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**STARTER Put this number in scientific notation.**

The mass of an electron is : kg Put this number in scientific notation.

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Scientific Notation If numbers are very large, like the mass of the Earth kg Or very small like the mass of an electron : kg then standard decimal notation is very cumbersome, so we use scientific notation.

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**Scientific Notation Example: 5.9 x 1024 Example: 6.2 x 10-4**

A number in scientific notation has two parts: 1st part: a number between 1 and 10 2nd part: 10 to some power. Example: x 1024 1024 Means move the decimal 24 places to the right. Example: x 10-4 10-4 Means move the decimal 4 places to the left.

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**Examples – Put the number in Scientific Notation**

Answer: = 3.45 x 105 b Answer: = 3.4 x 10-4

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Calculators To enter a number in scientific notation into a calculator, the most common method is to use the EE button. Example: to enter 1.56 x 104 Press: 1.56(EE) Display: 1.56E4 In other words, E4 stands for “x 104 “

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**Multiplication and Division**

Rule Example xmxn = xm+n x2x3 = x2+3 = x5 xm/xn = xm-n x6/x2 = x6-2 = x4 (xm)n = xmn (x2)3 = x2×3 = x6 (xy)n = xnyn (xy)3 = x3y3 (x/y)n = xn/yn (x/y)2 = x2 / y2 x-n = 1/xn x-3 = 1/x3

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**Examples Simplify: (2 x 103)(4 x 106) = (2)(4) x 103(106) = 8 x 109**

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Significant Figures How to count the number of significant figures in a decimal number. Zeros Between other non-zero digits are significant. a has three significant figures b has five significant figures

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Significant Figures Zeros in front of nonzero digits are not significant: 0.892 has three significant figures has one significant figure

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**Significant Figures Zeros that are at the end of a decimal**

number are significant. 57.00 has four significant figures 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

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Summary For decimal numbers, start from the left and find the 1st nonzero digit. This digit and all others to the right are counted. has 5 sig. figs. For non-decimals, start from the left and find the 1st nonzero digit. This digit and all others to the right are counted until you get to only zeros which are not counted. has 5 sig. figs

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Non-Decimal Numbers Major pain to try to figure out the significant figures – it depends on the number’s history. Don’t Use Them. Use Scientific Notation to express any number to a desired amount of significant figures. Example: Express 234 to 4 sig. figs x 102

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**Practice Find the number of significant figures. 2.00450 .0034050 1450**

6 sf’s. 5 sf’s 3 sf’s 4 sf’s

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**Significant Figures After 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 = 6.8 36.5/3.414 = 10.7

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**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: = 103.2

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**Percent Error and Difference**

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Accuracy vs. Precision

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**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? m (3.28ft/m) = 6.56 feet How many meters in 10 feet? ft(1m/3.28ft) = 3.05 meters

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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 94 in2. So…… 94 in2 = __________cm2 94 in2(2.54cm/1 in)2 = 94(6.45 cm2) / (1 in2) = 606 cm2

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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

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Using S.I. Prefixes

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**Examples 12nm = 12 x 10-9 m Finished. Change 12nm to meters.**

n = x 10-9 so replace it: 12nm = 12 x 10-9 m Finished.

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**Examples 250g ( 1 kg/1x103 g) = .250 kg Change 250 grams to kilograms.**

1 kg = 1x103 gram 250g ( 1 kg/1x103 g) = kg

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**Example Use the fact that c = x 10-2**

A metal plate is 12.0cm by 4.0cm. What is the area in square meters? Use the fact that c = x 10-2 Area = (12.0cm)(4.0cm) = (12.0x10-2m)(4.0 x 10-2 m) = 4.8 x 10-3m2

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**Exit Physics uses the S.I. metric system,**

also known as the “mks” system. In this system, what are the base units for mass, time, and length?

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Title: Significant Figures and Rounding Objective: I will be able to determine the amount of significant figures when given a quantifiable number and round.

Title: Significant Figures and Rounding Objective: I will be able to determine the amount of significant figures when given a quantifiable number and round.

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