Significant Digits

1
Significant Digits

• Ch 1 Notes

2
Significant Digits

• Used to round measured values when involved in
  calculations
• When in scientific notation, all numbers on left
  side of number are significant

3
Significant Digits

• Nonzero s are always significant
• 349 3 sig figs
• 1639 4 sig figs

4
Significant Digits

• Leading Zeros are never significant
• 0.0055 2 sig figs
• 0.0000000393 3 sig figs
• Captive Zeros are always significant
• 5908 4 sig figs
• 2100004 7 sig figs

5
Significant Digits

• Trailing Zeros are significant IF
• there is a decimal point in the
• 800 1 sig fig
• 2900 2 sig figs
• 800.0 4 sig figs
• 2900. 4 sig figs

6
Operations with Sig Figs

• Multiplication/Division rule
• Retain the same number of sig figs in the
  answer as the factor containing the least number
  of sig figs.
• 4.5 x 2 9.0 rounds to 9
• 2000 x 21 42000 rounds to 40000
• 11 x 3 x 212 6996 rounds to 7000

7
Operations with Sig Figs

• Addition/Subtraction Rule
• leave the answer rounded to the same precision
  (same decimal place) as the least precise number
  involved in the operation.
• 2 2.3 4.3 rounds to 4
• 120 11 131 rounds to 130
• 1.65 3 2.90 1.75 rounds to 2

8
Sig Fig Examples

• 1 23.0
• 4.25
• 25,620
• 2 2.3 x 10-4
• 316

9
Examples Solutions

• 1 23.0
• 4.75
• 25,620
• 25,647.75
• rounds to 25,650
• 2 2.3 x 10-4 2sf
• 316 3sf
• 7.27 x 10-7
• rounds to 7.3 x 10-7

10
Sig Fig Situation 1 Lets Not But Say We Did

• Dont worry about rounding combo problems until
  all the work in the calculator is done, but heed
  the rules as if you did to find out of digits
  needed in the end
• (3.5 2.9454) / 357 (6.4454)/357
• 0.018054341
• Rounding addition to tenths digit, which would
  leave 2 sig figs. 2 sig figs divided by 3 sig
  figs leaves 2 in answer 0.018

11
Sig Fig Situation 2 Less than Zero

• 2000 (1 sig fig) vs. 2001 (4 sig figs)
• What if you want 2000 to have 4 sig figs like
  2001?
• 2.000 x 103 for 4 sig figs
• 2.00 x 103 for 3 sig figs
• 2.0 x 103 for 2 sig figs
• 2 x 103 for 1 sig fig

12
Sig Figs Situation 3 Exact s

• Whenever a quantity has no uncertainty, it does
  not affect the of sig figs in answer if x///-
• Ex four sides of a squareif one side has a
  length of 2.0 m, then
• 4 (exact ) x 2.0 m 8.0 m (retain two sig figs
  cause exact doesnt matter to sig fig rounding

13
Sig Figs Situation 4 Units!

• Units are to be treated in the same algebraic
  sense as variables
• Units do not affect sig figs but must be common
  to add/subtract values
• 23 g 32.00 g 55.00 rounds to 55 g
• 23 g x 32.00 g 736.0000 rounds to 740 g2
• 23 kg 27 ml cannot be simplified