Significant Figures

1
Significant Figures

• Why are they necessary?

2
Add the following

• 2.34? g
• 1.2?? g
• 6.752 g
• 10.2?? g
• The ? represents the unknown measurement
• What can you conclude about your final answer
  when you are adding numbers?

3
What is the final answer using significant
figures?
206 23.45 13.236

• 242.686
• 242
• 243

4
Add everything first and then cut off.

• 206.???
• 23.45?
• 13.236
• 242.686
• Round before you cut off
• 243

5
Try this one
0.0023 g 1.679 g 7.9 g

• 9.5813 g
• 9.58 g
• 9.5 g
• 9.6 g

6
Answer

• 0.0023 g
• 1.679? g
• 7.9??? g
• 9.5813 g
• Round 9.6 g

7
What rule can you come up with, for adding
significant figures?

• Line up the numbers
• Add
• Cut off at the least number of decimal places
• Round up (if the number after is 5 )
• Keep number (if the number after is lt 5 )

8
What about subtraction?

• The same rule!!!!

9
What is the difference between 5.459 2.20 ?

• 5.5
• 3.5
• 3.259
• 3.26

10
Rule for and -?

• Line up the numbers
• Add or subtract
• Cut off at the least number of decimal places
• Round up (if the number after is 5 )
• Keep number (if the number after is lt 5 )

11
What other operations are we missing?

• and

12
Solve the following

• 2.11
• x 0.2?
• ???
• 422
• .422?
• The final answer is .4

13
Sig. Figs

• The two kinds of numbers in the world are
• Exact numbers
• Values obtained by COUNTING
• Inexact numbers
• Values obtained by MEASURING
• Significant numbers include all digits that are
  certain plus the first uncertain number

14
For and , count the number of sig. figs

• Rules for counting
• Leading 0s are NOT significant
• 0.002 1 sig. fig.
• .00356 3
• 0.06 1
• 0.0230 3

15
Trailing 0s are NOT significant

• 100 1
• 1220 3
• 450 2
• 10 1

16
Trailing zeros are significant only if the
decimal point is specified

• 100.0 4
• 2030 3
• 2030. 4
• 0.00250 3
• 80.002 5

17
All numbers in scientific notation are
Significant!

• 2.300 x 10-2 4
• 4.7 x 103 2
• 1.006 x 109 4

18
How many significant figures are in each of the
following?

• 1.23 ____ 250.
  ______
• 0.00123 _____ 2.50 x 102 ______
• 2.0 ____ 3.228 x 10-5
  ______
• 0.020 ______ 2.0005 x 101 _____
• 100 ______
• 100. ______
• 100.00 ______
• 250 ______

19
How many significant figures are in each of the
following?

• 1.23 _3___ 250.
  ___3___
• 0.00123 _3_ 2.50 x 102 ___3___
• 2.0 _2__ 3.228 x 10-5
  __4____
• 0.020 ____2__ 2.0005 x 101
  ___5__
• 100 ___1__
• 100. __3__
• 100.00 __5__
• 250 ___2___

20
The answer to an operation cannot be more precise
than the least precise measurement

• Ex. 6.534
• x 0.56
• Ex. 6.534 4 sig.figs
• x 0.56 2 sig. figs
• 3.6590
• 3.7 2 sig.figs

21
Which of the following measurements has the
greatest number of significant figures?

• 0.7600
• 0.00760
• 7.6 x 108
• 0.00076
• 760

22
The number of significant digits in 200.000 is

• 3
• 1
• 5
• 6

23
Rounded correctly, 2.000 cm 10.0 cm

• 20
• 20.000
• 20.00
• 20.0

24
5.5234 mL of mercury is transfered to a graduated
cylinder with scale marks 0.1 mL apart. Which of
the following will be the correct reading taken
from the graduated cylinder?

• 5.5
• 5
• 5.523
• 5.52

25
How many zeros are significant figures in a
measured mass of 0.010010 g?

• 5
• 0
• 1
• 3

26
The number of significant digits in 540.00610 is

• 3
• 6
• 8
• 7

27
Correctly rounded, 20.0030 - 0.491 g

• 19.51 g
• 19.512 g
• 19.5120 g
• 20 g

28
Rounded correctly, 30.00 g / 10.0 mL

• 3
• 3.0
• 3.00
• 3.000

29
What is the volume of a rectangular strip of wood
that measures 10.0 cm x 100.0 cm x 1.0 cm?

• 111.0 cm3
• 1000.0 cm3
• 1.0 x 103 cm3
• 1.00 x 103 cm3