Question

What is 0.7 as a fraction?

Answer 1

`0.7 = 7/10`

Explanation:

The positional decimal system is based on the idea that the value of a number is equal to
the sum of each (digit times the weight of the position in which the digit is found).

Where the decimal weights are
`color(white)("XXX")1` to the immediate left of the decimal point (or the right-most position if there is no decimal point).

`color(white)("XXX")10 xx` the weight of the position to its immediate right (`rarr 1/10 xx` the weight of the position to its immediate left).

`{:("position weights:", "...",1000,100,10,1,".",1/10,1/100,1/1000,"..."):}`

For the given example `(0.7)`, we have:

`{: ("digits:" , , , , , color(red)(0),".",color(red)(7) , , , ), ("position weights:", "...", 1000,100,10, 1,".",1/10,1/100,1/1000,"..."), ("value:" , 0, +0, +0,+0,color(blue)(+0),".",color(blue)(+7/10),+0,+0,+0) :}`

for a total value of `7/10`