Another thing you’ll use basically every day from now on. Significant Figures Another thing you’ll use basically every day from now on.

What is “one gram”? What is the mass? Exactly one gram? Do they have the same mass? Exactly? [Picture of paperclip on centigram balance.], [picture of calibration weight on centigram balance.]

Now do they both still have mass of one gram? Pictures of both weight and paperclip on analytical balance

Measurements vs Exact numbers Measurements are never exact. They are always rounded. example Exact numbers are not rounded off. 1 dozen = 12 20 people 1km = 1, 000 m Significant figures are used to determine how specific a measurement is. ex. 56,000 people attend a soccer game. What place is this value rounded to? Which is the estimated digit?

Some instruments do the rounding for you. What place are each of these rounded to? What are the estimated digits?

Counting significant figures. Find first non-zero digit Is there a decimal point? No  Find the last non-zero digit. (It’s estimated.) 1020  3 sig figs Yes  Find the last digit. (It’s estimated.) 21.400  5 sig figs How many sig figs are there in each measurement? 56,000 1.00 g 1.0000 g 0.00311 0.00800 100.00001 120 m 120.0 m 120. m

Sig Figs in Calculations ex. This room is 9.1 m wide and 11.9348 m long. Find area. 9.1 m × 11.9348 m = 108.6067 m2 What is this rounded to? Make sense? Multiplication and Division: The answer should have the same number of sig figs as least specific number in problem Round to 2 sig figs, so 108.6067 m2 = 110 m2

Sig Figs in Calculations, cont. ex. The sun is 146,000,000,000 m away. If you go upstairs, you get 3 m closer. Find new distance. 146,000,000,000m – 3m = 100,000,000,000m Make sense? Nope. Addition and Subtraction: Answer is rounded to same place as least specific number in problem 146,000,000,000 – 3 = 145,999,999,997 Round to billions place, so 146,000,000,000 ex. 652.3 + 2.005 = More practice