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Whole Numbers and Decimals Define: Whole Numbers Decimals Read and write: Whole Numbers Decimals Round: Whole Numbers Decimals Add and Subtract: Whole Numbers Decimals Order of Operations: By hand In Excel Multiply and Divide: Whole Numbers Decimals Omitting zeros when multiplying or dividing Math Word-Application Problems: Translating words into math symbols Steps to solve math word-application problems Estimating an answer Whole Numbers: numbers to the left of the decimal point. Uses the ten one-place digits: 0,1,2,3,4,5,6,7,8,9. No "parts of the whole", or no numbers between 1 and 0. Use a comma every third place. Trillions Billions Millions Thousands Ones Hundred Thousands Hundred Trillions Hundred Millions Hundred Billions Ten Thousands Ten Trillions Ten Millions Ten Billions Thousands Trillions Millions Billions 4 5 6 7 5 8 4 5 2 4 Fifteen Million, Seven Hundred Eighty Nine Thousand, Four 15,789,458 Hundred Fifty Eight Whole Four Hundred Thirty Trillion, Four Hundred Fifty Seven Billion, Eight Numbers Hundred Forty Five Million, Eight Hundred Ninety Six Thousand, 430,457,845,896,214 Two Hundred Fourteen Four Hundred Fifty Six Billion, Seven Hundred Fifty Eight Million, Four Hundred Fifty Two Thousand, One Hundred Nineteen And 456,758,452,119.155 One Hundred Fifty Five Thousandths Decimal Two Hundred Fifty Four Thousand, Four Hundred Nineteen Numbers 0.254419 Millionths One Hundred Fifty Four Thousand Five Hundred Eighty Seven $154,587.25 Dollars And Twenty Five Cents Decimals: numbers to the right decimal point. Uses of the decimal point - The word representing parts of a whole - ,9. No "parts of the "and" goes "a whole" is the number 1 and Use a comma every here when the "parts" is a number between you say the 1 and 0. Define Decimal ==> A word number written with a decimal Ones such as 4.987 or .062 Hundred-Thousandths Decimal Point (and) Ten-Thousandths Thousandths Hundredths Hundreds Millionths Tenths Ones Tens 1 1 9 1 5 5 5 6 3 2 5 4 4 1 9 Formatting is like a façade on a house: it is only what is on top. Formatting does not necessarily refle number General Number Currency Accounting Date Time Shows date Shows "floating" Shows "fixed" format, Shows time No commas, Shows commas dollar sign, dollar sign, underneath is the format, shows as many and as many commas and as commas and as number of days underneath is the decimals as you decimals as you many decimals as many decimals as since Jan. 1, proportion of one type in tell it to show you tell it to show you tell it to show 1900 24 hour day 12569.45698 12,569.46 $12,569.46 $ 12,569.46 7/3/2006 8:00:00 AM 12569.45698 12569.45698 12569.45698 12569.45698 38901 0.333333333 12569.45698 12569.45698 12569.45698 12569.45698 38901 0.333333333 s not necessarily reflect the underlying Percentage Fraction Shows Percentage format (slides decimal to right two positions and then adds the percentage Division symbol). What is represented with underneath is a a numerator and decimal or whole a denominator number (.06 or 1 and a line )) between the two 6.00% 1/4 0.06 0.25 0.06 0.25 Rules for Rounding by hand Select the position to which you would like to round. We will call this the 1 "selected position". If you are rounding to a whole number draw a line under the "selected position". If you are rounding to a decimal position, draw a vertical line after the "selected position" to indicate that you will drop the remaining digits. 2 Look one position to the right If this digit is 5 or more, increase the digit in the "selected position" by one If this digit is 4 or less, DO NOT CHANGE the digit in the "selected position" Change all the digits to the right of the 3 "selected position" to zeros. If you have decimal positions that have zeros, you can drop them. by hand Financial Statements are often rounded to the Thousands position $5,698,700,459.25 Income Taxes are rounded to the ones position $555.25 Payroll deductions are rounded to the hundredths position $98.2569 ROUND function in Excel To round to the thousands position use "- 3" as the second function argument =ROUND(C2,-3) To round to the ones position use "0" as the second function argument =ROUND(C3,0) To Round to the Hundredths Position use "2" as the second function argument =ROUND(C4,2) ROUND function Financial Statements are often rounded to the Thousands position $5,698,700,459.25 Income Taxes are rounded to the ones position $555.25 Payroll deductions are rounded to the hundredths position $98.26 Increase/Decrease decimals with formatting Use the Increase/Decrease Decimal button on the Formatting toolbar Formatting (Façade) Income Taxes are rounded to the ones position $555.25 Payroll deductions are rounded to the hundredths position $98.2569 Name Gross Pay Deduction 1 Net Pay Suix Chin 5,468.25 Stephanie Walting 7,667.54 Rachel Hensley 6,900.20 Totals Assumption Deduction Rate 0.32 Rule for when to use the ROUND function: If you will use the result of a formula in a subsequent Excel formula and you are multiplying or dividing decimals where you are required to round to a certain position, you must use the ROUND function to get a correct answer. In the range C4 to C6 (green color) create efficient formulas that 5) Because each deducti calculate the deduction based on the rate in cell B10 (Gross * subtracted from each pay deduction rate). Then calculate the net pay in the range D4:D6. function. The Decimal bu Then add totals in cells C7 and D7. Hint: When we calculate a are Rounded, but they ar deduction, we must round to the penny. Name Gross Pay Deduction 1 Net Pay Name Gross Pay Suix Chin 5,468.25 1,749.84 3,718.41 Suix Chin 5,468.25 Stephanie Walting 7,667.54 2,453.61 5,213.93 Stephanie Walting 7,667.54 Rachel Hensley 6,900.20 2,208.06 4,692.14 Rachel Hensley 6,900.20 Totals 6,411.51 13,624.48 Totals Assumption Assumption Deduction Rate 0.32 Deduction Rate 0.32 1) Your boss looked at your table without the ROUND function 2) and then typed the numbers she saw into the cells here. 3) When she added them up she got a different number than you did. Her number is correct because what you see is what the SUM function is adding! 5) Because each deduction is a bunch of pennies that are subtracted from each paycheck, you must use the ROUND function. The Decimal button on the toolbar makes it look like they are Rounded, but they are not. Deduction 1 Net Pay 1,749.84 3,718.41 2,453.61 5,213.93 2,208.06 4,692.14 6,411.52 13,624.47 1,749.84000 2,453.61280 1749.84 2,208.06400 2453.61 2208.06 6411.51 4) In your original calculations, if you increase your decimals, you can see there are some decimals that you originally could not see, but the SUM function does see them. The SUM function sees them and used them when it adds. That is why your SUM shows 6,411.52 (it has more decimals to add and so it gets one penny more). Whole Numbers 16 + 15 62 - 43 Decimals 16.256 + 15.128 62.07 - 43.29 Whole Income From Bookkeeping 15,580.00 Income From Tax Preparation 11,504.00 add Total Revenue Rent Expense 1,000.00 Insurance Expense 1,300.00 Salary Expense 3,145.00 Supplies Expense 526.00 Depreciation Expense 244.00 add Total Expenses subtract Net Income s Decimals Income From Bookkeeping 15,580.58 Income From Tax Preparation 11,504.19 Total Revenue Rent Expense 1,000.12 Insurance Expense 1,300.26 Salary Expense 3,145.37 Supplies Expense 526.86 Depreciation Expense 244.86 Total Expenses Net Income Name Gross Pay Deduction 1 Deduction 2 Deduction 3 Total Deductions Name 1 881.13 13.06 12.94 29.76 Name 2 690.13 24.94 12.58 20.38 Name 3 1086.01 18.26 26.8 24.8 Name 4 672.43 19.99 25.02 25.56 Name 5 937.85 25.66 21.59 14.08 Name 6 994.07 31.72 14.94 29.51 Name 7 1005.24 16.27 35.35 37.27 Name 8 988.26 24.7 27.42 29.17 Name 9 688.82 37.78 15.61 15.62 Totals 7943.94 212.38 192.25 226.15 Name Gross Pay Deduction 1 Deduction 2 Deduction 3 Net Pay Name 1 881.13 13.06 12.94 29.76 Name 2 690.13 24.94 12.58 20.38 Name 3 1086.01 18.26 26.8 24.8 Name 4 672.43 19.99 25.02 25.56 Name 5 937.85 25.66 21.59 14.08 Name 6 994.07 31.72 14.94 29.51 Name 7 1005.24 16.27 35.35 37.27 Name 8 988.26 24.7 27.42 29.17 Name 9 688.82 37.78 15.61 15.62 Totals 7943.94 212.38 192.25 226.15 Name Gross Pay Suix Chin 5,468.25 Stephanie Walting 7,667.54 Rachel Hensley 6,900.20 Totals Assumption Deduction Rate 0.32 Net Pay efficient formula =B15-SUM(C15:E15) inefficient formula =B16-C16-D16-E16 Deduction 1 Net Pay 1,749.84 3,718.41 2,453.61 5,213.93 2,208.06 4,692.14 6,411.51 13,624.48 d67cc0eb-3fd2-449d-8e1c-09d4495967ae.xls - Order of Operations Arithmetic