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**Introduction to Chem Math 2**

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**Learning Goals Write a number in scientific notation**

Determine the number of significant figures in measured numbers Adjust calculated answers to the correct number of significant figures.

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Review State the type of measurement (mass, length, volume, or temperature) indicated by the unit in each of the following 45.6 kg b L c. 45 m d. 315 K Give the SI unit and abbreviation that would be used to express the following measurements. Length of a football field Daytime temperature on Mars The mass of an electric car

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Review continued A fish company delivers 22 kg of salmon, 5.5 kg of crab, and 3.48 kg of oysters to your seafood restaurant. What is the total mass in kilograms of the seafood? In grams?

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Review Continued When three students use the same meter stick to measure the length of a paperclip, they obtain results of 5.8 cm, 5.75 cm, and 5.76 cm. If the meter stick has millimeter markings, what are some of the reasons for the different values?

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Scientific Notation Used to write cumbersome numbers in a compact manner 1.2 x 10-10 exponent (n) Decimal part exponential part To convert a number to scientific notation: 1. move the decimal point to obtain a number between 1 and 10. 2. multiply by 10 raised to the number of places you moved the decimal point -if decimal moved left: positive exponent -if decimal moved right: negative exponent

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**Scientific Notation The diameter of Earth 12 800 000 m**

1. Move the decimal point to give a number between one and ten 2. Multiply the number by 10 raised the number of places the decimal was moved 1.28 x 107 m 3. The exponent is positive because we moved the decimal to the left (The original number was greater than 1)

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**Human Hair Width of a human hair 0.000 008 m 8 x 10-6 m**

Notice the original number is less than 1, so your exponent is negative. Hairs on a human scalp hairs 1 x 105 hairs

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Scientific Notation Write the following measurements in scientific notation. 350 g L m m g

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**Rules for determining significant figures:**

All nonzero digits are significant 2. Interior zeros (zeros between 2 numbers) are significant 3. Trailing zeros (zeros after a decimal point) are significant 4. Leading zeros ( zeros to the left of the first nonzero number) are not significant. They only serve to locate the decimal point.

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Practice Problems 2.0012 0.001 4.100 0.1000 100.25

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**Solutions to Problems 0.00789 3 significant figures (0.00789)**

(2.0012) (0.001) (4.100) (0.1000) ( ) (100.25)

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Exact numbers Exact numbers have an unlimited number of significant figures 3 sources 1. accurate counting of discrete objects 3 atoms means atoms 2. defined quantities 100 cm = 1 m means cm =1.00m 3. integral numbers that are part of an equation radius = diameter/ 2

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**Significant Figures in Calculations**

An answer involving measured numbers can not be more precise than the initial numbers!! In multiplication or division, the result carries the same number of significant figures as the factor with the fewest significant figures In addition or subtraction, the result carries the same number of decimal places as the quantity carrying the fewest decimal places

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Rounding Numbers Round off each of the following numbers to three significant figures. Round them off to two significant figures.

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**Multiplication and Division: Give answers with the correct number of significant figures.**

45.7 x x x x 3.6 x / / (4 x 125) (0.2465)(25)/1.78 (3.5 x 0.261)/(8.24 x 20.0)

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**Addition and Subtraction: Give answers with the correct number of significant figures.**

45.48 cm g g mL mL mL – mL g g g 1.08 L – L cm cm m L – L

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Remember!! Your units must be the same for all numbers in order to add and subtract them. This is like finding a least common denominator in math class before adding fractions

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Significant Figures 1.All non-zero digits are significant (2.45 has 3 SF) 2.Zeros between (sandwiched)non- zero digits are significant (303 has 3 SF)

Significant Figures 1.All non-zero digits are significant (2.45 has 3 SF) 2.Zeros between (sandwiched)non- zero digits are significant (303 has 3 SF)

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