Decimals Greater than 1

Decimals Greater than 1 exercise

• What does a decimal represent?

  Hints

  Decimals can be greater than one.

  Decimals and fractions represent the same number, but in different forms.

  Solution

  A decimal represents a whole number and a fractional part of a whole number. We use decimals when counting money and measuring objects, so it is important to understand what they represent.

• What are the steps to convert a decimal greater than 1 to a fraction?

  Hints

  In this example, the decimals have been converted to improper fractions.

  • 1.1 is equal to $\frac{11}{10}$.
  • 1.11 is equal to $\frac{111}{100}$.

  Here, the fractions have been converted to all have the same denominator of 100.

  Solution

  The steps to converting a decimal greater than one to a fraction are as follows:

  1. Write the decimal in the place value chart.
  2. Write each place value as a fraction.
  3. Convert the fractions so they have a the same denominator.
  4. Find the sum and simplify if needed.

• Which equation best represents the decimal 4.23?

  Hints

  Remember to find the greatest denominator and convert the other fractions to have the same denominator.

  This example shows you how to write each place as a fraction before converting the denominators.

  Convert all fractions to the greatest denominator. In this example, the greatest denominator is 100.

  Solution

  The correct answer is $\frac{400}{100}$ + $\frac{20}{100}$ + $\frac{3}{100}$ = $\frac{423}{100}$. This simplifies to 4 $\frac{23}{100}$

  As you can see in the picture, all the fractions need to have a denominator of 100 because it is the greatest. You convert each fraction to have a denominator of 100 by multiplying them by a multiple of ten. Once you do that, you can add the numerator of each fraction together to get your answer.

• Match the decimal to the fraction.

  Hints

  You could convert the improper fractions in to mixed numbers first to help you, for example, $\frac{124}{100}$ = 1 $\frac{24}{100}$. This can then be written onto a place value chart.

  In the example, you can see that the decimal has been expanded into the chart by place value. We then use this chart to create fractions.

  Here is an example of how an improper fraction has been converted into a mixed number and a decimal.

  Solution

  The matches are:

  1. 2.67 and $\frac{267}{100}$
  2. 5.6 and $\frac{56}{10}$
  3. 7.8 and $\frac{78}{10}$
  4. 4.25 and $\frac{425}{100}$

• Expand and convert the decimal 2.97.

  Hints

  When looking at a number, do we read it left to right or right to left?

  The tenths column means the fraction is out of 10 and the hundredths column means the fraction is out of 100.

  In the decimal 6.5, the 5 is in the tenths place because it represents $\frac{5}{10}$ .

  Solution

  The position of the number tells its value, e.g. the 2 represents two ones, the 9 is in the tenths place so represents nine tenths and the 7 is in the hundredths place so represents seven hundredths.

  You then have to convert the decimal to fractions which looks like this: 2 $\frac{9}{10}$ $\frac{7}{100}$

• Match the place value chart to the equations.

  Hints

  Write the decimal onto a place value chart to find how many ones, tenths and hundredths it is made up of.

  When the fractions are added, convert an improper fraction to a mixed number, e.g. $\frac{54}{10} = 5\frac{4}{10}$.

  Solution

  We use place value to expand decimals and think about the digits and their values.

  Let's take a closer look at the first decimal. 6.7 is $\frac{60}{10}$ + $\frac{7}{10}$ which equals $\frac{67}{10}$ This is equivalent to 6 wholes and 7 tenths. This same concept applies to the rest of the problems.

  1. 8.43 is $\frac{800}{100}$ + $\frac{40}{100}$ + $\frac{3}{100}$
  2. 1.25 is $\frac{100}{100}$ + $\frac{20}{100}$ + $\frac{5}{100}$
  3. 3. 6 is $\frac{30}{10}$ + $\frac{6}{10}$
  4. 4.5 is $4\frac{5}{10}$
  5. 4.05 is $4\frac{5}{100}$