What is #0.33%# (repeating) as a fraction?
2 Answers
Explanation:
Careful with percentages—they're not the same as regular decimal numbers! First, we convert the percentage to a decimal number, using this idea:
A percent symbol is short for "divide this number by 100".
For example,
So we now know
The numerator (top number) of our fraction will be the digits under the bar (in this case,
The denominator (bottom number) is found by writing this string of digits:
- Count the number of digits under the bar; write this many 9's.
- Count the number of digits between the decimal and the bar; write this many 0's after the 9's.
So, for the number
(This simplified rule works because the digits before the 3 are all 0's. When these are non-zero digits, the fraction takes a bit more work.)
Okay—all of this means our final number is:
#0.333...%" "=" "0.00bar3" "=" "3/900#
But wait—
#3/900=(3divide 3)/(900divide3)=1/300#
And there we have it!
Explanation:
Write
Let
Then
So
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But we have to include the