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Quantitative Reasoning›Percentages

Percentages

Work with percentages confidently—learn how to convert, calculate and estimate percentages and spot traps in common errors.
5 min

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A percentage is a very common rate format. A percentage turns actual values into parts per hundred.

It may be more useful to think of a percentage in a part of the whole. You could calculate this rate in other formats if you divide to find a decimal or fraction.

But in the UCAT, you will use decimals and percentages in many QR calculations.

The image illustrates the concept of percentage as parts per 100. The title reads 'PERCENTAGE = PARTS PER 100'. A grid of 100 squares is shown, with 25 squares shaded in red to represent 25%. Annotations explain that '25% means 25 out of 100 parts'. Below the grid, there is a mathematical expression: '25% = 25/100 = 0.25'. At the bottom, a note states '100 parts (the whole)'. Another annotation at the bottom reads 'Percentages turn actual values into parts per hundred'. © Medify is noted in the bottom right corner.
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You will work extensively with percentages in the UCAT.

To save time, remember:

  • Convert a decimal to a percentage by moving the decimal point two places to the right. Examples: 0.725 = 72.5%; 0.0018 = 0.18%; 3.4 = 340%.
  • This is equivalent to multiplying by 100 and adding a percentage sign.
  • Convert a percentage to a decimal by moving the decimal point two places to the left. Examples: 6.95% = 0.0695; 1,470% = 14.7; 0.02% = 0.0002
  • This is equivalent to dividing by 100 and removing the percentage sign.

If you can internalise these steps, you will minimise calculations by simply doing them in your head before you go to the answer choices.

Just watch out for wrong answer traps that omit the conversion or do the conversion improperly, which could therefore be off by a factor of 10 or 100.

A chart providing quick reference conversions between decimals and percentages. The top section shows examples of converting decimals to percentages, including 0.725 to 72.5%, 0.0018 to 0.18%, and 3.4 to 340%. The bottom section shows examples of converting percentages to decimals, including 6.95% to 0.0695, 1,470% to 14.7, and 0.02% to 0.0002. Instructions for conversion methods are included.
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You can use a three-part formula to solve for a percentage.

You can apply this formula in a range of contexts involving percentages. Just take care not to use it when the percentage change formula is required, as that depends on the passage of time as the actual values increase or decrease.

Image titled 'The Three-Part Formula for Percentages'. It shows the formula: Percentage = (part/whole) × 100. The term 'part' is annotated with 'portion or subgroup' in orange, and 'whole' is annotated with 'total value or entire group' in green. Below the formula, text reads: 'Rearrange the formula to solve for the missing value.' © Medify.
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Walkthrough question

Percentage

Let’s use the percentage formula in a QR question.

You can rearrange the percentage formula to solve for an unknown.

You may have to find a new percentage, but you may well have to solve for the part or solve for the whole.

Students made 48 cakes for a charity event, only to discover on the day that they took orders for 162.5% of the cakes made. How many orders for cakes did they take?

Here, we are told the number of cakes made, and we need the number of cakes ordered. This is expressed as a percentage of cakes made, so cakes made is the whole, and cakes ordered is the part.

Thus, we can rearrange the percentage formula to solve for the part:

Notice how the percentage formula applies even when the part and whole are less obvious. Think to yourself: what is the main group, or the reference group? The group used as the foundation for the comparison is the whole.

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Take care when selecting data to ensure you use the correct part and whole before you calculate.

The UCAT sets wrong answer traps by using incorrect values as the part and the whole. Thus, a likely maths error can lead you to select a wrong answer trap.

You can easily go wrong – even if you are strong at maths – in a few common cases:

  • The part and whole are unusual groups, so you might invert them.
  • The numbers are super simple so you calculate in your head, only you use a wrong value or invert the values.
The image features a title 'CHOOSE THE RIGHT PART AND WHOLE' with a question mark icon and text asking 'What percentage of students study Science?'. A table is provided with two columns labeled 'Subject studied' and 'Number of students'. The rows list 'Science' with '120', 'Maths' with '80', 'English' with '60', and a 'Total' of '260'. Annotations indicate 'Part' as '120', the number of students who study Science, and 'Whole' as '260', representing all students. Below the table, a formula calculates the percentage: 'Percentage = 120/260 x 100 ≈ 46.2%'. The bottom text advises to 'Check the part and whole first.' The image is © Medify.
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Dividing the part by the whole will give you the percentage in decimal form, which must then be multiplied by 100 to get the percentage.

You will see this step included in QR explanations from Medify and the UCAT Consortium, but you will likely do it in your head to minimise calculator use.

Over the course of the QR section, you can make up several seconds – perhaps even the better part of a minute – by mentally converting between decimals and percentages.

Illustration with the title 'MENTAL CONVERSIONS SAVE TIME' at the top. Below is a conveyor belt with gears and a central section displaying a brain icon. On the left side of the brain, three sections labeled 0.25, 0.5, and 0.75 are shown, each with a corresponding color: red, yellow, and blue. On the right side, three sections labeled 25%, 50%, and 75% are displayed in the same colors. Below the conveyor belt, text reads 'Convert between common decimals and percentages in your head.' At the bottom right, there is a copyright notice '© Medify'.
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Walkthrough question

Percentage

Now, attack another QR question using the percentage formula.

Before calculating, look at the answer choices. If they are far apart, a rough estimate may be enough to identify the correct answer or eliminate options that are clearly too large, too small, or out of scale.

If the answer choices are close together, estimation is risky. In that case, calculate carefully, then confirm and click your answer.

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When time is short, estimation can help you keep moving. Eliminate any obviously incorrect answers and make the most informed choice you can.

If you answer using estimation without fully calculating, flag the question for review and return to it if time allows.

If there is no time to return, choose your best answer rather than leaving the question blank.

The image is titled 'Estimate When Answers Are Far Apart.' It presents a math estimation problem: 'A jacket cost £39. Approximately, how much would 21 jackets cost?' A quick estimate is shown as '40 x 20 = 800.' Below, there are five possible answers: £420 (marked with a red cross and labeled 'Too low'), £600 (marked with a red cross and labeled 'Too low'), £819 (marked with a green check and labeled 'Closest estimate'), £1,218 (marked with a red cross and labeled 'Too high'), and £1,590 (marked with a red cross and labeled 'Too high'). At the bottom, it reads 'Estimate enough to rule out obvious wrong answers.'
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Walkthrough question

Estimating a percentage

Let's try using estimation to tackle this QR question.