Executive Assessment Rounding Rules

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You have likely encountered a question on a homework problem or test that involves rounding to the nearest tenth, or even worse, being told to “round your answer to the nearest hundredth.” Learning decimal rounding rules is an important skill, and it’s quite important for getting a great score on the Quant section of the Executive Assessment (EA). For example, you may encounter an EA Quant question asking you to round your answer to the nearest integer. If you don’t know how to round correctly, you could very well miss the question.

In this article, we’ll present the rounding rules and some examples, and we’ll provide you with Executive Assessment Quant rounding tips as well.

Here are the topics we’ll cover:

• What Is an Integer?
• Decimal Numbers and Place Value
• Rounding to the Nearest Integer
  • Rounding to the Nearest Integer Quick Practice
• Two Special Situations for Integer Rounding
  • Rounding an Integer Up when the Number Has a 9 in the Ones Place
  • Rounding If the Only Digit to the Left of the Decimal Point Is 0
• Practice Problems: Rounding to the Nearest Integer
  • Example 1: Rounding to the Nearest Integer
  • Example 2: Rounding to the Nearest Integer
• How to Round Decimals
  • Place Value Rounding
    • Additional Examples of Place Value Rounding
  • Rounding the Digit 9
  • Example 3: Place Value Rounding
• Summary
• Frequently Asked Questions (FAQ)
  • Why Do We Round Decimals?
  • What Do I Do If the Number after the Rounding Place Is a 5?
  • Is Decimal Rounding the Same as Rounding Whole Numbers?
• What’s Next?

Let’s start with some important definitions.

What Is an Integer?

The most basic type of rounding problem involves rounding a number to the nearest integer. Before you can do that correctly, you need to understand what an integer is.

An integer is any number that can be written without a fractional or decimal part. Examples of integers include -62, -17, -2, -1, 0, 6, 95, and 230.

Numbers such as 1.34, -2/5, 0.8, and π are not integers because they contain decimals or fractions. Note that numbers like 3.00 or -7.0 are considered integers. They can be re-expressed as a whole number without a decimal.

Let’s review some key terms related to integers.

Positive integers are all integers greater than or equal to 1. They are 1, 2, 3, and so on.

Negative integers are all integers less than or equal to –1. They are  –1,  –2,  –3, and so on.

Remember, 0 is neither positive nor negative. Therefore, when we refer to nonnegative integers, we mean all positive integers along with zero: 0, 1, 2, 3, and so on.

Decimal Numbers and Place Value

To round a number to the nearest integer, it is helpful to first understand what a decimal number is. A decimal number is any number that includes a decimal point — for instance, 3.10, 5.992, or 4.5.

Each digit in a decimal number has a place value, which represents a power of 10. Moving 1 place to the left multiplies the value by 10, while moving 1 place to the right divides it by 10. To the left of the decimal point, the place values are ones, tens, hundreds, and so on. To the right, they are tenths, hundredths, thousandths, and so forth. The table below shows how these place values are arranged:

Thousands	Hundreds	Tens	Ones (Units)	Decimal Point	Tenths	Hundredths	Thousandths
1,000	100	10	1	.	0.1	0.01	0.001

Being able to identify place values quickly is essential when applying rounding rules. After all, you can’t round a decimal to the nearest hundredth unless you know exactly where the hundredth place is.

Rounding to the Nearest Integer

Rounding a decimal to the nearest whole number (or integer) means focusing on the digit immediately to the right of the ones place, which is the tenths place. When we round to the nearest integer, we check this tenths digit to decide whether to increase the ones digit or leave it as is.

For instance, to round 24.8 to the nearest integer, we look at the tenths digit (8). After rounding, our answer will be either 24 (rounded down) or 25 (rounded up).

Here are the rounding rules:

Round Up: If the tenths digit is 5, 6, 7, 8, or 9, round up the ones digit.

Round Down: If the tenths digit is 0, 1, 2, 3, or 4, we do not round up; we keep the ones digit the same (sometimes called “rounding down”).

We see that 24.8 will be rounded up to 25 because the tenths digit is 8.

Rounding to the Nearest Integer Quick Practice

Let’s look at 2 basic rounding examples.

• When rounding 15.9 to the nearest integer, we focus on the digit in the tenths place, which is 9. Because this digit is 5 or greater, we increase the ones digit from 5 to 6. Therefore, 15.9 rounded to the nearest integer is 16.
• When rounding 7.3 to the nearest integer, the tenths digit is 3. Since this is less than 5, we keep the ones digit as it is. Thus, 7.3 rounded to the nearest integer remains 7.

When you’re rounding to the nearest integer, only the digit in the tenths place matters. Ignore all other digits to the right of the decimal point, except for the digit in the tenths place.

For instance, to round 61.899455 to the nearest integer, we look solely at the tenths digit, which is 8. Because it is 5 or greater, we round up to get 62.

Two Special Situations for Integer Rounding

Rounding an Integer Up when the Number Has a 9 in the Ones Place

If rounding to the nearest integer seems simple, don’t get too confident yet! There are a few additional rounding cases you should understand.

