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Bergman Rolf

Express the following rational numbers as decimals 10 state which are terminating repeating decimal is 2125​

answers: 1
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69 cents Narn
Answer:

Answer:

Theorem: Let x=  

q

p

 be a rational number, such that the prime factorisation of q is of the form 2  

n

5  

m

, where n, m are non-negative integers. Then, x has a decimal expansion which terminates.

(i)

3125

13

 

Factorise the denominator, we get

3125=5×5×5×5×5=5  

5

 

So, denominator is in form of 5  

m

 so,

3125

13

 is terminating.

(ii)

8

17

 

Factorise the denominator, we get

8=2×2×2=2  

3

 

So, denominator is in form of 2  

n

 so,

8

17

 is terminating.

(iii)

455

64

 

Factorise the denominator, we get

455=5×7×13

So, denominator is not in form of 2  

n

5  

m

 so,

455

64

 is not terminating.

(iv)

1600

15

 

Factorise the denominator, we get

1600=2×2×2×2×2×2×5×5=2  

6

5  

2

 

So, denominator is in form of 2  

n

5  

m

 so,

1600

15

 is terminating.

(v)

343

29

 

Factorise the denominator, we get

343=7×7×7=7  

3

 

So, denominator is not in form of 2  

n

5  

m

 so,

343

29

 is not terminating.

(vi)

2  

3

5  

2

 

23

 

Here, the denominator is in form of 2  

n

5  

m

 so,

2  

3

5  

2

 

23

 is terminating.

(vii)

2  

2

5  

7

7  

5

 

129

 

Here, the denominator is not in form of 2  

n

5  

m

 so,

2  

2

5  

7

7  

5

 

129

 is not terminating.

(viii)

15

6

 

Divide nominator and denominator both by 3 we get

15

3

 

So, denominator is in form of 5  

m

 so,

15

6

 is terminating.

476
Narn
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