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paulmdrdo
Active member
- May 13, 2013
- 386
0.17777777777 convert into a ratio.
what do you mean by "GP"?Hi,
This is [tex]0.1 + 0.077777=\frac{1}{10}+\frac{7}{100}+\frac{7}{1000}+...[/tex] where you have a GP to sum.
Or [tex] \text{Let } x=0.0777..[/tex] so that [tex]10x=0.777..[/tex].
Subtracting gives [tex]9x=0.7[/tex] and so [tex]x=\frac{7}{90}[/tex]. Now just add [tex]\frac{1}{10}+\frac{7}{90}[/tex] and simplify.
I should also say that we can write a decimal as a fraction but we can't write it as a ratio.
Sorry, I have to stop using abbreviations.what do you mean by "GP"?
[tex]\text{Convert }\,0.1777\text{...}\,\text{ to a fraction.}[/tex]
"a difference of two in the powers of ten" -- what do you mean by this? sorry, english is not my mother tongue. bear with me.Since two digits repeat, a difference of two in the powers of ten that you use leave no decimal part when you subtract.
If you use 1000 and 10 you will get
1000x=3547.474747...
10x=35.474747...
So 990x=3512 and x=3512/990=1756/495.
I'm adopting Soroban's approach as I prefer it to what I did earlier.
No problem."a difference of two in the powers of ten" -- what do you me by this? sorry, english is not my mother tongue. bear with me.
You want to multiply by a power of 10 which enables you to only have the repeating digits shown, and then multiply by a higher power of ten to have exactly the same repeating digits. We require this so that when we subtract, the repeating digits are eliminated.how would I decide what appropriate power of ten should i use?
for example i have 3.5474747474... how would you convert this one?