Express 0.85 as a fraction?

The decimal `0.85` can be converted to the fraction `85/100`, by definition of a decimal. This fraction, `85/100`, however, is not in simplest form. The fraction can be simplified to `17/20`, as both the numerator (top) and denominator (bottom) of the fraction are divisible by 5.

Therefore, your answer is `color(red)(17/20`.

I hope that helps!

The first step we can take is to put 85 over 100 because `.85` is the same thing as 85 hundredths (we can remember this by noting that there are two decimal places in `.85`, or the numerator, meaning that there are two zeros in the denominator), which is the same thing as `85/100`.

`.85 = 85/100`

We can simplify this by dividing the numerator and denominator by the greatest common factor (in this case, 5).

`85/100 -: 5/5 = 17/20`

17 is a prime number, so there's no way we can simplify this further.

`.85 = 17/20`

Another way of looking at the decimal of `0.85` is

`ubrace("count of 1's")+ubrace(("some count")/10)+ubrace(("some count")/100)+ubrace(("some count")/1000)+...`
`color(white)("dd.d")darrcolor(white)("dddddddd.d")darrcolor(white)("dddddddddd")darr color(white)("dddddddd.d")darr`
`color(white)("dddd")0color(white)("ddddddddddd")8color(white)("ddddddddddd")5`

So `0.85` is the same as `8/10+5/100`

Multiply by 1 and you do not change the value. However 1 comes in many forms. So write as:

`color(green)([8/10color(red)(xx1)]+5/100)`

`color(green)([8/10color(red)(xx10/10)]+5/100)`

`color(green)(color(white)("dd") [80/100]color(white)("dd")+5/100`

`color(green)((80+5)/100`

`color(green)(85/100)`
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But 5 will divide exactly into both 85 and 100

When dividing or multiplying what you do the top of a fraction you also do to the bottom. In doing so we 'simplify' to an 'equivalent' fraction

`color(green)((85-:5)/(100-:5) -= 17/20`

Where the symbol `-=` means 'equivalent to'