For example, let’s round 29.57 to the nearest integer. The digit in the tenths place is 5, so we know we need to round up. However, the ones digit is 9, so rounding up will push it to 10. In this situation, we change the 9 to 0 and increase the tens digit by 1. As a result, 29.57, rounded to the nearest integer, is 30.

Rounding If the Only Digit to the Left of the Decimal Point Is 0

Another rounding scenario that can feel confusing is when a number has a 0 in the ones place, such as 0.9 or 0.3, and you’re asked to round to the nearest integer.

For 0.9, since the tenths digit is 9, we round up to get 1.

For 0.3, the tenths digit is 3, so we do not round up, and the rounded result is 0. It might seem odd to say that something like 0.4 rounds to “nothing,” but remember that 0.4 is closer to 0 than it is to 1. Thus, rounding it to 0 is both accurate and logical.

Let’s practice some examples of rounding to the nearest integer.

Practice Problems: Rounding to the Nearest Integer

Let’s make sure we are solid on the use of the rounding rules for rounding to the nearest integer.

How to Round Decimals

The good news is that rounding decimal numbers follows the same basic process as rounding to the nearest integer. The key is to pay attention to the specific decimal place you’re rounding to.

Also, keep in mind that the rounding rules explained here apply to all EA problems involving decimals. You won’t encounter any unusual methods such as “round half up,” “round half down,” or “round half to odd” on the test.

Place Value Rounding

To ensure your mastery, let’s look at some Executive Assessment decimal rounding examples.

• We want to round the decimal number 37.2087 to the nearest hundredth. The digit in the hundredth position is 0. Now, the digit to the right of 0 is 8, which is in the thousandths place. Because its value is 8, we know to round the 0 up to 1. So, when we round 37.2087 to the nearest hundredth, the answer is 37.21.

In this example, note that after the rounding to the nearest hundredth is done, all extraneous digits are dropped. So, any digits beyond the hundredth place will not be part of the rounded number.

• If we round 14.5289 to the nearest tenth, we see that the digit in the tenths place is 5. The digit to its right is 2, meaning that we do not round up the 5. Thus, rounded to the nearest tenth, the number is 14.5.

 Note that we eliminated all digits past the tenths place after the rounding was completed.

Additional Examples of Place Value Rounding

• We want to round the decimal 29.1091 to the nearest hundredth. The digit in the hundredths place is 0, and the digit immediately to its right (in the thousandths place) is 9. Since 9 is greater than or equal to 5, we round the 0 up to 1. Therefore, when 29.1091 is rounded to the nearest hundredth, the result is 29.11.

After rounding, we drop all digits beyond the hundredth place. These digits no longer appear in the rounded number.

• Now, let’s round 11.6178 to the nearest tenth. The digit in the tenths place is 6, and the digit to its right is 1. Because 1 is less than 5, we do not round the 6 up. Thus, rounded to the nearest tenth, the number is 11.6.

Again, we remove all digits beyond the tenths place once the rounding is complete.

Rounding the Digit 9

Earlier, we saw that a decimal number such as 39.6, rounded to the nearest integer, results in rounding up the 9 to 10. Thus, the digit 9 in the ones place becomes 0, and the number 3 in the tens place must be increased by 1 to become 4. So, when we round 39.6 to the nearest integer, we obtain 40.

We use the same logic for rounding decimal places with a 9, and it doesn’t matter where the 9 is located. For example, to round the number 21.397 to the nearest hundredth, we see that the digit to the right of the 9 is 7. Thus, we will round up. The 9 in the (current) hundredths place must be rounded up to 10, so the hundredths place will now contain a 0, and the tenths place will increase from 3 to 4. Therefore, we round 21.397 to 21.40.

Note: In the above example, the rounded number of 21.40 could be re-expressed as 21.4. But because we needed to round to the nearest hundredth, we should leave the answer as 21.40.

Let’s try another example.

Summary

• An integer is a whole number that does not include a decimal point or a fractional part. An integer can be positive, negative, or zero.
• In a number, the place values to the left of the decimal point are ones, tens, hundreds, and so on. To the right of the decimal point, they are tenths, hundredths, and thousandths, and so on.
• When rounding to a specific place value, look at the digit immediately to its right. If that digit is 5, 6, 7, 8, or 9, round up. If it is 0, 1, 2, 3, or 4, leave the digit as is.
• These same rounding rules apply whether you are rounding whole numbers or decimal numbers.

Frequently Asked Questions (FAQ)

Why Do We Round Decimals?

Rounding numbers makes it easier to interpret data and perform calculations with them.

What Do I Do If the Number after the Rounding Place Is a 5?

Round up if the number after the rounding place is 5, 6, 7, 8, or 9.

Is Decimal Rounding the Same as Rounding Whole Numbers?

Rounding whole numbers is a special case of the more general decimal rounding. Rounding whole numbers refers to rounding to the nearest integer, whereas in decimal rounding, you can round to the nearest hundred, ten, one, tenth, hundredth, etc.

What’s Next?

It’s important to know how to round numbers for your Executive Assessment preparation. Rounding is an essential skill. However, you should be familiar with all the EA Quant topics you’ll need to master to reach your target score.

Follow these EA Quant tips to craft a great study plan and get the most out of your valuable study time.