Converting Decimals and Fractions

Converting Decimals and Fractions exercise

• What is the equivalent fraction?

  Hints

  Begin by writing the decimal onto a place value grid. Here, 0.8 is written on to the grid.

  Identify the value of the digit by finding its position on the place value grid, an 8 in the tenths column means eight tenths.

  To make a fraction that has a denominator of 100 into tenths, divide both the denominator and the numerator by 10. For example, $\frac{60}{100}$ ÷ 10 = $\frac{6}{10}$ which is the same as 0.6.

  Solution

  The equivalent fractions and decimals are:

  • 0.2 = $\frac{2}{10}$ = $\frac{20}{100}$
  • 0.5 = $\frac{5}{10}$
  • 0.6 = $\frac{6}{10}$
  • 0.8 = $\frac{8}{10}$

  When we write 0.2 on a place value grid, there are zero ones and two tenths so we can say $\frac{2}{10}$. We can also write 0.20 meaning there are twenty hundredths, so we can also say $\frac{20}{100}$.

• How do we write fractions as decimals?

  Hints

  The denominator of the fraction is 100, so the numbers need to go as far as the hundredths column of the place value grid.

  There are no ones in $\mathbf{\frac{75}{100}}$ so there will be no ones in the ones column of the place value grid.

  Solution

  $\mathbf{\frac{75}{100}}$ is made up of 7 tenths and 5 hundredths, or 75 hundredths, so there will be a 7 in the tenths column and a 5 in the hundredths column.

• Representing numbers.

  Hints

  Look how many parts there are in total, this is the denominator. How many parts are shaded? This is the numerator.

  Once you know the fraction out of ten or one hundred, write this onto a place value grid. For example, 25 hundredths would be written as 0.25.

  Simplify the fraction you are trying to find, to find an equivalent fraction. For example, 0.25 is the same as $\frac{25}{100}$ and would be simplified to $\frac{1}{4}$.

  Solution

  • The first image shows 5 parts out of 10 shown. This is the same as a half or fifty out of one hundred.

  • The second image shows 75 parts shaded out of 100. This is the same as seventy five out of one hundred or zero point seven five.

  • The third image shows 30 parts out of 100 or 3 out of ten. This is the same as zero point three, thirty hundredths or three tenths.

• Order the fractions and decimals.

  Hints

  Begin by converting all the amounts into the same value. You could make every amount into hundredths.

  To convert $\frac{7}{10}$ to hundredths, multiply the numerator and denominator by ten to get $\frac{70}{100}$.

  To convert a decimal into hundredths, write the decimal onto a place value grid. For example, 0.08 would have zero ones, zero tenths and eight hundredths ($\frac{8}{100}$).

  Try drawing a hundred square and shading in the amount shown in the numerator when the denominator is 100, then see which fraction has the most shaded in.

  Solution

  The correct order from smallest to greatest values is:

  • 0.04 or $\frac{4}{100}$. 0.04 is equivalent to zero ones, zero tenths and four hundredths.
  • 0.2 or $\frac{20}{100}$. 0.2 is equivalent to zero ones and two tenths which is equivalent to twenty hundredths.
  • $\mathbf{\frac{4}{10}}$ or $\frac{40}{100}$.
  • 0.48 or $\frac{48}{100}$. 0.48 is equivalent to zero ones, four tenths and eight hundredths which is the same as forty-eight hundredths.
  • $\mathbf{\frac{63}{100}}$
  • $\mathbf{\frac{7}{10}}$ or $\frac{70}{100}$

• Find the fraction to match.

  Hints

  When we write 0.03 onto a place value grid, how many hundredths are there?

  Can you find a fraction that has 100 as the denominator?

  Solution

  0.03 = $\mathbf{\frac{3}{100}}$. When we write the decimal onto a place value grid we can see that there are zero ones, zero tenths and three hundredths.

• Converting fractions to decimals.

  Hints

  To convert a fraction to a decimal, first convert the fraction so that it has a denominator of 10 or 100. To convert $\frac{6}{20}$, we can divide the numerator and denominator by 2 to get $\frac{3}{10}$.

  Once the fraction is written as out of 10 or 100, write it on to a place value grid. $\frac{3}{10}$ has zero ones, 3 tenths and zero hundredths, so is equivalent to 0.3.

  When a fraction has 5 as a denominator, multiply both the numerator and denominator by two so that the fraction is out of 10.

  Solution

  1. $\frac{35}{100}$ = 0.35 ✅
  2. $\frac{2}{10}$ = 0.02 ❌ $\frac{2}{10}$ = 0.2
  3. $\frac{3}{5}$ = 0.3 ❌ $\frac{3}{5}$ = 0.6
  4. $\frac{4}{5}$ = 0.8 ✅
  5. $\frac{12}{20}$ = 0.6 ✅
  6. $\frac{2}{20}$ = 0.2 ❌ $\frac{2}{20}$ = 0.1
  7. $\frac{7}{100}$ = 0.07 ✅
  8. $\frac{1}{5}$ = 0.5 ❌ $\frac{1}{5}$ = 0.2