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: 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 rounded to 2 sig figs becomes 2.6

Rounding rules 2. If the rounding number is greater than 5, we increase by one example: 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 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: round to two sig figs the last digit is 5 the 7 that precedes the 5 is odd, so we increase by one rounded to two sig figs becomes 2.8

Rounding practice Round each value to two sig figs: a) 36.4f) x 10 b) 729g) c) 0.145h) 497 d) 8.357i) 507 e) j)

Rounding practice Round each value to three sig figs: a) f) k) b) g) l) c) h) 597m) d) i) n) e) j) 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: mm mm 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: contains 4 sig figs and contains 5 sig figs is the LEAST precise measurement, so we keep 4 sig figs in our final calculation m x = m 2

Tutorial on the Use of Significant Figures = = = = × 2.5 = / = × 273 =...

Tutorial on the Use of Significant Figures = = = = × 2.5 = / = × 273 = 0.87