Unit conversions
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In Quantitative Reasoning, you often must convert between units.
At its simplest, you will use data in one or more units to solve for an answer in different units.
Sometimes, the unit conversion will be built into the logic of the maths required to solve. In these cases, to convert units you must simply set up and solve correctly.
Walkthrough example
Units built into maths logic
Let's look at an example of converting between units.
Some QR questions will require a conversion factor – the equation, fraction or rate that links the two units.
The UCAT will normally tell you the conversion factor if you must convert between metric and imperial units or between temperature scales.
The key question is whether to multiply or divide using a unit equivalence equation. This can be more challenging when one of the values is 1. As a rule, you must either:
- Divide by the units you want to eliminate (the ‘old units’), or
- Multiply by the units you want to change to (the ‘new units’) to eliminate the old units.
Remember that dividing by a number is the same as multiplying by its reciprocal. This can apply to integers as well as fractions and is useful when working with unit equivalence equations expressed in terms of 1 unit.
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Walkthrough example
Unit equivalence - multiply or divide?
Try these two examples using unit conversions.
When you multiply or divide, the original units will cancel out, leaving you with the new units in your answer.
Remember as well that dividing is the same as multiplying by the reciprocal. Thus, units cancel out the same as factors in a fraction.
Walkthrough example
Using fractions to cancel out units
Let's look at another example with unit conversions.
Make a quick mental note of the answer choice units. Use these units to guide your mental maths as you set up and solve.
This will ensure that you convert units at the best possible moment to minimise maths.
Most commonly, you will find it is best practice to convert units:
- At the first step if you must start from a value that does not match the units of the other data you must use to solve.
- In a middle step if you have a single value in the wrong units that you will use neither first nor last in your calculations.
- At the final step if the answer choices are in different units from the data used to solve.
Walkthrough example
When to convert units
Now try working through this unit conversion example.
Sometimes, a Quantitative set will give you lots of conversion factors. Or you may see equations, fractions or rates for possible conversions that are mixed into other text.
The key is to focus only on the units you need to solve the question.
Any additional text, including other conversion factors, is a distraction intended to slow you down and make it harder to solve.
Guide your work with the necessary conversions for your calculations and ignore the rest.
Walkthrough question
Unit conversions
Let’s work through a question with conversion factors.
Some common unit conversions require you to know the conversion factor, such as converting:
- Within metric units of the same base (such as cm to km, g to kg), as this is simply a matter of powers of 10.
- Between metric units of different bases (such as cubic metres to litres), as this is generally common knowledge, though sometimes the UCAT will provide a conversion factor.
- Between units of time that are common knowledge, such as hours to minutes or seconds or years to months or quarters.
The UCAT may or may not give the conversion factor when you must convert volume between metric units.
Memorise these volume conversion factors and save time in QR if the conversion factor is not provided.
- 1 ml = 1 cm3
- 1 L = 1,000 cm3
- 1,000 L = 1 m3
The UCAT will not specify how to convert between most units of time, as these are expected to be common knowledge.
The UCAT is not testing everyday knowledge, but at the same time, it will help to know the months in order from January to December, as questions may assume you can recognise the sequence of months in the same year.
Similarly, you should know the days of the week in order within the same week.
You should not need to know how many days are in each month, though there is no harm in learning this, or using a mnemonic or rhyme (‘Thirty days hath September’) to recall the number of days per month as needed.
Walkthrough example
Converting units of time
Take a look at this example converting units of time.
Watch out for non-standard units as you may see almost anything treated as a unit. The UCAT loves to come up with unusual concepts that will be challenging in timed conditions. It is very easy to make an error when working with unfamiliar units.
As always, look for the conversion factor in the data or accompanying text. Then, take a moment to consider whether to multiply or divide.
Walkthrough question
Unusual units
Work through this question using unusual units.
Watch out for rounding as you work and also as the final step.
The correct answer is based on full, accurate values used in every calculation. This means that if you round as you work, you may be slightly off in the final step. In most cases, this won’t make a difference as the answers will not be especially close.
However, you may find it helps to leave all the digits in the calculator in each step. Thus, if you plan your calculations in order so that the result from one step is the first number you need in the next step, you can keep the calculations flowing and end up with a precise answer.
When you must round as the final step, take a moment to consider the context.
In most cases, you can round as normal to the nearest decimal place in the answer choice. In most questions, the answers are integers, or they have one or two decimal places. By rounding in this way, your answer is an approximation following normal maths logic.
Sometimes, you must round your answer but the question wording will require a different logic. Two special cases:
- The correct answer discards the decimal, as the question asks for full units or complete units in a way that implies you do not count the partial amount that is short of one more whole unit.
- The correct answer rounds up to the next number even if the decimal is less than 0.5, as the question asks for the total units required, so you must include one more whole unit in order to cover the need. This tends to occur when the whole unit is indivisible, such as people or cars.
Walkthrough question
Rounding
Let's try using rounding to answer a QR question.
Glance briefly at the answer choices to guide the level of precision in your calculations.
If the answer choices include a wide range of values, you may eliminate wrong answers based on a quick estimate or partial calculations when you are pressed for time.