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Whole Numbers

# GED Mathematical Reasoning: Rounding and Estimating Whole Numbers

Example 1

Round to the nearest ten:  459

We’ll first underline the digit in the tens place – it is a 5

The digit to the right of the tens place is a 9

For step 3, since the value of the digit in step 2 is 5 or greater, we round UP. We add one to the 5, so the 5 becomes a 6, and each digit to the right – the 9 – changes to a zero. The final, rounded, result is: 460

Example 2

Round to the nearest thousand:  238,467

First, we’ll underline the digit in the thousands place – it is an 8

The digit to the right of the thousands place is a 4

For step 3, since the value of the digit in step 2 is a 4, we round DOWN. The 8 stays the same and each digit to the right – the 4, 6 and 7 – change to zeros. The final, rounded, result is: 238,000

Example 3

Round to the nearest ten dollars:  \$46.73

First underline the digit in the ten dollars place – it is a 4

The digit to the right of the ten dollars place is a 6

For step 3, since the value of the digit in step 2 is 5 or greater, we round UP. We add one to the 4, making the 4 a 5, and each digit to the right changes to a zero. The final, rounded, result is: \$50.00

Example 4

To re-paint her home, Lori will purchase 18 gallons of paint costing \$27.36 per gallon. What is the best estimate of the total cost of the paint?

1. \$300
2. \$400
3. \$500
4. \$600

To calculate the total cost of 18 gallons of paint given the price of each gallon, we will multiply. We are being asked to find an estimate, not the exact cost. The process, then, is to first round each value given and then use those rounded values to calculate the estimated cost.

Remember: we round FIRST, before multiplying. Rounding after multiplying with the exact numbers defeats the purpose of rounding, which is to make the calculation a bit easier.

And one final note: Like in this example, in the “real world” we are usually not given a place value for rounding. As a rule of thumb, we’ll round according to each number’s highest place value.

So…

18 gallons of paint, rounded to the highest place value of the tens place, is 20.

\$27.36 rounded to the highest place value of the ten dollars place is \$30.00.

We’ll multiply 20 by 30, which is \$600 – answer (4). Therefore, Lori can expect to pay approximately \$600 for the paint she needs.

Example 5

Ben has driven 789 miles of the 1,296 miles he needs to drive to reach his destination. What is the best estimate of the number of miles Ben has left to drive?

1. 100 miles
2. 200 miles
3. 500 miles
4. 600 miles

To calculate the number of miles Ben has left to drive we’ll subtract, but before we do so let’s round the values given.

789 miles, rounded to the highest place value of the hundreds place, is 800.

1,296 rounded to the highest place value of the thousands place is 1,000.

Now, we subtract 800 from 1000, which yields an answer of 200 miles – answer (2). Therefore, Ben has approximately 200 miles left to drive.

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