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Convert between fractions, decimals and percentages

Start a set of 8
Step 3 of 9

Move the slider away from zero. Compare the decimal and percentage readouts at several positions

A table starts with zero selected parts out of eight equal parts. The slider changes the selected count. Decimal and percentage readouts show the same share Row 1: Selected parts 0, Equal parts in total 8Selected partsEqual parts in total08
Decimal
0
Percentage
0%
0

Away from zero, how does the percentage number compare with the decimal?

Year 10, Chapter 2, 3 difficulty levels, Calculator allowedBuild a worksheet

Equivalent forms

A percentage is a number of hundredths. Choose the conversion direction and preserve the value

\[p\%=\frac{p}{100}\]
  1. Decimal to percentage Find the number of hundredths, then write the percentage \(\displaystyle \begin{aligned}0.56\times100&=56\\0.56&=56\%\end{aligned}\)
  2. Fraction to percentage Divide to find the decimal, then express it as a percentage \(\displaystyle \frac{7}{16}=0.4375=43.75\%\)
  3. Percentage to decimal Divide the percentage number by one hundred \(\displaystyle 134\%=\frac{134}{100}=1.34\)
  4. Percentage to fraction Write the percentage over one hundred and simplify \(\displaystyle \begin{aligned}6.5\%&=\frac{6.5}{100}\\&=\frac{65}{1000}\\&=\frac{13}{200}\end{aligned}\)

Worked example

Write the percentage as a decimal and a fraction in lowest terms

\[32.5\%\]
  1. \(\displaystyle 32.5\%=\frac{32.5}{100}\)A percentage counts hundredths
  2. \(\displaystyle 32.5\%=0.325\)Divide the percentage number by one hundred to get the decimal
  3. \(\displaystyle \frac{32.5}{100}=\frac{325}{1000}\)Multiply both parts of the fraction by ten to clear the decimal
  4. \(\displaystyle \frac{325}{1000}=\frac{13}{40}\)Divide both parts by their highest common factor

Common mistakes

Attaching a percent sign without converting
✕\(\displaystyle 0.28=0.28\%\)✓\(\displaystyle 0.28=28\%\)
The percent sign means per hundred. The percentage number must count the decimal's hundredths
Dividing in the wrong direction
✕\(\displaystyle 0.52=0.0052\%\)✓\(\displaystyle 0.52=52\%\)
To express a decimal as a percentage, multiply by one hundred to obtain the percentage number
Stopping before the requested lowest terms
✕\(\displaystyle 26\%=\frac{26}{100}\)✓\(\displaystyle 26\%=\frac{13}{50}\)
The first equality has the correct value, but it is unfinished when lowest terms are requested. Both parts still share a common factor

Difficulty levels

introConvert one familiar value at a time in each direction
standardConvert less familiar fractions, three-place decimals and percentages above one hundred
challengeConvert small percentages and fractional percentages without unnecessary rounding

Questions about this topic

Can a percentage exceed one hundred?+

Yes. Its decimal value then exceeds one

Does converting change the value?+

No. The fraction, decimal and percentage describe the same value

Must a terminating decimal have trailing zeros?+

Only when the question requests a fixed number of decimal places. Trailing zeros do not change its value

Can I use a calculator?+

A calculator is allowed unless a question is marked no calculator

Which year level and chapter is this?+

Year 10 Mathematics, chapter 2: Consumer arithmetic

In this chapter

Convert between fractions, decimals and percentagesFind a percentage of a quantityExpress one quantity as a percentage of anotherProfit, mark-up and discountIncrease or decrease a quantity by a percentageFind the original amount from a percentageAdd GST to a priceFind the GST and the pre-GST price from an inclusive priceIncome from wages, overtime, shifts and commissionIncome tax payableBudgeting with percentages and fixed valuesDecide which option is the better valueSimple interest, unknowns and repaymentsCompound interest and non-annual periodsPurchase cost from deposit and repaymentsBank interest on a minimum monthly balanceCompare simple and compound interest