logo for solving-math-problems.com
leftimage for solving-math-problems.com

Converting Recurring Decimal Into a Fraction











































I'm confused. I know the method and have been trying to convert 0.0999999 but
keep coming up with 1/10 as the answer which doesn't feel right given that 1/10
is 0.1 as a decimal. Here's the method I used,where am I going wrong?


x = 0.099999
100x = 9.9999

100x - x = 99x = 9.9

990x = 99 so x = 1/10!!!!

Comments for Converting Recurring Decimal Into a Fraction

Click here to add your own comments

May 10, 2011
Converting Recurring Decimal into a Fraction
by: Staff

The question:

I'm confused. I know the method and have been trying to convert 0.0999999 but
keep coming up with 1/10 as the answer which doesn't feel right given that 1/10
is 0.1 as a decimal. Here's the method I used,where am I going wrong?


x = 0.099999
100x = 9.9999

100x - x = 99x = 9.9

990x = 99 so x = 1/10!!!!


The answer:

Even though it shouldn’t be that way . . . Even though it is hard to believe, you are entirely correct.

0.099999… = 1/10



>>>>>

>>>>> The number of digits used to represent a number depends entirely on the numbering system:

>>>>>


Example 1

Using the number base of 10

½ (base 10) = 0.5 (base 10)

But when this same number is expressed using the number base of 2

½ (base 10) = 0.011111111111111111111111111111111111111111111111111111 (base 2)

Or when this same number is expressed using the number base of 7

½ (base 10) = 0.3333333333333333333532345065211213525246152246304514464052022156340626024455016523433003404232432654 (base 7)


Example 2

2/5 (base 10) = 0.4 (base 10)

But when this same number is expressed using the number base of 5

2/5 (base 10) = 0.2 (base 5)

Or when this same number is expressed using the number base of 4

2/5 (base 10) = 0.121212121212121212121212122 (base 4)



Thanks for writing.

Staff
www.solving-math-problems.com

Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Math Questions & Comments - 01.



Copyright © 2008-2015. All rights reserved. Solving-Math-Problems.com