Significant Figures
Pacific
Atlantic
Decimal is Present
Decimal is Absent
• Start on the correct
side (is decimal
present or absent?)
move toward the
US
• First non-zero
number and those
after all are
significant
1. 3.0800
6. 3.200 x 109
2. 0.00418
7. 250
3. 7.09 x 10-5
8. 750, 000, 000
4. 91,600
9. 0.0101
5. 0.003005
10. 0.00800
Sig Figs
• Multiplying and Dividing
– Answer must have same number of significant
figures as the measurement with the fewest
significant figures
3.20 * 3.65 * 2.05 = 23.944 = 23.9
24 * 3.26 = 78.24 = 78
120 * 0.10 = 12.000 = 12
4.84 ÷ 2.4 = 2.016 = 2.0
168 ÷ 58 = 2.8965 = 2.9
Sig Figs
• Adding and Subtracting
– Answer must have same # of digits to the right of decimal
as the value w/ the fewest digits to the right of decimal
(4.32*103) – (1.6*103) = 2.72*103 = 2.7 * 103
28.0
23.538
+ 25.68
77.218 = 77.2
Scientific Notation
• Convenient way of writing very small or large
numbers
• Consists of two parts
– Number & ten raised to an exponent
• Exponent is negative, number will be smaller than 1
• Exponent is positive, number will be bigger than 1
0.000 000 000 000 000 000 000 162 378
1.62 x 10 -22
136,392,412,792
1.36 x 1011
1. 47,800
5. 26.23
2. 0.0035
6. 0.23
3. 573
7. 0.00036
4. 9256
8. 0.0000501
9. 4.2 x 103
11. 2.05 x 10-3
10 1.12 x 102
12. 4.5 x10-5
11. 1.02 x 101
13. 1.002 x 108
12. 2.5 x107
14. 1.002 x 10-4
Scientific Notation
•
Multiplying
1) Multiply the first factors
2) Add the exponents
(2*103) * (3*103) = 6*106
(4*106) * (2*10-4) = 8*102
•
Dividing
1) Divide the first factors
2) Subtract the exponents
(6*104) ÷ (3*102) = 2*102
(9*103) ÷ (3*10-4) = 3*107
(3- (-4)) = 3+4
1. 6.25 x10-4 / 4.1 x101
2. 4.18 x10-2 / 2.4 x10-2
3. 3.24 x10-4 / 4.8 x10-2
4. 4.1 x103 x 5.2 x 10-4
5. 5.24 x 106 x 6.76 x 102
6. 2.3 x 103 x 9.8 x 10-4
Scientific Notation
• Adding and Subtracting
– Exponents MUST BE THE SAME before doing the math!
– Add the numbers and rewrite x10exponent
(2.7*107) + (1.56*105)
(270*105) +(1.56*105) = 271.56*105
= 2.7 * 107
(8.3*108) – (4.1*106)
(830*106) – (4.1*106) = 825.9 *106
= 8.3 *108
7. 0.0256 + 0.0032
8. 4.1 x105 – 2.8 x 102
9. 3.1 x105 + 5.2 x103
WebAssign
rounding sig figs
Round to four sig figs
84791 kg
226.85 cm
36.8152 g
5.1676 m
Graphs
• Visual display of data
Setting up the Graph
Adjust your scale to ensure the graph occupies the most space
Your values need to increase at a steady rate (for example count by 2)
•
Always on vertical axis
Always dependent variable
–
–
Y axis
Setting up the graph…
• X axis
–
–
Always on horizontal axis
Always independent variable
Which is dependent variable?
• Amount of fertilizer
• Growth rate of plants
• Number of years
• Increase in population
• Inches of rain that fell
• Month rainfall occurred
• Amount due on cell phone bill
• Minutes used
Interpolation
• Finding an unknown point between 2
measured points
B
C
A
Extrapolation
• Finding an unknown point that is outside of 2
measured points
B
A
C
Best fit line
• line that averages the data points
• DOES NOT MEAN CONNECT THE POINTS