Transcript Significant Figures Notes

Significant Figures
Significant figures in a measurement
includes all of the digits that are known,
plus a last digit that is estimated.
•All measurements are approximations…….
•no measuring device can give perfect measurements
without experimental uncertainty.
•The numbers reported in a measurement are limited
by the measuring tool
Read the bottom of the meniscus
This cylinder is accurate to the
ones place = 35 mL
We can see that the meniscus
falls right on the line for 35,
so we estimate to the tens
place = 35.0 mL
Significant figures (sig figs)

When we measure something, we
can (and do) always estimate
between the smallest marks.
4.5 cm
1
2
3
4
5
Significant figures (sig figs)
The better marks the better we can
estimate.
 Scientist always understand that the
last number measured is actually an
estimate.

4.55 cm
1
2
3
4
5
Significant figures (sig figs)

The measurements we write down
tells us how accurate the ruler is
that we measured with
142.13cm
141
142
Counting Significant Figures
All non-zero digits are significant.
SF?
38.15 cm
5.6 ft
65.6 lb
122.55 m
ANSWERS
4
2
3
5
Counting Significant Figures
Any zero between nonzero digits are
significant.
SF?
50.8 mm
2001 mi
0.702 lb
0.00405
ANSWERS
3
4
3
3 THE
SANDWICHED
ZEROS
Counting Significant Figures
All zeroes to the left of nonzero digits
are not significant.
SF?
0.008 mm
0.0156 oz
0.0042 lb
0.000262 mL
ANSWERS
1
3
2
3 PLACE
HOLDERS,
ONLY
Counting Significant Figures
Zeroes to the right of nonzero digits
ARE significant if a decimal pt. is
present.
SF?
25.00 in.
0.0200 yr
1.0 gal
ANSWERS
4 IF THEY
WEREN’T
3 SIGNIFICANT
2 THEN WE
WOULDN’T
WRITE THEM
Counting Significant Figures
Zeroes to the right of nonzero digits
ARE NOT significant if a decimal pt. is
absent.
SF?
25,000 in.
200 yr
48,600 gal
ANSWERS
2
ONLY
1
BEING
USED AS
3
PLACE
HOLDERS
Adding and Subtracting
The answer has the same number of decimal
places as the measurement with the fewest
decimal places.
25.2
one decimal place
+ 1.34 two decimal places
26.54
answer 26.5 one decimal place
Multiplying and Dividing
Round (or add zeros) to the calculated answer
until you have the same number of significant
figures as the measurement with the fewest
significant figures.
Learning Check
A. 2.19 X 4.2 =
1) 9
B. 4.311 ÷ 0.07 =
1) 61.58
C.
2) 9.2
2) 62
2.54 X 0.0028 =
0.0105 X 0.060
1) 11.3
2) 11
3) 9.198
3) 60
3) 0.041