# Video: Pack 2 • Paper 1 • Question 8

Pack 2 • Paper 1 • Question 8

02:43

### Video Transcript

Order the numbers from smallest to largest.

All four of the numbers have the digits 1.9745. The first number has the five recurring. The second number has no numbers recurring. The third number has the four and the five recurring. And the fourth number has the nine, seven, four, and five recurring.

The first number can be rewritten as 1.97455555 and so on with the five repeating forever. As the second number has no recurring digits, we can rewrite this as 1.97450000. Once again, we can write zeros forever. The third number has the digits four and five recurring. We can rewrite this as 1.97454545 and so on. The four and the five will repeat forever. Finally, we can write the fourth number as 1.97459745 and so on. All four digits after the decimal point — the nine, the seven, the four, and the five — repeat forever.

We were asked to order the numbers from smallest to largest. Well, the first four numbers after the decimal point are identical in each number. Therefore, the important column is the one that is labelled. The smallest number in this column is zero in the second number 1.9745. The second smallest number in this column is the four, the third number down. The third smallest number in this column is the five, which is the top number. And finally, the largest number in this column is the nine which is in the bottom number.

This means that the order from smallest to largest is firstly 1.9745, then 1.9745 with the four and five recurring, then 1.9745 with the five recurring, and finally the largest number 1.9745 with all four digits after the decimal point recurring.