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7.3 Whole numbers: rounding

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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to round whole numbers. By the end of the module students should be able to understand that rounding is a method of approximation and round a whole number to a specified position.

Section overview

  • Rounding as an Approximation
  • The Method of Rounding Numbers

Rounding as an approximation

A primary use of whole numbers is to keep count of how many objects there are in a collection. Sometimes we're only interested in the approximate number of objects in the collection rather than the precise number. For example, there are approxi­mately 20 symbols in the collection below.

An arrangement of symbols.

The precise number of symbols in the above collection is 18.

Rounding

We often approximate the number of objects in a collection by mentally seeing the collection as occurring in groups of tens, hundreds, thousands, etc. This process of approximation is called rounding . Rounding is very useful in estimation. We will study estimation in Chapter 8.

When we think of a collection as occurring in groups of tens, we say we're rounding to the nearest ten . When we think of a collection as occurring in groups of hundreds, we say we're rounding to the nearest hundred . This idea of rounding continues through thousands, ten thousands, hundred thousands, millions, etc.

The process of rounding whole numbers is illustrated in the following examples.

Round 67 to the nearest ten.

On the number line, 67 is more than halfway from 60 to 70. The digit immedi­ately to the right of the tens digit, the round-off digit, is the indicator for this.

A number line from 0 to 70. At the dash for the number sixty is a label, 6 tens. At the dash for 70 is a label, 7 tens. In between the two dashes is a dot on the number 67. Below, is a statement. 67 is closer to 7 tens than it is to 6 tens.

Thus, 67, rounded to the nearest ten, is 70.

Round 4,329 to the nearest hundred.

On the number line, 4,329 is less than halfway from 4,300 to 4,400. The digit to the immediate right of the hundreds digit, the round-off digit, is the indicator.

A number line from 0 to 4,400. The mark for 4,300 is labeled, 3 hundreds. The mark for 4,400 is labeled, 4 hundreds. A dot on the number 4,329 is in between the two marks. Below the number line is a statement. 4,329 is closer to 43 hundreds than it is to 44 hundreds.

Thus, 4,329, rounded to the nearest hundred is 4,300.

Round 16,500 to the nearest thousand.

On the number line, 16,500 is exactly halfway from 16,000 to 17,000.

A number line from 0 to 17,000. The 16,000 mark is labeled, 6 thousands. The 17,000 mark is labeled, 7 thousands. In between the two marks is a dot on the number 16,500.

By convention, when the number to be rounded is exactly halfway between two numbers, it is rounded to the higher number.

Thus, 16,500, rounded to the nearest thousand, is 17,000.

A person whose salary is $41,450 per year might tell a friend that she makes $41,000 per year. She has rounded 41,450 to the nearest thousand. The number 41,450 is closer to 41,000 than it is to 42,000.

The method of rounding whole numbers

From the observations made in the preceding examples, we can use the following method to round a whole number to a particular position.

  1. Mark the position of the round-off digit.
  2. Note the digit to the immediate right of the round-off digit.
    1. If it is less than 5, replace it and all the digits to its right with zeros. Leave the round-off digit unchanged.
    2. If it is 5 or larger, replace it and all the digits to its right with zeros. Increase the round-off digit by 1.

Sample set a

Use the method of rounding whole numbers to solve the following problems.

Round 3,426 to the nearest ten.

  1. We are rounding to the tens position. Mark the digit in the tens position
    3,426, with the 2 labeled, tens position.
  2. Observe the digit immediately to the right of the tens position. It is 6. Since 6 is greater than 5, we round up by replacing 6 with 0 and adding 1 to the digit in the tens position (the round-off position): 2 + 1 = 3 .
    3,430

Thus, 3,426 rounded to the nearest ten is 3,430.

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Source:  OpenStax, Contemporary math applications. OpenStax CNX. Dec 15, 2014 Download for free at http://legacy.cnx.org/content/col11559/1.6
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