0.123 repeating as a simplified fraction

122/990

Step-by-step explanation:

x = 0.123 (23 is repeating)

*100 *100     (Multiply both sides by 100)

100x = 12.3232323

x       = 0.1232323    (Now subtract both equations)

-----------------------------

99x  12.2

99     99

Now Multiply the fraction by 10 to get rid of the decimal

12.2 * 10 = 122

99 * 10   =  990

Final

112

990

I hope this helps :D and have a great rest of your day, evening or afternoon!

for ex: the reciprocal of 3/4 is 4/3. it is the opposite.

reciprocal definition:

a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4