### Unit 2 - Significant Figures

```The exactness of a measured number
What?
How close is the measurement to the true number
That is accuracy
Who closely grouped are is the data?
The tighter the grouping the more precise.

You can be precise and not accurate
You can be accurate and not precise
1.
Sig Figs only apply to measured data
Are counted numbers measured?
2.
ALL nonzero digits are significant
What numbers are included in that statement
ALL whole numbers that are not zero
3.
All zeros between nonzero digits are
significant
For example
1003 has 4 sig figs
7.301 has 4 sig figs
30201 has 5 sig figs
4.
ALL trailing zeros after a decimal are
Significant
Examples
30.0 has 3 sig figs
6.50000000000 has 12 sig figs
5.
NOT significant
Examples
011 has 2 sig figs
0.011 has 2 sig figs
0.0110 has 3 sig figs
6.
If no decimal is present, trailing zeros are
NOT significant
Examples
1500 has 2 sig figs
15000000000000 has 2 sig figs
7.
Scientific notation shows
ONLY sig figs
Examples
1.50 x 103 has 3 sig figs
4.567 x 108 has 4 sig figs
1.00 x 10-11 has 3 sig figs
8.
A decimal following a zero makes all zeros
SIGNIFICANT
Examples
10. has 2 sig figs
15000. has 5 sig figs
200000000000000. has 15 sig figs
Do you want more rules?
ME EITHER
Let’s make it easier

1.
If it ain’t zero count it
2.
If zero is trapped count it
3.
If zero follows numbers after zero and after a
decimal, count it
4.
Determine the number of significant digits in each of
the following:
a)
b)
c)
d)
e)
f)
g)
h)
i)
6.571 g
0.157 kg
0.106 cm
0.12090 mm
28.0 ml
0.0067 g
2.690 g
2500 m
0.0700000 g
The sum or difference cannot be more significant
than the least precise measurement.
HUH?!
The answer can only have as many sig figs as the
smallest number (in terms of sig figs)
1.
2.
3.
4.
5.
6.
7.
8.
15.36 - .36 = ?
32.43 – 0.1 = ?
100 – 5 = ?
16.5 + 8 + 4.37 = ?
13.25 + 10.00 + 9.6 = ?
2.36 + 3.38 + 0.355 + 1.06 = ?
0.0853 + 0.0547 + 0.0370 + 0.00387 = ?
25.37 + 6.850 + 15.07 + 8.056 = ?
The product or quotient of measured data cannot
have more sig figs than the least precise measured
data.
HUH?!
The answer cannot have more sig figs than the smallest
measured number (in terms of sig figs)
a)
b)
c)
d)
e)
f)
g)
h)
2.6 x 3.78 = ?
6.54 x 0.37 = ?
3.15 x 2.5 x 4.00 = ?
0.085 x 0.050 x 0.655 = ?
35 / 0.62 = ?
39 / 24.2 = ?
3.76 / 1.62 = ?
0.075 / 0.030 = ?
If the operations in a compound calculation are all
of the same kind (multiplication/division OR
simultaneously using standard order of
operations before rounding to the correct number
of significant figures.
Do ALL the MATH 1st and then round
If a solution to a problem requires the combination of
multiplication/division operations, rounding the
intermediate solutions may introduce excess
a.
For intermediate calculations, you should
underline the estimated digit in the result and
retain at least one extra digit beyond the estimated
digit. Drop all remaining numbers and do not
round
b.
Round the final calculation to the correct sig fig
according to the applicable math rules taking into
account the underlined estimated digits in the
1.
2.
3.
4.
If the math is not the same then do all the
same stuff
Take the answer, go one number beyond the
required sig fig, drop all other numbers
Finish the math
Use sig fig rules for final answer
Three students are assigned the task of calculating
the total floor area of the school’s science lab. The
first student finds that the area of the main lab
floor is 9.3 m by 7.6 m. Meanwhile, the second
student measures the floor area of the chemical
storage area to be 3.35 m by 1.67 m. The third
student determines that the closet floor area is
93.5 cm by 127.6 cm.
What is the total floor area in square meters?
1.
2.
3.
4.
Angles are measured in radians in SI