Decimals Greater than 1 as Fractions

Decimals Greater than 1 as Fractions 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 needed in order to convert a decimal greater than 1 to a fraction?

  Hints

  In this example, the decimals have been converted to fractions. 1.1 goes to the tenths place, so we write the fraction over 10. 1.11 goes to the hundredths place, so we write the fraction over 100.

  Like means the same. So, in this example, the fractions were changed 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 like 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.

  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

  Decimals can be converted to fractions that have a denominator of ten. In this example the denominator is 100 which is a multiple of ten. So you change the original fractions to fractions over 100.

  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.

  Decimals greater than one are going to be a mixed number. This means there will be a whole number and a fractional part like 2 $\frac{1}{2}$.

  Solution

  The matches are:

  1. 2.67 and $\frac{267}{100}$
  2. 5.6 and $\frac{560}{100}$
  3. 7.8 and $\frac{78}{10}$
  4. 4.25 and $\frac{425}{100}$

  In order to match the pairs correctly, you had to use place value. Each match is based on ten. So if the decimal goes to the tenths place, the fraction will also have a denominator of ten. If the decimals goes to the hundredths place, the fraction will have a denominator of one hundred.

• 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 $\frac{9}{10}$, and the 7 is in the hundredths place so represents $\frac{7}{100}$.

  You then have to convert the decimal to fractions which looks like this: $\frac{2}{1}$ $\frac{9}{10}$ $\frac{7}{100}$

• 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 $4\frac{5}{100}$