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Significant Figures
When we take measurements or make
calculations, we do so with a certain
precision. This precision is determined
by the instrument we use to take those
measurements. So, when we do
calculations based on our
measurements, the calculations must
be as precise as the measurements.
Rules: How to determine how many
significant figures (ie. How precise?)
• All numbers between 1 and 9 (non-zero) are
always significant.
• Zeros between 2 non-zero numbers are always
significant.
• Example:
234.7
4 significant figures
2008
4 sig. figs.
200.8
4 sig. figs.
23.47
4 sig. figs.
• All numbers after (to the right) of the
decimal are significant.
2.89
3 sig. figs.
2.00
3 sig. figs.
2.0
2 sig. figs.
2.0004
5 sig. figs.
• Any zeros before the decimal are not
significant.
0.345
3 sig. figs.
0.230
3 sig. figs.
• Zeros that serve to indicate the position of the
decimal are not significant.
2300
2 sig. figs.
100
1 sig. fig.
These 2 numbers indicate 23 hundred and
1 hundred. If there was a decimal at the end of
these numbers, it would change the precision
and therefore change the number of significant
figures.
2300.
4 sig. figs.
100.
3 sig. figs.
Problems: Indicate the number of
significant figures...
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
1.235
2.90
0.0987
0.450
5.00
2300
230
230.0
9870345
1.00000
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Adding and subtracting with Sig. Figs.
• The last sig fig in a measurement is an estimate (not
known with certainty). Measurements can only
have one estimated digit.
• The answer, when you add or subtract, can not be
better than your worst estimate.
• You have to round the answer to the place value of
the measurement (in the problem) with the greatest
uncertainty.
For example
27.93 + 6.4

+
First line up the decimal places
Then do the adding
27.93
Find the estimated
6.4
numbers in the problem
34.33 This answer must be
rounded to the tenths place
Rules for addition and subtraction:
1. Determine which number has the least
amount of significant figures after the
decimal.
26.24 + 4.1245 = 30. 5645
answer =30.56
26.46 - 4.2 = 22. 26
answer = 22.3
Problems: addition and subtraction
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
2.634 + 0.02
2.634 - 0.02
230 + 50.0
0.034 + 1.00
4.56 - 0.34
3.09 - 2.0
349 + 34.09
234 - 0.98
238 + 0.98
123.98 + 0.54 - 2.3
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MULTIPLICATION and DIVISION
Multiplication and division
1.Determine which number has the least amount
of significant figures in total. This is the
number of significant figures your answer will
have.
2.61 x 1.2 = 3.132
2.61 ÷ 1.2 = 2.175
answer = 3.1
answer = 2.2
***sometimes you have to “round-off”!!
•
•
•
•
•
Rounding rules
Look at the digit in the place value following the one you’re
rounding.
If the first digit to be cut is 0 to 4 don’t change it (round
down)
If the first digit to be cut is 6 to 9 make it one bigger (round
up)
If the first digit to be cut is exactly 5 (followed by nothing or
zeros), round the number so that the preceding digit will be
even.
Round 45.462 cm to:
four sig figs
to three sig figs
to two sig figs
to one sig fig
45.46 cm
45.5 cm
46 cm
50 cm
Problems: multiplication & division
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
42.3 x 2.61
32.99 x 0.23
46.1 ÷ 1.21
23.3 ÷ 4.1
0.61 x 42.1
47.2 x 0.02
47.2 ÷ 0.023
100 x 23
120 ÷ 0.12
120 x 12 ÷ 12.5
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