How do you rewrite 0.1000000 into scientific notation?

1x10 to the 7th power = one times ten to the seventh = 1x10⁷ = 10000000.0

All this "one times ten to the" junk starts at the "one's place" so that 1x10⁷

is a one followed by seven zeros and then the decimal point.

1x10³ = 1000 one followed by three zeros, decimal place is understood.

1x10⁶ = 1,000,000.0

1x10^-3 = 0.001 this is the same except the one is preceded by three zeros to the one's place

So it follows that 0.1000000 = 1x10^-1 and if you're worried about the zeros then express it as 1.000000x10^-1

More often today the "x10 or times ten" is replaced with "E" which means exponent and since we use base ten in everyday use
1E7 = 10000000.0
1.000000E-1 = 0.1000000