Download Significant_figuresexamples

Significant Figures
Significant figures tell us
the range of values to
expect for repeated
measurements
The more significant
figures there are in a
measurement, the smaller
the range of values is; the
more precise.
12.3 cm
has 3 sig. figs.
and its range is
12.2 to 12.4 cm
12.30 cm
has 4 sig. figs.
and its range is
12.29 to 12.31 cm
1
Counting Significant Figures
All non-zero digits are significant
– 1.5 has 2 sig. figs.
Interior zeros are significant
– 1.05 has 3 sig. figs.
Trailing zeros after a decimal point are
significant
– 1.050 has 4 sig. figs.
2
Counting Significant Figures
Leading zeros are NOT significant
– 0.001050 has 4 sig. figs.
1.050 x 10-3
5. Zeros at the end of a number are
significant figures
4.
150 has 3 sig. figs. then 1.50 x 102
3
Example 2.4 – Determining the Number
of Significant Figures in a Number
How many significant figures are in each
of the following numbers?
0.0035
1.080
2371
2.97 × 105
4
Example 2.4 – Determining the Number
of Significant Figures in a Number
How many significant figures are in each of the
following numbers?
0.0035
2 sig. figs. – leading zeros not sig.
1.080
4 sig. figs. – trailing & interior zeros
sig.
2371
4 sig. figs. – all digits sig.
2.97 × 105
3 sig. figs. – only decimal parts count
sig.
5
Multiplication and Division with
Significant Figures
When multiplying or dividing measurements
with significant figures, the result has the
same number of significant figures as the
measurement with the fewest number of
significant figures; round final answer:
5.02
×
3 sig. figs.
5.892
89,665
×
5 sig. figs.
0.10 = 45.0118 = 45
2 sig. figs.
2 sig. figs.
÷ 6.10 = 0.96590 = 0.966
4 sig. figs.
3 sig. figs.
3 sig. figs.
6
Rules for Rounding
When rounding to the correct number of
significant figures, if the number after the
place of the last significant figure is
1. 0.0 to 0.4, round down
–
–
2.
drop all digits after the last sig. fig. and leave
the last sig. fig. alone
add insignificant zeros to keep the value if
necessary
0.5 to 0.9, round up
–
–
drop all digits after the last sig. fig. and
increase the last sig. fig. by one
add insignificant zeros to keep the value if
necessary
7
Rounding
Rounding to 2 significant figures
2.34 rounds to 2.3
– because the 3 is where the last sig. fig. will be
and the number after it is 4 or less
2.37 rounds to 2.4
– because the 3 is where the last sig. fig. will be
and the number after it is 5 or greater
2.349865 rounds to 2.3
– because the 3 is where the last sig. fig. will be
and the number after it is 4 or less
8
Determine the Correct Number of
Significant Figures for each Calculation and
Round and Report the Result
1. 1.01 × 0.12 × 53.51 ÷ 96 = 0.067556
2. 56.55 × 0.920 ÷ 34.2585 = 1.51863
9
Determine the Correct Number of
Significant Figures for each Calculation and
Round and Report the Result
1.
1.01 × 0.12 × 53.51 ÷ 96 = 0.067556 = 0.068
3 sf
2 sf
4 sf
2 sf
result should 7 is in place
have 2 sf of last sig. fig.,
number after
is 5 or greater,
so round up
2.
56.55 × 0.920 ÷ 34.2585 = 1.51863 = 1.52
4 sf
3 sf
6 sf
result should
have 3 sf
1 is in place
of last sig. fig.,
number after
is 5 or greater,
so round up
10
Addition and Subtraction with
Significant Figures
When adding or subtracting measurements
with significant figures, the result has the
same number of decimal places as the
measurement with the fewest number of
decimal places
5.74 +
0.823 + 2.651= 9.214 = 9.21
2 dec. pl.
4.8
3 dec. pl.
-
3.965 =
1 dec. pl
3 dec. pl.
3 dec. pl.
0.835 =
2 dec. pl.
0.8
1 dec. pl.
11
Determine the Correct Number of
Significant Figures for each Calculation and
Round and Report the Result
1. 0.987 + 125.1 – 1.22 = 124.867
2. 0.764 – 3.449 – 5.98 = -8.664
12
Determine the Correct Number of
Significant Figures for each Calculation and
Round and Report the Result
1.
0.987 + 125.1 – 1.22 = 124.867
3 dp
1 dp
2 dp
= 124.9
result should 8 is in place of last
sig. fig., number
have 1 dp
after is 5 or greater,
so round up
2.
0.764 – 3.449 – 5.98 = -8.664
3 dp
3 dp
2 dp
result should
have 2 dp
=
-8.66
6 is in place
of last sig. fig.,
number after
is 4 or less,
so round down
13
Both Multiplication/Division and
Addition/Subtraction with Significant
Figures
When doing different kinds of operations
with measurements with significant figures,
do whatever is in parentheses first, find the
number of significant figures in the
intermediate answer, then do the remaining
steps
3.489 × (5.67 – 2.3) =
2 dp
1 dp
3.489
×
3.4
=
12
4 sf
1 dp & 2 sf 2 sf
14