Chemistry September 9, 2014 Dimensional Analysis

Science Starter (2) Duration: 2 minutes 1. What is the difference between accuracy and precision? 2. What is the difference between a hypothesis, theory and law?

OBJECTIVES (1) SWBAT – Convert units – Apply SI units – Apply Scientific Notation – Apply Significant Digits

AGENDA (1) Do Science Starter (2) Activities – Dimensional Analysis – SI units – Scientific Notation – Significant Figures

ACTIVITY

MEASUREMENTS (0.5) Measurements is a collection of quantitative data Quantitative has amount while qualitative does not

PART 1 (2) Using a ruler, measure the blueprint of the apartment below Measure using the feet and inches side. Write the measurement directly onto the blueprint You have 2 minutes Work with your partner

DIMENSIONAL ANALYSIS Convert from foot into meter 1 foot = meter

SETUP

PART 2 (8) Model the Living Room Guided Practice the Bedroom 1 Independently do the Bedroom 2, Kitchen and Bathroom (you have 5 minutes)

DIMENSIONAL ANALYSIS(CONT) Definition: Math system using conversion factors to move from one unit of measurement to a different unit of measurement. Why we use it: Make doing calculations easier when comparing measurements given in different units.

PART 3 Making the apartment design bigger for Mr. Giant Multiply your answer in Part 2 by 100,000 Change into scientific notation to make it easier to read

SCIENTIFIC NOTATION Use to write very large number and very small number (more manageable) Parts: – Before the decimal point = 1 number – After the decimal points = more than 1 numbers (can be optional) – Exponential number = the number of places the decimal is moved

EXAMPLE (3) STEP 1: – Multiply the number by 100,000 STEP 2: – Change into scientific notation

SI UNITS International System of Units (SI) 7 SI base units – ampere (A) – measures electric current – kilogram (kg) – measure mass – meter (m) – measure length – second (s) – measure time – kelvin (K) – measure thermodynamic temperature – mole (mol) – measure amount of substance – candela (cd) – measure luminous intensity

SI PREFIXES PrefixAbbreviationMeaning Exponential Notation Number teraT1 trillion ,000,000,000,000 gigaG1 billion10 9 1,000,000,000 megaM1 million10 6 1,000,000 kilok1 thousand10 3 1,000 hectoh1 hundred dekada1 ten10 decid1 tenth centic1 hundredth millim1 thousandth microµ1 millionth nanon1 billionth picop1 trillionth femtof1 quadrillionth

EXAMPLES (3) 1 m = 100 cm 1 m = 10 dm 1 m = 0.01 hm 1 m = km

EXAMPLES (1) 1 g = 100 cg 1 g = 10 dg 1 g = 0.01 hg 1 g = kg

PART 4 Convert the living room measurements from cm to hm Use dimensional analysis Remember: conversion factor is – 1 meter = 0.01 hm or 1 hm = 100 m – 1 meter = 100 cm

PART 4 Take 5 minutes to do the rest

AREA PART 5 – Find the area (A=wl) of Mr. Giant’s apartment

PERIMETER PART 6 – Find the perimeter (P = 2(w+l)) of the apartment of Mr. Giant

SIGNIFICANT FIGURES definition: a prescribed decimal place that determines the amount of rounding off to be done based on the precision of the measurement consist of all digits known with certainty and one uncertain digit.

RULES FOR SIGNIFICANT FIGURES

RULE 1 nonzero digits are always significant – example: 46.3 m has 3 significant figures – example: g has 4 significant figures

RULE 2 Zeros between nonzero digits are significant – example: 40.7 m has 3 significant figures – example: 87,009 m has 5 significant figures

RULE 3 Zeroes in front of nonzero digit are not significant – example: m has 4 significant figures – example: g has 1 significant figure

RULE 4 Zeroes both at the end of a number and to the right of a decimal point are significant – example: g has 4 significant figures – example: has 5 significant figures

PRACTICE Do problems 1a – 1d on the Measurement Calculation Page

MULTIPLICATION/DIVISION RULES Rules for using significant figures in multiplication and division – The number of significant figure for the answer can not have more significant figures than the measurement with the smallest significant figures

EXAMPLE Example: x = – = 5 significant figures – = 4 significant figures – Answer = (4 significant figures)

ADDITION/SUBTRACTION The number of significant figure for the answer can not have more significant number to the right of the decimal point

EXAMPLE Example: = – 3.95 = has 2 significant figures after the decimal points – has 3 significant figures after the decimal points – has 1 significant figures after the decimal points – Answer = (1 significant figure)

ROUNDING – Below 5 – round down – 5 or above - roundup

EXACT VALUES has no uncertainty – example: Count value – number of items counted. There is no uncertainty – example: conversion value – relationship is defined. There is no uncertainty do not consider exact values when determining significant values in a calculated result

WARNING CALCULATOR does not account for significant figures!!!!

SCIENTIFIC NOTATION RULES FOR CALCULATION

RULE 1 Exponents are count values

RULE 2 For addition and subtraction, all values must have the same exponents before calculations

EXAMPLE Problem: 6.2 x x 10 3 Step 1: 62 x x 10 3 Step 2: 69.2 x 10 3 Step 3: 6.92 x 10 4 Step 4: 6.9 x 10 4 (Significant rule: can only have as many as the least significant figure to the right of the decimal)

RULE 3 For multiplication, the first factors of the numbers are multiplied and the exponents of 10 are added

EXAMPLE Problem: (3.1 x 10 3 )(5.01 x 10 4 ) Step 1: (3.1 x 5.01) x Step 2: 16 x 10 7 Step 3: 1.6 x 10 8 (Significant rule: can only have as many as the least significant figure)

RULE 4 For division, the first factors of the numbers are divided and the exponent of 10 in the denominator is subtracted from the exponent of 10 in the numerator

EXAMPLE Problem: (7.63 x 10 3 ) / ( x 10 4 ) Step 1: (7.63 / ) x Step 2: x Step 3: 8.85 x (Significant rule: can only have as many as the least significant figure)

PRACTICE Do problems 2a – 2d Do problems 3a – 3d

SCIENCE EXIT (2) Which measurement contains three significant figures? A cm B cm C. 800 cm D cm

SCIENCE EXIT 2 Given: (52.6 cm) (1.214 cm) = cm What is the product expressed to the correct number of significant figures? 64 cm cm cm cm 2