# Video: Pack 3 • Paper 2 • Question 1

Pack 3 • Paper 2 • Question 1

04:12

### Video Transcript

What is the reciprocal of 0.08?

For a number 𝑥, the reciprocal of 𝑥 is given by one over 𝑥 or one divided by 𝑥. Another way of saying this is that the product of a number and its reciprocal is always one. That means then that the reciprocal of 0.08 is one divided by 0.08. In a calculator exam, we can type this into our calculator, giving us an answer of 12.5. However, we might get asked this in a non-calculator exam. So it’s useful to know how to answer this question.

0.08 is equivalent to eight one hundredths, since eight is in the hundredths column. We might choose to simplify this immediately by dividing both the numerator and the denominator by four to get two twenty-fifths, although we could actually complete this step later.

The reciprocal then of two twenty-fifths is one over two twenty-fifths or one divided by two twenty-fifths. To divide by a fraction, we change the divide sign to a multiply. Then we flip the second fraction. That is to say, we swap the numerator and the denominator. That gives us one multiplied by 25 over two, which is simply 25 over two.

In fact, we can generalize this by saying that, to find the reciprocal of any fraction, we simply swap the numerator and the denominator. The reciprocal of two twenty-fifths is 25 over two. And our final step is to perform that division, 25 divided by two. Half of 25 is 12.5. So we’ve correctly calculated the reciprocal of 0.08 without a calculator.

Calculate cos of 36 degrees plus 3.9 divided by 19 multiplied by 0.12 all cubed. Give your answer correct to two decimal places.

This is a question that’s testing our ability to use our calculator. Now many scientific calculators possess all the buttons we need to be able to answer this in one step. Typing this sum in with the brackets as shown and a fraction inside the first pair of brackets will give us the answer we need. And then once we’ve done this, we can perform an intermediate step and write this down.

It’s sensible to do this whenever we type a long sum into our calculator as it provides us with method mark should we make a mistake when inputting values. However, if we’re not using a scientific calculator to answer this question, then we need to know how to perform each of the intermediate steps to help us answer this question.

We’ll start by calculating the value of the numerator and the denominator. Cos of 36 degrees is 0.809. Many scientific calculators will open up a bracket automatically when we type cos. We must make sure to close those brackets when we’re doing our calculations. Cos of 36 is equal to 0.809. That means that cos of 36 plus 3.9 is 4.709.

Notice the use of these three dots. It’s a way of showing that we’ve not yet rounded our answer. Rounding too early can cause errors in our final solution, so we want to avoid doing that wherever possible. 19 multiplied by 0.12 is 2.28. So our sum becomes 4.709 divided by 2.28 all cubed. Remember, that fraction line means divide, so we’ll divide our answer of 4.709 by 2.28 to get 2.065.

Finally, we can cube this to get 8.8102, which is what we would have got had we typed this sum into our calculator. We mustn’t forget to round our answer to two decimal places. And that gives us a solution of 8.81.