Figuring out the fraction of a repeating decimal
The sure way of knowing the fraction of a decimal
Many of us do not think twice about repeating decimals. We either put a bar over the repeating portion of round off, but that does not always allow for accurate calculations.
If you were to see .666666.... or .66667, you'd probably go "that's 2/3". However that's from previous knowledge.
What happens if the number is 7.1111111....?
Some might recognize the .111111... as 1/9, and correctly assume this to be 7 + 1/9, or 64/9.
Well that's fine and dandy, but what if it's something like 136.78678678678....?
Not so easy now is it? There is cut-and-dry method of figuring it out. First locate the repeating pattern (678).
Then let x be the full number.
x = 136.78678....
If you can somehow remove the repeating portion, it wouldn't be so hard to figure out the fraction. But how do you take the repeating portion out?
Multiply x by a multiple of 10 that results in a number with the same repeating decimals in the same spot. Since the repeating number is 678 - a 3 digit number - I will conveniently use 1000.
1000x = 136786.78678...
     x =    136.78678...
This is a system of equations. Notice how the repeating end match? Now you can subtract the equations, which gives you:
999x = 136650
Solve for x
x = 136650 / 999
There's your answer!
Or you can simplify it to get 45550/333, which is 136 + 262/333.
See? As long as you manipulate so he repeating part subtracts itself, you'll get a fraction. I used 1000, but I could have used .001 or 1000,000.
-
U Teach Your Child Fractions 5: Equivlent Fractions
| By lloyd | in General
A discussion on equivalent fractions and how they are generated....
-
How to MULTIPLY or DIVIDE any two Fractions QUICKLY
| By zadocksmath | in College and University
In many Math Tests several problems involve the addition, subtraction, the MULTIPLICATION and the DIVISION of fract...
-
Adding or taking 2 mixed fractions. (improper fractions and mixed fractions)
| By catman3000 | in General
Learn how to add or take 2 mixed fractions, and how to change a mixed fraction to an improper fraction....
-
U Teach Your Child Fractions 6: Addition
| By lloyd | in General
This note is a continuation of the U Teach Your Child series. It opens with the statement of a work problem. Then ...
-
How to calculate Fractions online
| By DrABELL | in College and University
Article contains thorough explanation of Fractions math and provides detailed instruction on practical Fractions ca...
-
Planning your College Courses | By koopalo | in College and University
Knowing what college courses you're going to take ahead of time saves you a lot of time, stress, and sometimes even...
-
How to Choose a College Major | By koopalo | in College and University
Do you feel pressured to choose a college major and don't know how to decide? Deciding on the right one for you can...
-
Exaggerated Claims of Executive Privilege; Archibald Cox – A Man of Uncompromising Integrity | By marie.thomas | in College and University
Just one day after President Nixon refused to comply with a federal appeals court order to surrender the hostage â€...
-
Guide to buying your textbooks cheap. | By luvikavi | in College and University
Buying textbooks for college courses is probably one of the most daunting aspects of our college career. Read this ...
-
Benefits of Online Education | By kateperez | in College and University
In today's busy world where everyone is scrambling to either keep their job or find a job, online educations is ful...
-
Tips for My Sims Agents | By Squimpleton | in Computer & Video Games
Some tips for My Sims Agents (covering Evelyn, Morcubus, Dispatch missions, Ginny, and Thief V)...
-
How to go in suspend mode in PSP | By Squimpleton | in Gadgets & Gizmos
How to go in suspsend mode in the PSP, as well as a look at the Pause feature of the PSP Go....
-
How many mp3 songs can the PSP hold? | By Squimpleton | in Gadgets & Gizmos
A look into how many mp3's a PSP/PSP G can hold with different memory cards, as well as the price of such cards....
-
Guaranteeing a successful tooth fairy | By Squimpleton | in Children
Ways to make sure the tooth fairy becomes a pleasant memory for your child. ...
-
A warning before buying an HDTV | By Squimpleton | in General
What to expect when buying an HDTV and a look into whether or not it's worth it....
No comments yet.