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The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form, p q what can you say about the prime factors of q? 43.123456789

The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form, p q what can you say about the prime factors of q? 
43.123456789 

Grade:12

2 Answers

Harshit Singh
askIITians Faculty 5964 Points
7 months ago
Dear Student

43.123456789
Since it has a terminating decimal expansion, it is a rational number in the form of p/q and q has factors of 2and 5 only.

Thanks
Ram Kushwah
110 Points
7 months ago
43.123456789 is having terminating decimal expansion
so the number is a rational number
 
Now 43.123456789=43123456789/1000000000
=43123456789/10^9
=43123456789/ 2^9 *5^9
so p=43123456789
 
and q=2^9 *5^9
 
Thus q is in the form of 2^m *5^n
here m=9 and n=9
 
 

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