Hope this helps!

For example

a) 38/99

b) 61/99

c) 5/9

If you wanted to do .04040404 repeating, it would be 4/99

a) 0.38888…

b)0.61111…

c)0.55555… i know that any single digit that repeats is that digit divided by 9. (you can expand this to say that any 2 digits that repeat are those two digits divided by 99, any 3 are divided by 999…. so on. this is a phenomenon caused by our base ten numbering system and it is always true, so just live with it and learn to exploit it)

for a) and b), this is how i figured them out:

i attempt to reassemble the numbers from the fact that 1/9=.1111… and 8/9=.8888…

let’s take .38888…

if you were to multiply by 10 you would get 3.88888…

now you can subtract 3 from this answer to get .88888…

and you know that .8888…=8/9

so (.8888…+3)/10=.38888…

or (8/9+3)/10=.38888…

follow order of operations to get just a fraction on the left side…

(8/9+27/9)/10=(35/9)/10= 35/90

the problem is that this is not in lowest terms…so divide numerator and denominator by 5

(35/5)/(90/5)=7/18

check this on your calculator by dividing 7/18 😀

keep in mind that your calculator will round the final digit.

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the other trick where you multiply by a factor of 10 to the repeated digit only works if all the digits repeat.

.383838…=x declare x equals your value

38.3838…=100x multiply by 10 until one set of your repeatded numbers are to the left of the decimal

38.3838… -x =100x-x subtract x from both sides

38=99x solve for x

x=38/99

actually, my favorite is this one:

.999…=x

9.999…=10x

9.999… -x = 10x -x

9=9x

x=1 how cool is that?

first we said that x=.999…, but we just proved that x=1!

When you get out of school you’ll find everybody uses calculators and computers. When I was in school I used to really try to get straight A’s and I did but when I got out of school I realized what a joke our educational system was.

It’s really just to indoctrinate our kids into thinking they came from monkeys. he he. But seriously, its a Godless educational system thats been ranked one of the lowest achieving in the world.

A)19/50

B)61/100

C)1/2

Google how to properly figure these numbers, I just did them in my head.

GOOD LUCK!

a.) .38=38/100=19/50

b.) .61=61/100

c.) .d=1/2

just change it (._=_/10;.__=__/100;.___=___/10000 and then simplify with gcf (greastest common factor [divisor {biggest number you can divide both by}])