**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**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 = ...**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