Significant Figures

• Start on the correct side (is decimal present or absent?) move toward the US

• First non-zero number and those after all are significant

PacificDecimal is Present

AtlanticDecimal is Absent

1. 3.0800

2. 0.00418

3. 7.09 x 10-5

4. 91,600

5. 0.003005

6. 3.200 x 109

7. 250

8. 750, 000, 000

9. 0.0101

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 = 23.924 * 3.26 = 78.24 = 78120 * 0.10 = 12.000 = 124.84 ÷ 2.4 = 2.016 = 2.0168 ÷ 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 3781.62 x 10 -22

136,392,412,7921.36 x 1011

1. 47,800

2. 0.0035

3. 573

4. 9256

5. 26.23

6. 0.23

7. 0.00036

8. 0.0000501

9. 4.2 x 103

10 1.12 x 102

11. 1.02 x 101

12. 2.5 x107

11. 2.05 x 10-3

12. 4.5 x10-5

13. 1.002 x 108

14. 1.002 x 10-4

Scientific Notation• Multiplying

1) Multiply the first factors2) Add the exponents

(2*103) * (3*103) = 6*106

(4*106) * (2*10-4) = 8*102

• Dividing1) Divide the first factors2) 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

WebAssignrounding sig figs

Round to four sig figs

84791 kg

36.8152 g

226.85 cm

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)

Setting up the graph…

• X axis– Always on horizontal axis– Always independent variable•

Y ax

is–

Alw

ays

on v

ertic

al a

xis

–Al

way

s de

pend

ent v

aria

ble

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

A

B

C

Extrapolation

• Finding an unknown point that is outside of 2 measured points

A

B C

Best fit line

• line that averages the data points• DOES NOT MEAN CONNECT THE POINTS