Transcript Significant figures

Significant Figures
(sig figs if you’re cool)
What are significant figures?

A process for reporting measurements using
the number of digits and decimal places that
tell you how EXACT the measurement is.
– 121 is less exact than 121.5
– The difference: a more precise tool was used to
measure the 121.5
– Reporting 121.5 tells anyone that the person
was able to measure the quantity up to the
tenths place.
So, why should I care about these?

When reporting measurements:
– You need to know how to report measurements
in lab correctly (both the measurement and the
precision of the tool used)

Calculations with significant figures:
– You need to know how to calculate values so
you don’t report answers that are more exact
than the numbers used to calculate that value.
Significant Figure Rules
#1 Non-zero digits are always significant
#2 Any zeros between two significant digits
are significant (zero sandwich)
#3 A final zero or trailing zeros in the decimal
portion ONLY are significant
How Many Sig Figs?
Example
23
203
4500
4500.2
0.0012
1.0012
51,003
43,251
8
8.0
Number of Sig Figs
2
3
2
5
2
5
5
5
1
2
Rounding Sig Figs


Sometimes you’ll need to round numbers to the
correct number of sig figs
For example:
– Round 90,970 to 2 sig figs  91,000
Example
678,510 miles
0.0070894 km
67,548 kg
0.010798 cm
Round to:
3
4
2
4
Result
679,000 miles
0.007089 km
68,000 kg
0.01080 cm
Addition & Subtraction

Significant Figures in Calculations
– Addition & Subtraction: The number of
decimal places in the answer should be equal to
the number of decimal places in the value with
the fewest decimal places. Round only your
FINAL answer!
Example:
12.0035 g
3.72 g
0.015 g
15.7385
15.74g
(4 decimal places)
(2 decimal places)
(3 decimal places)
(4 decimal places,
need to round final
answer to 2)
Multiplication and Division

Significant Figures in Calculations
– Multiplication & Division: The number of
significant figures in the answer should be the
same as the value with the fewest significant
figures. Only round FINAL answer!
Example:
12.36 mL
4 sig. fig.
x
2 sig. fig.
1.7 g
mL
= 21.012 g
round to 21g
2 sig. fig.
– Note: Definitions and counted numbers have an unlimited number of
significant figures.
– Note: If your answer is being used in another equation, use the calculated
answer, not the sig fig answer.
To change numbers to scientific notation:
 Make sure number is between 1.0 and 9.9
 Count the number of decimal places the decimal was
moved
– If moved to the left, the exponent is positive
– If moved to the right, the exponent is negative


On your calculators: use EE or EXP to replace x10^
Changing numbers to scientific notation will help you
count numbers of sig figs
54,970,000
0.000786
23.001
0.0000002456
5.497 x 10^7
7.86 x 10^ -4
2.3001 x 10^1
2.456 x 10^ -7