Estimation
Written by tutor Jeff S.
When we estimate, we’re making an educated guess. We’re using what we already know to make decisions about our data.
We estimate the answers to Math problems when our answers don’t have to be exact. For example, if you want to download mp3 songs from the Internet, you may need to purchase a gift card and add the points to your account before buying the music. If you want to buy six songs and each song costs between $.99 and $1.29 each, you can estimate the total cost of the songs to predict about how much money you’ll need.
This situation is an example of making an educated guess. You used what you already knew about the cost of the songs to guess the total cost so you could purchase the gift card. Estimating the cost helps you buy a gift card with enough money on it to pay for the downloads without leaving too much extra money in your account.
In order to estimate, we need to know how to round numbers. Below is an explanation of how to round numbers using the Common Method.
Rounding
When we round numbers, we either increase a number by 1 or leave it the same to make mental math easier. It also helps us to make some numbers easier to understand when we’re comparing sets of numbers.
One important thing to remember is that when we round numbers, our answers will not be as accurate as they would have if we had kept our original numbers.
Here’s how the Common Method of rounding works:
Step 1. Decide what number you want to keep. For example, if we want to know how many books we can buy for $15 or less and we’re comparing the prices of three books whose costs are $5.99, $4.98, and $7.99, we might decide to round to the nearest dollar. In that case, we’ll keep the 5, 4, and 7.
Step 2. Look at the number to the right of the number you decided to keep. If the number is a 5 or above, round the number you’re keeping up by adding 1. If the number is a 4 or less, round the number by keeping it the same.
In our book example, we round the prices to $6.00, $5.00, and $8.00 because the numbers to the right of the numbers we want to keep are above 5. That means we can buy the $6.00 and $5.00 books for under $15.00.
We round numbers when we estimate – just like in our book example above.
We wanted to know which books we could buy for less than $15, but we didn’t need to know the exact total cost. Estimation was close enough to give us the information we needed.
Estimation also helps us check our answers in Math. For example, if we add 1,540 to 575, we can round these two numbers to make checking our work easier. We could round the first number to 1,550 and the second to 580. These numbers are easier to add in our heads. When we add these numbers we get 2,130. If the answer we have is 2,800, we know we’ve gone wrong somewhere and we need to find our mistake.
You can also estimate decimal numbers. Use the two step Common Method of rounding. Decide what place (example: tenths, hundredths, etc.) you want to round your number to and use the number to the right of it and round up by adding 1 or round down by keeping it the same. Here are some examples of rounding to different decimal places (the number we need to round is in blue):
Number | Estimate | |
26.367 | round it to the tenths place. . . | 26.4 |
510.548 | round it to the hundredths place. . . | 510.55 |
49.6322 | round it to the thousandths place. . . | 49.632 |
Exercise 1. Use the Common Method to round each of the blue numbers below. Type your answer in the space given.
Answer: 360. The number to the right of the 5 is 6. Since it’s above a 5, we round the 5 up by adding 1. That gives us 360.
Answer: 2,800. The number to the right of the 7 is 5. Since it’s a 5 or above, we round the 7 up by adding 1. That gives us 2,800.
Answer: 500. The number to the right of the 5 is less than 5, so we round down by leaving it the same. That gives us 500.
Exercise 2. Read the situations below. Then, decide whether we can use estimation. Type “yes” in the box if we can estimate. Type “no” in the box if we can’t. Remember, when we estimate, our answers will not be as accurate as if we’d used the exact numbers.
Answer: Yes. We don’t need to know exactly how much flour is left to make our decision. We can subtract 4 cups of flour from the 12 – ^{1}/_{2} we had when we bought the bag and see that there are 8 – ½ cups of flour left. Then, we can multiply 3 by 2 and see that we’ll need 6 cups of flour for the bake sale cakes. Our measurement doesn’t need to be exact. As long as we know we have more than 6 cups of flour left, we know we don’t need to buy anymore.
Answer: No. The auditorium manager needs to know exactly how many “reserved” tickets are left for the report. If estimation is used, the board of directors may advertise that there are 100 “reserved” tickets when there are only 50! Customers may get angry if they learn that there aren’t enough tickets for their group.