Introduction

In this lesson, you will learn how to estimate answers by rounding.

When you’re in a hurry or don’t have a pen and paper, rounding can help you estimate harder arithmetic problems. This skill will help when quickly trying to see if you can afford everything on your grocery list or what this month’s budget adds up to. This is done by rounding to the highest place value you see (356 → 400 and 22.4 → 20). Then, addition and subtraction can be done on these rounded values much easier. The answer you get won’t be exact, but it will be a good estimate.

This video illustrates the lesson material below. Watching the video is optional.

• Estimating Answers Using Rounding (03:45 mins) | Transcript

Front-end Rounding

Front-end rounding is when you round to the largest place value.

Example 1

To round 2387, the thousands place is the largest place value, so this is the number you would round to. To do this, look to the next place value, which is a 3. This 3 tells us it is closer to 2000 than to 3000, so you would round down to 2000.

Example 2

To round 46, the tens place is the largest place value, so you would round to the tens place. The next place value is 6, so you would round up to 50.

Example 3

To round the number 983, the hundreds place is the largest place value, so this would be the number you would round. The next place value is 8, so this tells you to round up. In this case, rounding up brings it to 1000, which is ten hundreds.

Figure 1

Using Front-end Rounding to Estimate an Answer

Example 4

If you have the equation \(3791+532\) and you just need an approximate answer, first round each of these numbers, then add. Beginning with 3791, the seven tells you to round up to 4000. For 532, the three tells you to round down to 500. Now the equation is \(4000+500=4500\). This is a quick way to get an estimate of an otherwise more difficult problem. The actual answer is 4323, and the estimate is 4500. The estimate is close.

Figure 2

Example 5
\(43.75+56.12\)

The first number rounds to 40 and the second number rounds to 60. The result of this would be \(40+60=100\). 100 is a close approximation to the actual answer you would get, 99.87, if you solved the problem with the regular algorithm.

Figure 3

Example 6
\(527−789\)

This example is different because instead of adding, you are subtracting, and the answer will be negative because the larger number is negative. 527 rounds to 500, and 789 rounds to 800. The new equation is \(500−800=−300\). Again, this is not the exact answer, but it is close, and in this case, you are just looking for a close approximation.

Figure 4

Things to Remember

• Front-end rounding is rounding to the largest place value.
• Look at the next largest place value to determine if you need to round up or down.
• Although rounding is quicker, rounding will not give you exact answers, only approximate answers.

Practice Problems

1. What is the result when front-end rounding is applied to the number 35,073.290? (
   Solution

   x

   Solution: 40,000
   Details:
   Round to the highest place value, when using front-end rounding. The number 3 has the highest place value.
   \({\color{red}3}5,073.290\)
   
   To determine if 3 is to be rounded up or left unchanged, look to the right of 3 at the number 5.
   \({\color{red}3}{\color{orange}5},073.290\)
   
   Consider the position of the number 5 in the number line. The number 5 is in the middle of 0 and 10.
   
   
   Numbers 5 and greater indicate you should round up.
   
   The number 3 will increase to 4. All the numbers to the right become zeros.
   \({\color{red}4}{\color{orange}0},000.000\)
   
   The rounded answer is 40,000. (It is mathematically acceptable to drop all zeros after the decimal.)
   )Use rounding to estimate the solution to the problems:
2. \(26.37 + 61.72 = ?\) (
   Solution

   x

   Solution: 90
   Details:
   

   • 26.37 rounds to 30.
   • 61.72 rounds to 60.
   • So, \(26.37 + 61.72\) can be estimated: \(30 + 60 = 90\)
   )
3. \(739.6 + 479.6 = ?\) (
   Video Solution

   x

   Solution: 1200
   Details:
   

   
   (Estimate the Results of an Arithmetic Operation #3 (01:19 mins) | Transcript)
   | Transcript)
4. \(6.6 − 2.5 = ?\) (
   Solution

   x

   Solution: 4
   Details:
   

   • 6.6 rounds to 7.
   • 2.5 rounds to 3.
   • So, \(6.6 - 2.5\) can be estimated: \(7 − 3 = 4\)
   )
5. \(39.225 − 13.581 = ?\) (
   Solution

   x

   Solution: 30
   Details:
   

   • 39.225 rounds to 40.
   • 13.581 rounds to 10.
   • So, \(39.225 - 13.581\) can be estimated: \(40 − 10 = 30\)
   )
6. \(3299.06 − 5323.11 = ?\) (
   Video Solution

   x

   Solution: -2000
   Details:
   

   
   (Estimate the Results of an Arithmetic Operation #6 (01:35 mins) | Transcript)
   | Transcript)

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