operation signs in Excel: ( ) represents Parentheses ^ represents Exponents (powers and roots) * represents Multiplication / represents Division + represents Addition – represents Subtraction Order of Operations form Algebra class (Each one is left to right): Please Parenthesis ( ) Excuse Exponents ^ 2^2 = 4 or 4^(1/2) = 2 My Dear Multiplication * and Division / Aunt Sally Adding (SUM) + and Subtraction - Excel's Order of Operations: Parenthesis ( ) Ranges use of colon symbol ":" Example: =SUM(A1:A4) Evaluate unions (,) Example: =SUM(A1:A4,B2:C7) Negation (-) Example: =-2^4 16 Example: =-(2^4) -16 Converts % (1% .01) Exponents (^) Example 1: 4^(1/2) = 2 Example: 3^2 = 9 Multiplication (*) and division (/), left to right Adding (+) and division (-), left to right Text operators (& Concatenation) Comparative symbols: =, <>, >=, <=, <, > If anything is still left, then left to right Page 15 of 29 d67cc0eb-3fd2-449d-8e1c-09d4495967ae.xls - OOO (2) 3+3*2 =D1+E1*F1 3 3 2 (3+3)*2 =(D2+E2)*F2 3 3 2 2+(2+1)*3 =D3+(E3+F3)*G3 2 2 1 3 2-1+(3-1)*2 =D4-E4+(F4-G4)*H4 2 1 3 1 2 Page 16 of 29 Multiplying Whole Numbers 690 * 43 3 4 2 6 690 multiplicand factor 6 x 43 multiplier factor 4 2070 partial product (3 x 69) + 27600 partial product (4 x 69) 2 29,670 product (answer) 8 3 5 3 300 300 2 zeros * 70 x 70 1 zero 21 + 3 zeros 21,000 answer Omitting zeros when multiplying: "remove at beginning, add back at end" Dividing Whole Numbers 256 4 Numerator = Dividend 16 2 Denominator = Divisor 4 (Numerator) 2 (Denominator) = 2 (Quotient or answer) 2 (Denominator) 4 (Numerator) 108000 900 Zeros in division: 0/4 = 0 because 0 * 4 = 0 however 4/0 = ? = in not defined because what?*0 = 4 ???? 1080 Reciprocals: 1/2 and 2/1 are reciprocals 9 Omitting zeroes in division 108000 900 = 1080 9 = 120 876 2 2 3 Multiply Decimals 0.032 Items Boomerangs * 0.070 Quantity 5.00 Price 22.25 Total Hours 39.50 Gross - Wage 15.75 Tax Rate 0.06 Gross Tax Rate Divide Decimals 17.60 0.25 17.6 .25 = 1760 25 = 70.4 1,760.00 25.00 When the denominator is 15.00 between 1 and 0, the quotient will always be bigger than the 0.25 Numerator Different ways to express quotient: Quick way to estimate 20 29548 round up ==> 15 * 0.10 slide decimal to right 1.333333 1R5 1 1/3 Decimal Remainder Fraction slide decimal back to left <== 158 56,986 190 23 197 r) = 2 (Quotient or answer) ause what?*0 = 4 ???? 30000 1 30000 3000 Steps for solving word-application problems: Read problem carefully – be sure you know what Step 1 they are asking. List all relevant facts. List all information you want Step 2 to find. Step 3 Estimate reasonable answer. Step 4 Set up the problem and solve. Step 5 Check your answer. Write answer in words – go back and use the Step 6 nouns and verbs from the problem. Short list of steps for solving word-application problems: Step 1 Read problem carefully and list all relevant facts Step 2 Set up problem, solve, check and double check Write answer in words – go back and use the Step 3 nouns and verbs from the problem. Translate words into math symbols Add Subtract Multiply Division Equal Powers plus less product divided by is squared more subtract double divided into the same as raised to more than subtracted from triple quotient equals to the second power added to difference times goes into equal to cubed increased by less than of divide yields to the 12th power sum fewer twice divided equally results in total decreased by twice as much per are sum of loss of increase of minus gain of take away add reduced by The three invoices each had a total of $14.26 listed on the bottom line. What is the total that is owed? If the total gross earnings for the year were $29,013.45 and the first $15,000 of those gross earnings were taxed at a rate of .10 and the remaining amount was taxed at .15. What is the total tax paid for the year if you round your answer to the dollar? 