SIGNIFICANT
FIGURES
AMOLE
2 015
WHAT & WHY?
 Refer to them as “Sig Figs” for short
 Used to communicate the degree of
precision measured
 Example - Scientists records: 50 mL
Does that mean…
 50 mL exact?
Could he only measure to the ones place?
Did he round up from 49.8?
Is it really 50.12 mL?
RULE #1: NON ZEROS
 Every nonzero digit is significant.
 If it’s not a zero, it will count
 Examples:
 24 = 2 sig figs
 3.56 = 3 sig figs
 7
= 1 sig figs
RULE #2: CAPTURED ZEROS
 Also called “trapped” or “sandwiched”
zeros
 Zeros between non-zeros are significant
 Examples:
 7003 = 4 sig figs
 40.9 = 3 sig figs
 60.09 = ?
RULE #3: LEADING ZEROS
 Zeros appearing in front of non-zero digits
are not significant
Act as placeholders
Can’t be dropped, show magnitude
 Examples:
 0.00024 = 2 sig figs
 0.453 = 3 sig figs
 0.003 = ?
RULE #4: TRAILING ZEROS

Zeros at the end of a number with a
decimal point are significant.
At the end and to the right of a decimal point
 Examples:
 43.00 = 4 sig figs
 1.010 = 4 sig figs
 1.50 = ?
RULE #5: TRAILING ZEROS

Zeros at the end of a number without a
decimal point are not significant.
At the end and to the right of a decimal point
 Examples:
 300 = 1 sig figs
 27,300 = 3 sig figs
 120 = ?
 All non-zero digits DO count.
 Leading zeros DON’T count.
(zeros in front of numbers)
 Captive Zeros DO count.
(zeros between non-zero numbers)
 Trailing Zeros DO count IF the number
contains a DECIMAL.
(zeros at the end of numbers)
TRY THESE!
4.012
87,900
91.0005
500,001
0.005
0.6010
7,040, 100
2.100
= 4 sig. figs.
= 3 sig. figs.
= 6 sig. figs.
= 6 sig. figs.
= 1 sig. figs.
= 4 sig. figs.
= 5 sig. figs.
= 4 sig. figs.
ADDING & SUBTRACTING
 The answer cannot be more precise than the values in
the calculation
 The answer is rounded off so it contains the same
decimal places as the number in the problem with the
fewest .
 Example: 12.11 + 18.0 = 30.11
12.11 = 2 decimal places
18.0 = 1 decimal place
12.11 + 18.0 = 30.1
YOU TRY:
 2.140 + 0.023 = ?
2.140 = 3 decimal places
0.023 = 3 decimal places
 Answer unrounded: 2.163
 Answer with appropriate sig figs: 2.163
MULTIPLYING & DIVIDING
 The answer cannot be more precise than the values in
the calculation
 Answer should contain the same number of sig figs as
the number with the least sig figs in the problem:
 Example: 4.56 x 1.4 = 6.38
4.56 = 3
1.4 = 2
4.56 x 1.4 = 6.4
YOU TRY:
1.20 x 0.51 = ?
1.20 = 3
0.51 = 2
Answer unrounded: 0.612
Answer with appropriate sig figs: 0.61
TRY THESE!
4.01 + 0.03
= 4.04
= 4.04
87.957 – 85.1 = 2.857
= 2.9
4.13 x 1.2
= 4.956
= 5.0
500 / 5.5
= 90.90909
= 90
PUTTING IT ALL TOGETHER
(1.2 x 103) x (3 x 104) = ?
(3.6 x 107) / (4.0 x 105) = ?
(1.2 x 10-3) x (3 x 104) = ?
(3.6 x 107) / (4.0 x 10-5) = ?