An estimate is solution to a trouble that is close to the solution, yet not necessarily exact. Estimating can come in handy in a variety of situations, such together buying a computer. Friend may have to purchase numerous devices: a computer tower and keyboard for $1,295, a monitor because that $679, the printer for $486, the warranty because that $196, and software for $374. Estimating can help you know around how much you’ll spend without actually including those numbers exactly.

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Estimation usually needs rounding. Once you round a number, you find a brand-new number it is close come the initial one. A rounded number uses zeros for several of the place values. If you round to the nearest ten, friend will have a zero in the persons place. If you round to the nearest hundred, friend will have actually zeros in the ones and tens places. Because these location values are zero, including or individually is easier, so friend can find an calculation to an accurate answer quickly.

It is often valuable to calculation answers before calculating them. Climate if your answer is no close to her estimate, you understand something in her problem-solving process is wrong.


Using round off to estimate Sums and also Differences


Suppose girlfriend must add a collection of numbers. You deserve to round every addend come the nearest hundred to estimate the sum.


Example

Problem

Estimate the amount 1,472 + 398 + 772 + 164 by round off each number come the nearest hundred.

1,472….1,500

398……. 400

772……..800

164……..200

1,5 0 0

4 0 0

8 0 0

+ 2 0 0

2,9 0 0

First, round each number come the nearest hundred.

Then, include the rounded number together.

Answer The estimate is 2,900.


In the example above, the specific sum is 2,806. Note how close this is to the estimate, i m sorry is 94 greater.

In the instance below, an alert that round off to the nearest ten to produce a far an ext accurate estimate 보다 rounding come the nearest hundred. In general, rounding to the lesser location value is much more accurate, however it takes more steps.


Example

Problem

Estimate the amount 1,472 + 398 + 772 + 164 by very first rounding each number come the nearest ten.

1,472….1,470

398…….. 400

772……...770

164……...160

1 2

1 4 7 0

4 0 0

7 7 0

+ 1 6 0

0 0

1 2

1 4 7 0

4 0 0

7 7 0

+ 1 6 0

8 0 0

1 2

1 4 7 0

4 0 0

7 7 0

+ 1 6 0

2 8 0 0

First, round every number to the nearest ten.

Next, add the ones and also then the tens. Here, the amount of 7, 7, and 6 is 20. Regroup.

Now, add the hundreds. The sum of the digits in the hundreds place is 18. Regroup.

Finally, include the thousands. The sum in the thousands ar is 2.

Answer The calculation is 2,800.


Note that the estimate is 2,800, which is just 6 much less than the actual amount of 2,806.

In 3 months, a freelance graphics artist earns $1,290 for depicting comic books, $2,612 for designing logos, and also $4,175 for designing web sites. Estimate just how much she deserve in total by an initial rounding every number to the nearest hundred.

A) $8,200

B) $7,900

C) $8,000

D) $8,100


Show/Hide Answer

A) $8,200

Incorrect. You more than likely rounded one or an ext numbers up as soon as you should have rounded them down. The exactly answer is $8,100.

B) $7,900

Incorrect. You most likely rounded one or more numbers down as soon as you should have rounded them up. The exactly answer is $8,100.

C) $8,000

Incorrect. You probably rounded each number to the nearest thousand rather of come the nearest hundred before adding. The correct answer is $8,100.

D) $8,100

Correct. You most likely rounded the number to $1,300, $2,600, and also $4,200 and added them with each other successfully.

You can likewise estimate as soon as you subtract, together in the instance below. Since you round, you perform not have to subtract in the tens or hundreds places.


Example

Problem

Estimate the distinction of 5,876 and also 4,792 by first rounding each number to the nearest hundred.

5,876….5,900

4,792….4,800

5,9 0 0

– 4,8 0 0

1,1 0 0

First, round every number to the nearest hundred.

Subtract. No regrouping is needed because each number in the minuend is greater than or same to the equivalent number in the subtrahend.

Answer

The estimate is 1,100.


The estimate is 1,100, which is 16 higher than the actual distinction of 1,084.

Estimate the distinction of 474,128 and also 262,767 by rounding to the nearest thousand.

