# Video: AQA GCSE Mathematics Higher Tier Pack 1 • Paper 3 • Question 4

AQA GCSE Mathematics Higher Tier Pack 1 • Paper 3 • Question 4

02:19

### Video Transcript

Circle the decimal that is closest in value to one-sixth. Is it 0.166, 0.167, 0.1666, or 0.1667?

Let’s begin by working out what one-sixth is as a decimal. Remember, this little fraction line is just another way of saying divide. So we can type one divided by six into our calculator to find the value of one-sixth as a decimal. Now if you have a scientific calculator, you might find that that shows the original fraction which isn’t hugely helpful. But there is a button which could help. It’s this one. The letters stand for standard to decimal, but I’ve also heard it called the super duper button.

If we press the super-duper button, we can see that one sixth is equal to 0.16 with the six recurring or 0.166666 and so on. So which of these decimals is closest in value to one-sixth then? Well we can fairly quickly disregard the first two options. The reason for this is that they’re only accurate to three decimal places or the nearest one thousandth. Since our decimal is recurring, the more decimal places we have, the closer the number will be to the exact value. So we now need to decide whether 0.16 recurring is closer in value to 0.1666 or 0.1667.

Let’s look at what would happen if we wrote the next digit in the number. It would be 0.16666. This is called truncating a number. We haven’t considered the value of the digit afterwards to round at. We’ve just locked the digits off. The final six is larger than five. This means this number 0.16666 is closer in value to 0.1667 than it is to 0.1666. And this in turn means that 0.16 recurring must be closer in value to 0.1667 than 0.1666. The decimal that is closest in value to one-sixth is 0.1667.