In this section of our ParaPro Study Guide, we will cover rounding and its application in estimation. Rounding is beneficial when we have difficult calculations to work out without the help of a calculator, and it is an important concept to understand ahead of the ParaPro Exam.
Place Value and Rounding
Sometimes, in order to make calculations easier, we must make a number simpler while keeping it as close as possible to the original. We do this by rounding to a certain number of digits (or accuracy). To round a number, we need to know place values.
The value of a digit is based on its location in a number, or its place value. The chart below will help to identify the place value of each digit in a number.
Example 1
Identify the value of the underlined digits in the number 279.18.
7 is in the tens place. It represents 7 tens or 70.
8 is in the hundredths place. It represents 8 hundredths or 0.08.
How Do You Round Numbers?
A number can be rounded to any place value – the nearest tenth, whole (no decimals), ten, hundred, etc. – depending on the question or requirement. The method to round in each case is the same.
If we wish to round to the nearest ten, we must look at the ones digit. If the digit in the ones place is greater than or equal to 5, then we round up; if not, we round down. This can be remembered with the mnemonic five and up, bump it up; four and below, let it go.
When rounding up to the nearest ten, we replace all the digits to the right of the tens place with 0 and increase the tens digit by one. When rounding down to the nearest ten, we replace all the digits to the right of the tens place with 0 and leave the tens digit unchanged.
Let’s look at two examples.
Example 2
Round 45.32 to the nearest whole.
To round to the nearest whole means to round to the ones place, eliminating everything to the right of the decimal point.
Step 1: Check the digit to the right of the ones place (the tenths place).
Step 2: Compare tenths digit with 5. In this case, 3 < 5, so we want to round down.
Step 3: Replace all digits to the right of the decimal point with 0 and leave the ones digit unchanged.
The number after rounding to the nearest whole is 45.00 or simply 45.
Example 3
Round 176 to the nearest hundred.
Step 1: Check the digit to the right of hundreds place (the tens place).
Step 2: Compare the tens digit with 5. In this case, 7 > 5, so we want to round up.
Step 3: Replace all digits to the right of the hundreds place with 0 and increase the hundreds digit by 1.
The number after rounding to the nearest hundred is 200.
Estimation
Sometimes, we don’t have to find the exact value of a calculation and an estimate is sufficient. In such cases, we can use rounding to make the calculation simpler and thus work out an estimated answer.
The example below illustrates estimation.
Example 4
Estimate the value of 2.92 × 891.2.
Step 1: Round the numbers suitably to make the calculations simpler.
2.92 can be rounded to the nearest whole to get 3.
891.2 can be rounded to the nearest hundred to get 900.
Step 2: Perform the calculations.
3 × 900 = 2,700
Note that 2,700 is not the only estimate you can get by rounding. There are many ways you can round the numbers in the question. For instance, you may round 2.92 to 3 and 891.2 to 890. Then the estimate would change to 2,670.
Remember: in estimation, there’s no one correct answer. All answers depend upon how you round the numbers. The point of estimating is to make a quick calculation in your head for an equation that would otherwise need a calculator, so it is important to round in the manner that makes this possible. Be sure to check if the questions you encounter on the ParaPro Exam specify what place value you should be rounding to.
You should now have a firm grasp on place values, as well as how to use this knowledge for rounding numbers and estimating answers. Use the review test below to check how well you have understood this unit.