1) Setup for Math Problems In Excel 2) 3) 4) 5) 6) 7) 8) 9) If there are 10 Boomerangs for sale at $20 each and the cost for each boom is $10, what is the total profit if you sell them all? Summary Exercise Step 1 Read and list all relevant facts 1 Average wedding costs in USA in 2004 2 Cost of average 2001 wedding = $20,357.00 Average cost has increased as the average number of wedding guest has grown to over 3 200 4 Graph shows details Wedding reception $9,590.00 Rings (engagement and wedding) $5,099.00 Photographer $1,647.00 Misc. expense $1,583.00 Wedding dress and headpiece $1,242.00 Music $1,042.00 Bridesmaids' dresses (5) $992.00 Bouquets and other flowers $950.00 Rehearsal dinner $877.00 Men's formal wear $849.00 Mother's of the Bride apparel $297.00 Step 2 and 3 a The total Costs shown in the graph = The increase in the average wedding cost in b 2004 over the cost in 2001 = c Our cost for wedding = $7,000.00 Cost per guest = $32.00 The number of guests we can invite = Since we can not invite a part of a guest, we must round ==> Total costs for us = Amount left over = Number of guests that are invited to wedding d = 150 Budgeted amount for wedding = $7,000.00 Amount that can be spent on each person = Round to the nearest cent = e Budgeted amount for wedding = $4,000.00 Cost per guest = $27.00 The number of guests we can invite = Since we can not invite a part of a guest, we must round ==> Total costs for us = Amount left over = f Budgeted amount for wedding = $1,000.00 Cost per guest = $15.00 The number of guests we can invite = Since we can not invite a part of a guest, we must round ==> Total costs for us = Amount left over = g Number of bridal party bouquets = 5 Cost per bridal party bouquets = $36.25 Number of boutonnieres = 5 Cost per boutonnieres = $7.50 Total amount budgeted for flowers = $863.00 Amount spent for bridal party bouquets and boutonnieres = Amount left over s #1 Round to the nearest ten number to round = 844 Answer = 840 #2 Round to the nearest hundred number to round = 21,958 Answer = 22,000 #3 Round to the nearest thousand number to round = 671,529 Answer = 672,000 #4 Front End Round number to round = 50,987 Answer = 50,000 #5 Front End Round number to round = 851,004 Answer = 900,000 #6 Commissions Earned Monday $124.00 Tuesday $88.00 Wednesday $62.00 Thursday $137.00 Friday $195.00 Total = $606.00 The total commissions that Suzanne earned = Answer = $606.00 #7 Total Costs Cost per airless sprayer = $1,540.00 Number of airless sprayers purchased = 3 Total = $4,620.00 Cost per rototillers = $695.00 Number of rototillers purchased = 5 Total = $3,475.00 Cost per ladders = $38.00 Number of ladders purchased = 8 Total = $304.00 Total for all purchases = $8,399.00 #8 Round to the nearest cent 2 Number 21.0568 Answer = $21.06 #9 Round to the nearest cent 2 Number 364.345 Answer = $364.35 #10 Round to the nearest cent 0 Number 7246.49 Answer = $7,246.00 #11 add 9.6 8.42 3.715 159.8 Total = 181.535 #12 add 2.715 32.78 426.3 37 Total = 498.795 #13 Subtract 341.4 207.8 Difference = 133.6 #14 Subtract 3.8 0.0053 Difference = 3.7947 #15 Multiply 21.98 0.72 Product = 15.8256 #16 Multiply 218.6 0.037 Product = 8.0882 #17 Division Numerator (Dividend) 252.008 Denominator (Divisor) 21.8 Quotient = 11.56 #18 Division Numerator (Dividend) 57.358 Denominator (Divisor) 2.41 Quotient = 23.8 #19 Division Numerator (Dividend) 79.135 Denominator (Divisor) 18.62 4.25 #20 Total costs Number of solvent gallons to buy 32.6 Solvent cost per gallon $13.48 Total = $439.45 Number of acid gallons to buy 18.5 Acid cost per gallon $3.56 Total = $65.86 Total for solvent and acid = $505.31 #21 Total costs Roof Materials per 10x10 squares $84.52 Installation labor per 10x10 squares $55.75 Supplies per 10x10 squares $9.65 Total Costs per 10x10 square $149.92 Number of 10x10 squares 26.3 Total costs $3,942.90 #23 How much change was received Number of meters of electrical wire purchased 16.5 Electrical wire cost per meter $0.48 Number of meters of brass rod 3 Cost of brass rod per meter $1.05 Total cost $11.07 Amount of one fiver $5.00 Number of fivers 3 Total amount of money given to cashier $15.00 Amount of change he got from three fivers = $3.93 #24 Price of bananas per pound Price of bananas per kilogram $1.74 Number of pounds in one kilogram 2.2 Price for 2.2 pounds of banana $1.74 Price per 1 pound of banana $0.79 #25 Find Number of seedlings Ounces of concentrated fertilizer needed for one seedling 0.058 Ounces of concentrated fertilizer available for use 14.674 Number of seedlings that can be fertilized 253.0000 50,000 900,000 The total commissions that Suzanne earned = $606.00

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