Estimating Differences

Did you know it’s possible too to use rounding for estimating differences? At times whenever you do subtract between two large numbers, you do not wish to find out the precise differences. You only wish to know a fast estimate. It’s possible to get an estimate by rounding each of the numbers, then discovering a difference that’s near the precise difference.

Related Topics

• Estimating and Rounding
• Estimating Products
• Rounding Numbers

Ways to Estimate Differences to the Nearest Ten

Here is a fast review of the rules for rounding numbers.

STEP one: If the number one puts on the right of the targeted number was lower than (5), it gets rounded down ?

STEP two: If the digit to the right of the target place is (5) or higher, it gets rounded up ?

STEP three: Now it is possible to get the difference in-between these rounded numbers. Whenever the minuend and subtrahend in a subtraction equation are rounded, the subtraction gets easier.

Note: You merely must remember to maintain the difference near the precise answer

 Tip one: Unless it says something different, constantly round figures to the maximum feasible place value.

Tip two: You should pay attention to the fact we constantly write down the word “about” before the estimated difference. That shows you the result isn’t the precise answer, merely the estimate.

Estimating Differences – Example 1:

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$27.99 Original price was: $27.99.$17.99Current price is: $17.99.

Estimate differences by rounding each added to the nearest ten.

(85-34=)___

Solution:

First, round (85) to the closest ten. Check out the numeral on the right of the tens position. It is (5). So, (85) is rounded up to (90). Do the same for (34). Then (34) is rounded down to (30). Now subtract (30) from (90): (90-30=60)

Estimating Differences – Example 2:

Estimate differences by rounding each added to the nearest ten.

(53-26=)___

Solution:

First, round (53) to the closest ten. Check out the numeral on the right of the tens position. It is (3) and this number is lower than (5). So, (53) is rounded down to (50). Do the same for (26). Then (26) is rounded up to (30). Now subtract (30) from (50): (50-30=20)

Exercises for Estimating Differences

Estimate differences by rounding each added to the nearest ten.

1. (color{blue}{77-23})
2. (color{blue}{ 94-48 })
3. (color{blue}{35-12 })
4. (color{blue}{ 62-53 })

1. (color{blue}{60})
2. (color{blue}{ 40 })
3. (color{blue}{30 })
4. (color{blue}{ 10 })

Estimating Differences with Larger Numbers and Decimals

The steps are the same for any size of number. Round both numbers to the same place, then subtract.

1. Pick a place value. Use the place the problem asks for. If it does not say, round to the largest place that still makes sense.
2. Round both numbers to that place.
3. Subtract the rounded numbers.

Notice that rounding to a smaller place, such as tens instead of hundreds, usually gives an estimate closer to the exact answer.

Word Problem and Common Mistakes

Example: A school library has 512 books. 287 are checked out. About how many books are still on the shelves?

• Round to the nearest hundred: 500 − 300 = 200 books.
• Round to the nearest ten for a closer estimate: 510 − 290 = 220 books.
• Check: the exact answer is 512 − 287 = 225, so both estimates are reasonable.

Watch out for these mistakes:

• Rounding only one of the numbers.
• Rounding the two numbers to different places, such as one to tens and one to hundreds.
• Rounding a 5 down. When the digit to the right is 5 or more, round up.
• Writing the estimate as if it were exact. Use “about” or the ≈ sign.

Frequently Asked Questions

What does “estimate the difference” mean?

It means finding a number that is close to the answer of a subtraction problem without working it out exactly. You round the numbers first so the subtraction is easy to do in your head. For example, 68 − 21 is about 70 − 20, which is 50.

How do you estimate a difference by rounding to the nearest hundred?

Look at the tens digit of each number. If it is 5 or more, round up to the next hundred. If it is less than 5, round down. Then subtract the hundreds. For 863 − 418, round to 900 − 400, so the estimate is 500. The exact answer is 445.

What is an example of an estimated difference?

Say you have $95 and spend $38. Round to the nearest ten: $100 − $40 = $60. So you have about $60 left. The exact amount is $57, which is close to the estimate. That is how you can tell the estimate is reasonable.

Why is my estimate different from the exact answer?

Rounding changes the numbers a little, so the answer changes a little too. That is expected. An estimate only needs to be close. If your estimate and your exact answer are far apart, recheck both, because one of them probably has a mistake.

What is front-end estimation for subtraction?

In front-end estimation, you keep only the first digit of each number and replace the other digits with zeros, then subtract. For 6,815 − 2,370, you get 6,000 − 2,000 = 4,000. It is fast, but it is usually less accurate than rounding.