SOLUTION: Please help me Find the fractions equal to the given decimals 1. 0.82222...

Question 750467: Please help me
Find the fractions equal to the given decimals
1. 0.82222...
Found 2 solutions by Alan3354, DrBeeee:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find the fractions equal to the given decimals
0.82222...
n = 0.8222...
10n = 8.2222...
-n = -0.8222...
----------------
9n = 7.4
n = 7.4/9 = 74/90
n = 37/45

Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Change to a rational number the given number:
(1) n = 0.8222...
First we "fix" the decimal to be a whole number plus a repeating decimal. In this case
(2) n = 8.222.../10 or
(3) n = (8 + .222...)/10
We know that a single digit m divided by 9 is
(4) m/9 = 0.mmm... or .m repeated
In the given case in (3) we have
(5) 0.222.... which by applying (4) becomes
(6) 2/9 = 0.222...
Now place the identity of (6) into (3) and get
(7) n = (8 + 2/9)/10
Now simplify (7) to get
(8) n = ((72+2)/9)/10 or
(9) n = (74/9)/10 or
(10) n = 74/90 or
(11) n = 37/45
To ckeck the answer do the following
Is (0.8222.. = 37/45)?
Is (0.8222.. = 74/90)?
Is (90*0.8222...) = 74)?
Is (9*8.222... = 74)?
Is (72 + 9*0.222... = 74)?
Is (72 + 9*2/9 = 74)?
Is (72 + 2 = 74)?
Is (74 = 74)? Yes
Answer: 37/45 is the rational number equivalent of the decimal 0.8222...
Hint: If you have a two digit repeating number, such as
(12) 0.ababab.... it is the rational number
(13) ab/99 and if you have a three digit repeating number, such as
(14) 0.abcabcabc... it is the rational number
(15) abc/999 and four
(16) abcd/9999 etc.
PS You can do all of the above on a calculator.

RELATED QUESTIONS
Please help with me Find the fractions equal to the given decimals 1.... (answered by jim_thompson5910)
Find the fractions equal to the given decimals 1.... (answered by tommyt3rd)
Choose the correct solution set. 5x^2-11x+2=0 Options are {1/6,-3}... (answered by josgarithmetic)
i'm not sure if i'm under the right category or not, this was the only section of... (answered by JBarnum)
find two fractions equivalent to the given fractions:... (answered by stanbon,mananth)
PLEASE HELP ME W/ CHANGING COMPLEXPERCENTS TO DECIMALS LIKE {1 21/25} PLEASE SHOW ME... (answered by josmiceli)
a. Separate the fractions 2/6, 2/5, 6/13, 1/25, 7/8, and 9/29 into two categories: those (answered by Edwin McCravy)
please help me to Find the value for (x) which make the fractions equal:... (answered by JBarnum)
One third of a number is eight.what is the number? Can you help me please? I am bad at... (answered by Stitch)