Significant Figures

1
Significant Figures

• Another thing youll use basically every day from
  now on.

2
What is one gram?

• What is the mass?
• Exactly one gram?
• What is the mass?
• Exactly one gram?
• Do they have the same mass? Exactly?

3

• Now do they both still have mass of one gram?

4
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?

5

• ex. How long is the nail?
• What is the estimated digit?
• What place is 6.35 cm rounded to?

Back
6

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

7
Counting significant figures.

• Find first non-zero digit
• Is there a decimal point?
• No ? Find the last non-zero digit. (Its
  estimated.)
• 1020 ? 3 sig figs
• Yes ? Find the last digit. (Its 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
8
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

9
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