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, <u>we use as many zeros at the bottom as there are decimals and lose the dot atop</u>, 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}](https://tex.z-dn.net/?f=%5Cbf%20%5Cunderset%7B%5Ctextit%7B2%20decimals%7D%7D%7B0.%5Cunderline%7B25%7D%7D%5Cimplies%20%5Ccfrac%7B025%7D%7B%5Cunderset%7B%5Ctextit%7B2%20zeros%7D%7D%7B1%5Cunderline%7B00%7D%7D%7D%5Cimplies%20%5Cstackrel%7Bsimplified%7D%7B%5Ccfrac%7B1%7D%7B4%7D%7D%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bso%20then%20we%20can%20write%20that%7D%7D%7B4.25%5Cimplies%204%2B0.25%7D%5Cimplies%204%2B%5Ccfrac%7B1%7D%7B4%7D%5Cimplies%204%5Cfrac%7B1%7D%7B4%7D)
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}](https://tex.z-dn.net/?f=%5Cbf%20%5Cunderset%7B%5Ctextit%7B6%20decimals%7D%7D%7B0.%5Cunderline%7B234578%7D%7D%5Cimplies%20%5Ccfrac%7B0234578%7D%7B%5Cunderset%7B%5Ctextit%7B6%20zeros%7D%7D%7B1%5Cunderline%7B000000%7D%7D%7D%5Cimplies%20%5Cstackrel%7Bsimplified%7D%7B%5Ccfrac%7B117289%7D%7B500000%7D%7D%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bso%20then%20we%20can%20write%20that%7D%7D%7B10.234578%5Cimplies%2010%2B0.234578%7D%5Cimplies%2010%2B%5Ccfrac%7B117289%7D%7B500000%7D%5Cimplies%2010%5Cfrac%7B117289%7D%7B500000%7D)
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.