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Chandler tells Aubrey that the decimal value of -1/7 is not a repeating decimal. Should Aubrey believe him?

 Nov 26, 2014

Best Answer 

 #3
avatar+98107 
+10

A fraction will have a terminating decimal only if we can write the denominator as (2n x 5n) where  n ≥ 0

To see why this is true......note that all terminating decimals can be written as   A / 10n  = A / (2 * 5)n = A / (2n x 5n) where A is the integer formed by moving the decinal point in the non-repeating decimal n places to the right.

For instance

1/4 = 1/(22 x 50)  = .25 = 25 / (22 x 52) = 25 / 100

And

1/5 = 1/(20 x 51) = .20 = 20 / (22 x 52) = 20 / 100

But, note that fractions such as 1/6,  1/13, 1/23  will repeat because the denominators cannot be factored solely in terms of 2 and 5.

 

 Nov 26, 2014
 #1
avatar
+10

- 1/7 = - 0.142857(142857)...

 

In fact, all fractions have repeating decimals (or a finite number of decimals).

 Nov 26, 2014
 #2
avatar+99282 
+10

Hi anon

Not all fractions have repeating decimals.  What about 1/2  that is just 0.5   nothing is repeating :)

 

$${\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{7}}}} = -{\mathtt{0.142\: \!857\: \!142\: \!857\: \!142\: \!9}}$$       but this is a repeating decimal just like you said  

 Nov 26, 2014
 #3
avatar+98107 
+10
Best Answer

A fraction will have a terminating decimal only if we can write the denominator as (2n x 5n) where  n ≥ 0

To see why this is true......note that all terminating decimals can be written as   A / 10n  = A / (2 * 5)n = A / (2n x 5n) where A is the integer formed by moving the decinal point in the non-repeating decimal n places to the right.

For instance

1/4 = 1/(22 x 50)  = .25 = 25 / (22 x 52) = 25 / 100

And

1/5 = 1/(20 x 51) = .20 = 20 / (22 x 52) = 20 / 100

But, note that fractions such as 1/6,  1/13, 1/23  will repeat because the denominators cannot be factored solely in terms of 2 and 5.

 

CPhill Nov 26, 2014
 #4
avatar+99282 
0

I had never thought about that before.  Thanks Chris :))

 Nov 26, 2014

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