Significant Figures
Objectives
• Determine significant figures
within standard number form.
• Identify the number of significant
figures in scientific notation.
Why?
Measure the length in cm.
Ruler 1
Ruler 2
Ruler 3
Why?
• Always some uncertainty in a measurement.
• The numbers reported indicate the precision
of the instrument used.
• The more numbers = the more precision.
1. All non-zero digits are significant.
Using this rule, how many significant figures are
there in the following numbers?
a)
b)
c)
d)
1462.99
26.2
0.000561
5.61 x 102
6
3
3
3
1. All non-zero digits are significant.
2. Zeros before non-zero digits are NOT
significant.
a) 0.0005671
b) 054
c) 0.0612
d) 1.6134 x 10-5
4
2
3
5
1. All non-zero digits are significant.
2. Zeros before non-zero digits are NOT
significant.
3. Zeros between non-zero digits are
significant.
a)
b)
c)
d)
0.00565
95.054
0.008706
1.5808 x 102
3
5
4
5
1. All non-zero digits are significant.
2. Zeros before non-zero digits are NOT significant.
3. Zeros between non-zero digits are significant.
4. Zeros at the end are only significant if there
is a decimal present.
a)
b)
c)
d)
5061.0
5200
0.0067010
9.0810 x 103
5
2
5
5
Practice
Find the number of significant digits in the
following:
1)5600
6) 89.543
2)45.00
7) 5,056,300
3)105.0
8) 95.0540
4)0.00565
9) 93,000,000
5)0.005400
10) 8.701 x 10-21
Rounding
Round to two significant digits.
1)3.64
2)4.55
3)7.250
4)0.0865
5)0.5182
6)2.473
Rounding
Round to three significant figures.
1)54.7421
2)0.9114
3)1.3511
4)79.2588
5)100.0925
Multiplying and Dividing
5. When multiplying and dividing measurement, the
answer must be recorded in the least number of
significant digits provided in the problem (use the
number with the least amount of significant digits).
a) 50. / 2
1
1
b) 8635 x 2
4
c) 82.00 x 206.523
d) 2.5 x 10-5 cm3 / 1.34 x 102cm 2
25
=30
17270 =20000
16934.886 =16930
4.664179104 x 1012
=4.7 x 1012cm
Solving for Volume
Volume = l x w x h
l = 2.1 x 103cm
w = 4.35 x 102cm
h = 2.96 x 101cm
Volume = (2.1 x 103cm)(4.35 x 102cm)(2.96 x 101cm)
Volume = 0.003718091 cm3
= 3.718091 x 10-3 cm3
= 3.7 x 10-3 cm3
Note: 1 cm3 = 1mL
Objectives
• I will identify the number of significant figures
needed for addition and subtraction
operations of measurement.
Addition and Subtraction
6. When adding and subtracting, your answer
should have the same number of decimal
places as the number in the problem with the
least amount of decimal places.
a) 2.01 + 8.5
b) 7-3.5
c) 82.635 – 45
d) 52.056 - 6.87777
10.51
3.5
75.17823
45.17823
1
10.5
0
0
3
4
75
45.178
Many Operations
• Remember PEMDAS
1.
2.
3.
4.
5.
6.
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Many Operations
• Work your way through step by step.
• Follow PEMDAS.
a) (86.53 + 22.3)
15
Addition
86.53 + 22.3 = 108.83
1 sig fig after the decimal
= 108.8
108.8 / 15 = 7.25333
Least amt of sig figs is 2
= 7.3
b) 18.3 x 16.25 + 52.876
Multiplication
18.3 x 16.25 = 297.375
Least amt of sig figs is 3
297
Addition
297 + 52.876 = 349.876
Least # sig figs after the decimal = 0
350.
Now You Try
(223.456 – 89.25)
16 x 22.34
Parentheses
223.456 – 89.25 = 134.206
Least amt of sig figs after decimal
2
134.21
Multiplication
16 x 22.4 = 358.4
Least amt of sig figs
2
360
Division
134.21/ 360 = 0.3728055
Least amt of sig figs
2
0.37
Independent Practice