Chapter 1 - XYZ Custom Plus

1.3 Rounding and Estimating27b. We add the numbers for all items except taxes and savings.House payments $10,200Food 5,296Car expenses 4,847Entertainment 2,142Miscellaneous 6,142Total$28,627 = $29,000 to the nearestthousand dollarsBEstimatingWhen we estimate the answer to a problem, we simplify the problem so that anapproximate answer can be found quickly. There are a number of ways of doingthis. One common method is to use rounded numbers to simplify the arithmeticnecessary to arrive at an approximate answer, as our next example shows.Example 6Estimate the answer to the following problem by roundingeach number to the nearest thousand.4,8721,691777+ 6,124Solution We round each of the four numbers in the sum to the nearest thousand.Then we add the rounded numbers.4,872 rounds to 5,0001,691 rounds to 2,000777 rounds to 1,000+ 6,124 rounds to + 6,00014,000We estimate the answer to this problem to be approximately 14,000. The actualanswer, found by adding the original unrounded numbers, is 13,464.Here is a practical application for which the ability to estimate can be a usefultool.Example 7On the way home from classes you stop at the local grocerystore to pick up a few things. You know that you have a $20.00 bill in yourwallet. You pick up the following items: a loaf of wheat bread for $2.29, a gallonof milk for $3.96, a dozen eggs for $2.18, a pound of apples for $1.19, and a boxof your favorite cereal for $4.59. Use estimation to determine if you will haveenough to pay for your groceries when you get to the cashier.6. Estimate the answer by firstrounding each number to thenearest thousand.a. 5,2872,561888+4,898b. 7023,9441,001+3,500NoteIn Example 6 we areasked to estimatean answer, so it isokay to round the numbers inthe problem before adding them.In Example 5 we are asked for arounded answer, meaning that weare to find the exact answer to theproblem and then round to theindicated place. In that case wemust not round the numbers in theproblem before adding.SolutionWe round the items in our grocery cart off to the nearest dollar:wheat bread for $2.29 rounds to $2.00milk for $3.96 rounds to $4.00eggs for $2.18 rounds to $2.00apples for $1.19 rounds to $1.00+ cereal for $4.59 rounds to + $5.00$14.00We estimate our total to be $14.00. Thus, $20.00 will be enough to pay for thegroceries. (The actual cost of the groceries is $14.21.)Answer5. a. $10,140 b. $8,300c. $29,0006. a. 14,000 b. 10,000