+0  
 
0
59
2
avatar

Identify which repeat and which terminate by not calculating. How do you know?

 

1. 1/40

2. 1/24

3. 2/125

4. 2/99

5. 7/300

6. 7/200

Guest Oct 26, 2017
Sort: 

2+0 Answers

 #1
avatar+78590 
+2

In a reduced form.....If we can express the denominator solely as a power of 2 or a power of 5 - or both - the fraction will terminate....else..it repeats.....

 

1/ 40  terminates  = 1 / [ 2^3 * 5]

1/ 24 does not =  1 / [ 2^3 * 3 ]

2/125 terminates  = 2 / 5^3

2/ 99 does not  =  2 / [ 3^2 * 11]  

7/ 300  does not =  7 / [ 2^2 * 5^2 * 3 ] 

7 / 200  terminates  =  7 / [ 2^3 * 5^2]

 

Here's the provision for the reduced form

 

3 / 300     appears to not terminate....however

 

3 / 300  =   1 / 100  =    1 /  [  2^2 * 5^2 ]    so this actually does terminate  !!!

 

And that's all there is to it  !!!!

 

 

cool cool cool

CPhill  Oct 26, 2017
 #2
avatar+90999 
+1

Thanks Chris,  

I had not thought about that before.

 

To put it another way..

If the decimal is to terminate then

The prime factors of the denominator must ONLY  be the prime factors of 10 

 (which are  2 and 5 )

 

----------------

 

I assume this can be extended to other bases.

So

1/5 base 8 is a recurring decimal because the prime factors of 5 are not the prime factors 8

That works.

I just did the division

and got 

\(\frac{1}{5_8}=0.14\bar6\bar3\)   (base8)    

How about that!     

 

Thanks Chris     laugh wink laugh

Melody  Oct 26, 2017

20 Online Users

avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details