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### Significant Figures

Starter

SN

A group of students are asked to express this number

( 00.003048 ) to three significant figures. Which of the

following are correct?

.003

.003050

3.048 x 103

3.05 x 10-3

.00305

d. and e. are both correct.

Conversions

Converting From One System of Units to Another

You will need a conversion factor like ( 1 meter = 3.28 ft).

It can be used two ways:

(1m/3.28ft) or ( 3.28ft/1m)

Multiply your given dimension by the conversion factor to obtain the desired dimension.

How many feet in 2 meters? 2m (3.28ft/m) = 6.56 feet

How many meters in 10 feet? 10ft(1m/3.28ft) = 3.05 meters

Converting Areas

To convert areas, you must square the conversion factor.

Conversion factor: 1 inch = 2.54cm

A page is 8.5 inches by 11 inches. What is the area in square centimeters?

The area in square inches is 95 in2. So……

95 in2 = __________cm2

95 in2(2.54cm/1 in)2 = 95(6.45 cm2) / (1 in2) = 613 cm2

Converting Volumes

To convert volumes, you must cube the conversion factor.

A cubic foot is how many cubic inches?

Conversion factor: 1 foot = 12 inches

1 ft 3 ( 12 in/ 1 ft)3 = 1 ft 3 ( 123 in3/ 13 ft3) =1728in3

Scientific Notation

If numbers are very large, like the mass of the Earth

5900000000000000000000000 kg

Or very small like the mass of an electron :

.000000000000000000000000000000911 kg

then standard decimal notation is very cumbersome,

so we use scientific notation.

Scientific Notation

A number in scientific notation has two parts:

1st part: a number between 1 and 10

2nd part: 10 to some power.

Example: 5.9 x 1024

1024 Means move the decimal 24 places to the right.

Example: 6.2 x 10-4

10-4 Means move the decimal 4 places to the left.

Examples – Put the number in Scientific Notation

a. 345000

Answer: 345000 = 3.45 x 105

b. .00034

Answer: .00034 = 3.4 x 10-4

Examples

Simplify: (2 x 103)(4 x 106)

= (2)(4) x 103(106) = 8 x 109

Simplify: (4 x 103)/(2 x 106)

= (4)/(2) x 103/106= 2 x 10-3

Simplify: (2 x 103)3

= 23x (103 )3= 8 x 109

How to count the number of significant figures in

a decimal number.

- Zeros Between other non-zero digits are significant.
- a. 50.3 has three significant figures
- b. 3.0025 has five significant figures

Significant Figures

Zeros in front of nonzero digits are not significant:

0.892 has three significant figures

0.0008 has one significant figure

Significant Figures

Zeros that are at the end of a decimal number are significant.

57.00 has four significant figures

2.000000 has seven significant figures

At the end of a non-decimal number they are not.

5700 has two significant figures

2020 has three significant figures

Non-Decimal Numbers

Major pain to try to figure out the significant figures – it depends on the number’s history.

Don’t Use Them.

Practice

SN

Find the number of significant figures.

2.00450

.0034050

1450

0.02040

6 sf’s.

5sf’s

3sf’s

4 sf’s

Significant FiguresAfter Division and Multiplication

After performing the calculation, note the factor that has the least number of sig figs. Round the product or quotient to this number of digits.

3.22 X 2.1 = 6.762 6.8

36.5/3.414 = 10.691 10.7

Significant Figures

- Addition or subtraction with significant figures:
- The final answer should have the same number of digits to the right of the decimal as the measurement with the smallest number of digits to the right of the decimal.
Ex:

97.3 + 5.85 = 103.15 103.2

- The final answer should have the same number of digits to the right of the decimal as the measurement with the smallest number of digits to the right of the decimal.

Example: Find the length of side a and the angles q and f.

q

f

5

3

q

a

a2 + 32 = 52 so a2 = 25 – 9 = 16, or a = 4

4/5 = cosq, so q = cos-1(4/5) = 36.9 degrees

f + q = 90-, so f = 90 – 36.9 = 53.1 degrees

SN

Express each of these in terms of a, b and c.

1. sin(f) = ____________ 2. cos(q) = __________

3. sin(q) = _____________ 4. tan(f) = ___________

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