# GED Mathematical Reasoning: Rounding and Estimating

**Example 1:**

Round to the nearest ten: 459

Let’s talk a bit about rounding and estimating before completing this example.

It is often useful to estimate when an exact answer is not necessary or when you are attempting to evaluate the reasonableness or accuracy of a result.

Here are some phrases to illustrate the use of an estimate:

When you ask someone for directions, she might say: “It’s about ten miles down on the right side.”

When a friend tells you how much he paid for his new car, he might say: “I paid close to $12,000.”

When a blogger references her website, she might say: “It gets, on average, 100 hits a day.”

When you consider your monthly salary, you may think: “I make approximately $3,000 per month.”

We can use __rounding__ as a tool to calculate estimates, like these examples. To do so, we follow a set of steps to __round__ individual values. And then use those rounded values to create an estimate result. The benefit is that using __rounded__ values often makes our calculations __easier__ because rounded values usually contain more zeros.

Here are the steps for rounding. By the way, when you are formally asked to round a number, a place value will be provided.

STEP 1. Identify the digit in the place value given – underline it

STEP 2. Locate the digit directly to the right of that place value

STEP 3. If the digit in step 2 is 0, 1, 2, 3, or 4 (in other words, less than 5) we “round down” by keeping the underlined place value digit the SAME and changing all digits to the right of the underlined digit to zero. If the digit in step 2 is 5 or greater (in other words 5, 6, 7, 8 or 9), we “round up” by increasing the underlined place value digit by 1 and changing all digits to the right of the underlined digit to zero.

To apply this process to our first example and round 459 to the nearest tens place:

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

Now let’s see an example of how rounding can play a part in finding an estimate.

**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?

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 D. 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?

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 B. Therefore, Ben has approximately 200 miles left to drive.