Estimation with Decimals

 

Learning Objective(s)

·         Estimate the answer to a decimal problem.

 

 

Being able to estimate your answer is a very useful skill. Not only will it help you decide if your answer is reasonable when doing homework problems or answering test questions, it can prove to be very helpful in everyday life. When shopping, you can estimate how much money you have spent, the tip for a restaurant bill, or the price of an item on sale. By rounding and then doing a quick calculation, you will at least know if you are close to the exact answer.

 

 

 

Consider this problem. Stewart wanted to buy a DVD home theater system that cost $345.23. He also wanted a universal remote priced at $32.90. He used a calculator to add the costs and the sum that he got was $674.23. He was surprised!

 

Whether Stewart can afford to spend $674.23 or not is not really the problem here. Rather, the problem is whether the system and remote would total $674.23. Round both item costs to the tens place: $345.23 is about $350, and $32.90 is about $30. Is $350 + $30 close to $674.23? Of course not!

 

Estimating an answer is a good skill to have. Even when using a calculator, you can get an incorrect answer by accidentally pressing a wrong button. When decimals are involved, it’s very easy to put the decimal point in the wrong place, and then your numbers can be drastically wrong.

 

 

 

You can use estimation to see if you have enough money for a purchase. In this case, it is best to round all the numbers up to make sure that you have enough money.

 

 

 

You will generally estimate when you compute the amount of tip to leave when you eat at a restaurant. Recall that an easy way to compute the tip is to double the tax. You can probably do this in your head, if you estimate this product by rounding to the nearest $1. You can round up if the service is good or round down if not.

 

 

When using rounding in addition and subtraction problems, you usually round all numbers to the same place value—this makes adding or subtracting a bit easier. However, when you use rounding to help you multiply or divide numbers, it’s usually better to round the numbers so they each have only one or two digits that are not 0. This is shown in the example below.

 

 

 

Evelyn is purchasing 287 ceramic tiles for her new kitchen. Each one costs $0.21. Which of the following is the most accurate estimate for the cost of purchasing the tiles for her kitchen?   A) $90   B) $60   C) $50   D) $40   Show/Hide Answer A) $90 Incorrect. You may have rounded 287 to 300 and then 0.21 to 0.30, to arrive at 300 · 0.30 = 90, or $90. This is too high; 0.21 rounds down to 0.20, not up to 0.30. The correct answer is $60.   B) $60 Correct. 287 rounds to 300, and 0.21 rounds to 0.20, to arrive at 300 · 0.20 = 60 or $60.   C) $50 Incorrect. You may have rounded 287 to 250 and then 0.21 to 0.20, to arrive at 250 · 0.20 = 50, or $50. This is too low; to the tens place 287 rounds up to 290 not down to 250. Then 290 · 0.20 = $58, the closest answer to this is the $60. The correct answer is $60.   D) $40 Incorrect. You may have rounded 287 to 200 and then 0.21 to 0.20, to arrive at 200 · 0.20 = 400, or $40. This is too low; to the hundreds place 287 rounds up to 300, not down to 200. The correct answer is $60.

 

 

Estimation is useful when you don’t need an exact answer. It also lets you check to be sure an exact answer is close to being correct. Estimating with decimals works just the same as estimating with whole numbers. When rounding the values to be added, subtracted, multiplied, or divided, it helps to round to numbers that are easy to work with.