Question

I need help with this plz explaining to me

Answer 1

is simply explaining a few ways how to go about to converting a decimal format to a fraction format.  Let's do a couple examples on that.

say we have a number hmmmm 4.25, we can write that as 4 + 0.25, because 4 + 0.25 = 4.25.

now let's convert the 0.25 part to a fraction, we use as many zeros at the bottom as there are decimals and lose the dot atop, since that's a mouthful, let's proceed to do so then.

$\bf \underset{\textit{2 decimals}}{0.\underline{25}}\implies \cfrac{025}{\underset{\textit{2 zeros}}{1\underline{00}}}\implies \stackrel{simplified}{\cfrac{1}{4}} \\\\\\ \stackrel{\textit{so then we can write that}}{4.25\implies 4+0.25}\implies 4+\cfrac{1}{4}\implies 4\frac{1}{4}$

let's do another example say hmmmmm a longer decimal.... say 10.234578.

so that'll be 10 + 0.234578, because 10 + 0.234578 = 10.234578.

so let's make a fraction of 0.234578.

$\bf \underset{\textit{6 decimals}}{0.\underline{234578}}\implies \cfrac{0234578}{\underset{\textit{6 zeros}}{1\underline{000000}}}\implies \stackrel{simplified}{\cfrac{117289}{500000}} \\\\\\ \stackrel{\textit{so then we can write that}}{10.234578\implies 10+0.234578}\implies 10+\cfrac{117289}{500000}\implies 10\frac{117289}{500000}$

so, notice, we first look at how many decimals are there, and for the fraction, we use that many zeros, with the "1", namely a base of 10 with as many zeros, and we lose the dot on the numerator, and simplify from there.