Order the numbers from smallest to
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.