A) 212,000

B) 211,000

C) 737,000

D) 447,700


Show/Hide Answer

A) 212,000

Incorrect. You more than likely rounded 474,128 approximately 475,000 when you should have rounded it under to 474,000. The exactly answer is 211,000.

B) 211,000

Correct. You most likely rounded the number to 474,000 and 263,000 and also subtracted successfully.

C) 737,000

Incorrect. You probably included instead of subtracting. The correct answer is 211,000.

D) 447,700

Incorrect. You most likely used 26,300 rather of 263,000 as the number the you subtracted indigenous 474,000. The exactly answer is 211,000.

Solving Application troubles by Estimating


Estimating is handy once you desire to be sure you have sufficient money come buy numerous things.


Example

Problem

When buying a brand-new computer, you discover that the computer tower and keyboard price $1,295, the monitor expenses $679, the printer prices $486, the 2-year warranty expenses $196, and a software application package prices $374. Estimate the total cost by an initial rounding every number to the nearest hundred.

1,295….1,300

679…….. 700

486……...500

196……...200

374……...400

2

1 3 0 0

7 0 0

5 0 0

2 0 0

+ 4 0 0

3,1 0 0

First, round each number come the nearest hundred.

Add.

After adding all the the rounded values, the approximated answer is $3,100.

Answer The complete cost is around $3,100.


Estimating can also be beneficial when calculating the total distance one travels over numerous trips.


Example

Problem

James travels 3,247 m to the park, climate 582 m come the store. He then travels 1,634 m earlier to his house. Discover the full distance traveled by first rounding each number come the nearest ten.

3247…..3,250

582…….580

1634…. 1,630

1

3 2 5 0

5 8 0

+ 1 6 3 0

6 0

1 1

3 2 5 0

5 8 0

+ 1 6 3 0

4 6 0

1 1

3 2 5 0

5 8 0

+ 1 6 3 0

5,4 6 0

First, round each number come the nearest ten.

Adding the numbers in the tens place offers 16, therefore you must regroup.

Adding the number in the hundreds place provides 14, therefore regroup.

Adding the numbers in the thousands place gives 5.

Answer The total distance traveled was around 5,460 meters.


In the example above, the last estimate is 5,460 meters, i beg your pardon is 3 less than the actual amount of 5,463 meters.

Estimating is also effective once you are trying to discover the difference in between two numbers. Problems managing mountains prefer the example listed below may be essential to a meteorologist, a pilot, or someone that is producing a map that a offered region. Together in other problems, estimating beforehand can assist you find response that is close come the precise value, staying clear of potential errors in your calculations.


Example

Problem

One mountain is 10,496 feet high and also another hill is 7,421 feet high. Find the difference in elevation by first rounding every number to the nearest 100.

10,496….10,500

7,421… ..7,400

1 0 5 0 0

– 7 4 0 0

3,1 0 0

First, round each number to the nearest hundred.

Then, align the numbers and subtract.

The final estimate is 3,100, i beg your pardon is 25 higher than the actual value of 3,075.

Answer The estimated distinction in height between the two mountains is 3,100 feet.


A space shuttle traveling at 17,581 miles every hour decreases its rate by 7,412 miles every hour. Calculation the rate of the space shuttle after ~ it has actually slowed under by rounding each number to the nearest hundred.

A) 10,100 mi/h

B) 10,200 mi/h

C) 25,000 mi/h

D) 25,100 mi/h


Show/Hide Answer

A) 10,100 mi/h

Incorrect. You more than likely rounded the subtrahend increase or the minuend down. Girlfriend should have rounded the subtrahend the 7,412 down to 7,400 and the minuend the 17,581 up to 17,600. The correct answer is 10,200.

B) 10,200 mi/h

Correct. You appropriately rounded both numbers and also subtracted castle successfully.

C) 25,000 mi/h

Incorrect. Girlfriend probably included when you should have subtracted. The correct answer is 10,200.

D) 25,100 mi/h

Incorrect. You most likely rounded wrongly and added when girlfriend should have subtracted. The correct answer is 10,200.

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Summary


Estimation is really useful when specific answer is no required. You can use estimation for problems related come travel, finances, and also data analysis. Estimating is frequently done before including or individually by round off to numbers that are simpler to think about. Complying with the rules of round off is crucial to the practice of accurate estimation.