Question

How do you convert 1.8 as a fraction?

Answer 1

I'd like to add the general way to convert finite decimal number into fractions: we know that, since we count in base `10`, dividing and multiplying by `10` shifts the beginning of the decimal digits, adding zeroes where necessary, so for example

`65*1\color(green)(0) = 65\color(green)(0)`, or

`48.26*10=482.5`, while

`65 div 10 = 6.5`, and

`48.26 div 10 = 4.826`.

Also, note that a power of ten is simply a one followed by as many zeroes as the exponent of the power, so for example

`10^\color(green)(3)=1\color(green)(000)`

Starting from this assumptions, it's easy to see that if you multiply (or divide) by a power of ten, you shift the beginning of the decimal digits right (or left) by a number of steps which is equal to the number of zeroes: working again with the examples above, we have

`65*1\color(green)(00) = 65\color(green)(00)`, or

`48.26*1000=48250`, while

`65 div 100 = 0.65`, and

`48.26 div 1000 = 0.04826`.

So, when you have a finite decimal number, you can alyaws see it as a whole number who has been divided by a proper power of ten. In your case, you can see `1.8` as `18`, with the beginning of the decimal digits shifted left by one. But for all we said above, shifting left by one means to divide by `10`, and so you have

`1.8=18/10 = 9/5`