Lesson 4 — Activity 1: Rounding Decimal Numbers


Getting Ready:


You looked briefly at decimal numbers when you were completing work on scientific notation. Let’s now look more closely at decimal numbers.


Here’s the place values for this decimal number:


This image shows the place values of this decimal number.

Try This:


Identify the place value of the underlined digit in the following numbers:

  • 3,456.578


  • 775,525.027


  • 32,194.647



  • 3,456.578: 5 is in the tenths place
  • 775,525.027: 7 is in the thousandths place
  • 32,194.647: 4 is in the hundredths place


Rounding decimal numbers is a good strategy to use when estimating amounts, such as the cost of items in a store.


Let’s first practise rounding decimal numbers to the nearest whole number:



If you saw an item in a store marked $8.56, you could do the following:


When rounding to the nearest whole number, begin by looking at the tenths place in the decimal number:
 
  • In the number 8.56, underline the number in the tenths place (the number 5 is in the tenths place).
  • If the underlined number is 4 or less, leave the number as it is; if the underlined number is 5 or greater, round up to the next whole number.
  • In this example, the underlined number is 5, so you would round up to the next whole number, which is 9.
  • $8.56 becomes $9.00 when rounded.

Now Try This:


Say you were looking at another item in a store and it was marked at $16.30.

Do the following:

  • Underline the number in the tenths place.
  • If the underlined number is 4 or less, leave the number as it is; if the underlined number is 5 or greater, round up to the next whole number.
  • What is $16.30 rounded to the nearest whole number?

  • You should have underlined the 3 as it is in the tenths place.
  • Since the 3, is 4 or less, you would leave the number as it is.
  • $16.30 rounded to the nearest whole number is $16.00.




Let's look now at further rounding of decimal numbers. First to the nearest tenths, then to the nearest hundredths.

Rounding to the Nearest Tenths


Michael works at a stockyard. His job is to weigh each of the calves as they are brought in. He must record the mass of each calf to the nearest tenths of a kilogram.

Calf #1 has a mass of 87.370 kg. Follow these steps to round:
  • In the number 87.370, underline the 3 which is in the tenths place.
  • Now look at the number to the right of the underlined number: see if it is 50 or greater or 49 or less.
  • In 87.370, 70 follows the underlined number and because it is 50 or greater, the 3 in the tenths place becomes a 4.
  • 87.370 rounded to the nearest tenths is 87.4.


What if the number is 49 or less: Let's look at Calf #2, which has a mass of 75.246 kg:
  • Underline the number in the tenths place: 75.246.
  • Look at the number to the right of the 2: see if it's 49 or less or 50 or greater.
  • It's 46, which is 49 or less, so in this case, drop that number and the tenths place remains the same.
  • 75.246 rounded to the nearest tenths is 75.2.


Rounding to the Nearest Hundredths

    Ski races uses hundredths to measure times.

In downhill skiing competitions, times are often only hundredths of a second apart.
Let's look at the following times and round them to the nearest hundredths of a second.

56.286:
  • Underline the 8, which is in the hundredths place: 56.286.
  • If the number to the right is 4 or less, drop it and the hundredths place number remains the same.
  • If the number to the right is 5 or greater, drop it and increase the hundredths place number by 1.
  • In this example, the 8 is 5 or greater, so 56.286 rounded to the nearest hundredths is 56.29.
Images courtesy of www.imagesgoogle.com

You can also use a number line to round decimal numbers. Click here to see how to do this.


Go to the next page to try a Self-check Activity on rounding decimal numbers.