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Significant Figures Notes and Guided Practice 1
To determine the number of significant figures (sig. figs.) in numbers we have measured we use the
Atlantic/Pacific Rule
1. Draw (imagine) a map of the United States and place the value in it.
2. Check to see if the decimal is Present or Absent, This tells you which side to start counting on.
If the decimal is Present, P for Present and P for Pacific so we start counting digits from the left.
If the decimal is Absent, A is for Absent and A is for Atlantic, so we start counting digits from the right.
3. You start counting with the first nonzero (1-9), never start with zero, digit then count every digit.
Example 102,000
A for Atlantic and A for
decimal absent
P for Pacific and P for decimal
Present
Step 2 The decimal is absent (not
written), so I start from the Atlantic
(right side).
count this way
102,000
Pacific
Step 1 Imagine the value on a map.
Start on this
side
Start with the 2
Atlantic
Step 3 I never start with 0’s, so I start
counting at the 2 and then count
everything.
So 102,000 has 3 sig. figs.
So 102,000 has 3 sig. figs.
A for Atlantic and A for
decimal absent
P for Pacific and P for decimal
Present
Step 2 The decimal is present
(written), so I start from the Pacific
(left side).
count this way
Start on this
side
Pacific
0.001030
Start with the 1
Step 1 Imagine the value on a map.
Atlantic
Step 3 I never start with 0’s, so I start
counting at the 2 and then count
everything.
So 0.01030 has 4 sig. figs
So 0.001030 has 4 sig. figs.
Now you do:
Part A: Identify the number of significant figures in each measurement.
A) 1707g
B) 0.00012s
C) 839,000m
D) 0.05600kg
E) 500cm
F) 9.30J
Significant Figures and Calculations When Multiplying or Dividing
An answer can not be more precise than the least precise value. In other words a calculation can only have as
many significant figures as the value with the least amount.
Example 1.23m x 4.5m = 5.535m2
Determine how many sig. figs. are in each of your starting values.
How many sig. figs. are in 1.23?
3 sf
How many sig. figs. are in 4.5?
2 sf
The answer must have the same number of Sig. Figs. as the value with the least amount, 2, so the answer is
written as 5.5m2
Significant Figures and Calculations When Adding or Subtracting
Example 3.21m + 5.4m= 8.61m
Determine how many decimal places are in each of your starting values.
How many decimal places are in 3.21?
2 decimal places
How many decimal places are in 5.4?
1 decimal place
The answer must have the same number of decimal places as the value with the least amount, 1, so the answer is
written as 8.6m. The answer 8.6m has 1 decimal place and 2sf. For addition or subtraction, you cannot report sf
until you round to correct decimal places.
Part B. Now do the following calculations.
Problem
Calculator Answer
3
A) 8.34m / 9.3m
Rounded Answer
B) 35 g/70.0 cm3
C) 0.05g x 2.50g
D) (9.830 x 104 s) x (2.05 s4)
E) 75.35cm – 25.2cm
F) 101.32kPa +173.024kPa
Answers
Top
A. 4
B. 2
C. 3
Bottom A. 0.90m2
B. 0.50L3
D. 3
E. 1
F. 3
C. 0.1g2
D. 202000s5
E. 50.1cm
F. 274.34kPa
Unit For Answer