Explanation:
what do do the different positions in a number mean ?
they represent the various powers of 10 times the digit value at that position.
it all starts with the first position to the left of the decimal point : it stands for 10⁰ = 1
so,
1, 2, 3, 4, ....
all stand for actually
1×10⁰ = 1
2×10⁰ = 2
3×10⁰ = 3
...
the second position to the left of the decimal point stands for 10¹ = 10
so, e.g. 20, 30, ...
stand for
2×10¹ = 20
3×10¹ = 30
and yes, we can combine it. so, e.g.
36 = 3×10¹ + 6×10⁰ = 30 + 6 = 36
so, in the same way this confines further to the left, with the positions standing for
10² = 100
10³ = 1000
...
now, what about the positions to the right of the decimal point ?
they continue the principle. with every position further to the right we have to subtract 1 from the power of 10.
remember, the first position to the left of the decimal point stands for 10⁰.
so, now going one position to the right (which is the first position to the right of the decimal point), this stands for 10^-1 = 1/10
and the second to the right stands for
10^-2 = 1/100
and so on.
so, now you see, it is totally simple
7.62 = 7×10⁰ + 6×10^-1 + 2×10^-2 = 7 + 6/10 + 2/100
to simplify this we need to bring everything to hundredths (full fraction) our just the already existing fractions to hundredths (mixed number).
so, for a full fraction we have
7 + 6/10 + 2/100 = 700/100 + 60/100 + 2/100 = 762/100 =
= 381/50
for a mixed number we get
7 + 6/10 + 2/100 = 7 + 60/100 + 2/100 = 7 62/100 =
= 7 31/50