2Learning Goals Write a number in scientific notation Determine the number of significant figures in measured numbersAdjust calculated answers to the correct number of significant figures.
3ReviewState the type of measurement (mass, length, volume, or temperature) indicated by the unit in each of the following45.6 kg b L c. 45 m d. 315 KGive the SI unit and abbreviation that would be used to express the following measurements.Length of a football fieldDaytime temperature on MarsThe mass of an electric car
4Review continuedA 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?
5Review ContinuedWhen 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?
6Scientific NotationUsed to write cumbersome numbers in a compact manner1.2 x 10-10 exponent (n)Decimal part exponential partTo 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
7Scientific Notation The diameter of Earth 12 800 000 m 1. Move the decimal point to give a number between one and ten2. Multiply the number by 10 raised the number of places the decimal was moved1.28 x 107 m3. The exponent is positive because we moved the decimal to the left (The original number was greater than 1)
8Human 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 hairs1 x 105 hairs
9Scientific NotationWrite the following measurements in scientific notation.350 gLmmg
10Rules for determining significant figures: All nonzero digits are significant2. Interior zeros (zeros between 2 numbers) are significant3. Trailing zeros (zeros after a decimal point) are significant4. Leading zeros ( zeros to the left of the first nonzero number) are not significant. They only serve to locate the decimal point.
12Solutions to Problems 0.00789 3 significant figures (0.00789) (2.0012)(0.001)(4.100)(0.1000)( )(100.25)
13Exact numbersExact numbers have an unlimited number of significant figures3 sources1. accurate counting of discrete objects3 atoms means atoms2. defined quantities100 cm = 1 m means cm =1.00m3. integral numbers that are part of an equationradius = diameter/ 2
14Significant 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 figuresIn addition or subtraction, the result carries the same number of decimal places as the quantity carrying the fewest decimal places
15Rounding NumbersRound off each of the following numbers to three significant figures.Round them off to two significant figures.
16Multiplication 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)
17Addition 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
18Remember!!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