GED Mathematical Reasoning: Rounding and Estimating Decimals

Decimal Point Decimal Place Values
 . tenths hundredths thousandths ten-thousandths hundred-thousandths millionths

To the right of the decimal point and reading from left to right you have the tenths place, then the hundredths, thousandths, ten-thousandths, hundred-thousandths, and then the millionths place.

The process for rounding decimals is very similar to the process of rounding whole numbers.

  1. Identify the digit in the place value given and underline it
  2. Locate the digit directly to the right of that place value
  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 dropping all digits to the right of the underlined digit. 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 dropping all digits to the right of the underlined digit.

As a side note: You may recall that when rounding whole numbers, we would change all digits right of the underlined digit to zero. But we’re dealing with decimals here, where trailing zeros are unnecessary. That’s why we are able to simply drop all digits to the right.

 

Example 1

Round 0.368 to the nearest tenth.

 

We’ll first underline the digit in the tenths place. It is a 3. Then, look at the digit to the right. It is a 6. Since this digit is five or greater, we’ll round UP by increasing the 3 to a 4 and dropping all digits to the right. So our final answer is 0.4.

 

Example 2

On a quick trip to the grocery store, Paul purchased a loaf of bread costing $2.79, a container of orange juice costing $2.49, and a carton of eggs costing $2.29. Estimate the total amount of money Paul spent on these items.

  1. $10.00
  2. $9.00
  3. $8.00
  4. $7.00

 

To estimate with decimals, round to the nearest whole number before you add, subtract, multiply or divide. Referring back to our example, finding a total implies the use of addition. But before we add, let’s round each item’s cost to the nearest dollar.

$2.79 rounded to the nearest dollar is $3.00.

$2.49 rounded to the nearest dollar is $2.00

$2.29 rounded to the nearest dollar is $2.00

We can quickly add $3 plus $2 plus $2 to estimate Paul’s grocery bill to be about $7 – answer (4).

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