1-3 Estimating by Rounding Up or Rounding Down 1-4 Estimating by Rounding to the Nearest Round any decimal up or down. Round any decimal to the nearest value of a decimal place. On August 29, 2005, Hurricane Katrina ripped through Louisiana with a Category 5 storm. The hurricane caused severe devastation in 80% of the major coastal cities. The damage was estimated at $76 billion, and about 1,600 people lost their lives. What are some other examples of a situation where an estimate might be preferred over an exact value?
Why are estimates needed? 1.An exact value may not be worth the trouble it would take to get it. For example: About 30,000 people attended the baseball game. 2.An estimation is often easier to work with than the exact value. For example: Instead of multiplying $169.95, let's use $170. 3.It may be safer to use an estimate than to try to use an exact value. For example: The home repairs will cost at least $18,000 as a result of the hurricane. So we will budget $20,000 to play it safe. 4.An exact value may change from time to time, forcing an estimate. For example: I estimate that the coin will land tails 5 times in 10 tosses. 5. Predictions of the future or notions about the past usually are estimates, since exact values may be impossible to obtain. For example: One estimate of the world population in the year 2025 is 12 billion.
4 Methods of Rounding **Rounding is the most common way of estimating.** *Rounding is done with a particular decimal place in mind.** Rounding UP - "to the next;" going to the higher point of the interval Rounding DOWN - "to the preceding;" going to the lower point of the interval Truncate - round down, or cut off 1325 1400 1300 900 1325 Truncated to the tens place: 1320 **Some calculators truncate long decimals to the preceding millionth (6 decimal place). For example: π = 3.1415926535 a calculator might truncate it to show 3.141592 Rounding to the NEAREST - given a decimal place, look to the value after it: if the value is 5 or greater, round up to the next number if the value is 4 or less, truncate Round 1325 to the nearest ten: 1330 Round 1325 to the nearest thousand: 1000
Round up or down. Example 1: Round 10.4554 up to the next ten. Round 10.4554 down to the previous tenth.
Round to the nearest. 4 or less, round down (truncate) 5 or greater round up (next) Example 2: 465,877,912.556 734 603 Round to the nearest million. Round to the nearest tenth. Round to the nearest ten thousandths. Round to the nearest unit.
What method should you use? Example 3: A certain type of CD-RWs are available only in 15 count packages. How many packages would you need to buy if you were to make a copy of your debut performance for each of your 110 classmates? Example 4: A cargo plane can carry 10,500 lbs. What weight limit may be placed on the cargo to be sure that the actual limit is not exceeded? Example 5: Pencils are sold in packages of 10. I need one pencil for each student in a class of 27. How many pencils must be bought? Example 6: The product of 0.1349 and 0.00024 is 0.000032376. What will a calculator with an 8-digit display and that rounds show for the answer? Example 7: My savings account earns monthly interest. My bank rounds down any fractions of a cent on interest paid on a savings account. How much interest would be paid if the calculated amount is $75.625? Example 8: Giant Eagle sells avocados at three for $1. You want just one. So you divide $1.00 by 3 to get the cost. Your calculator shows 0.333333. How must will you probably have to pay for the avocado? Example 9: The U.S. Interval Revenue Service allows taxpayers to round all amounts to the nearest dollar. In figuring income tax, to what value can you round each amount? a. $89.46 b. $165.50 c. $100.91 d. $5,324.28 Example 10: Avatar blue-ray costs $27.49 and John wants to buy 7. How he can use rounding to estimate the cost? Example 11: The total U.S. population as of 3:04pm on Sunday, September 12, 2010, was 310,230,947. Round this number to the nearest ten thousand.