Question

0.0001 is terminating number

Answer 1

ok as per the question 0.0001 is terminating number or not so let's find out:

let's convert the decimal form of the number into fraction that is 1/10000.

Step-by-step explanation:

so as to find out the number is terminating or not so there are two ways which are very simple one is to divide and find out the quotient if it is repeating and stops at a certain point then we can say that it is terminating number but another way is that that if the prime factorization of the denominator that is 10,000 here is two and five only likewise here the prime factorization of this numbers consists of only 2 and 5 i.e 2×2×2×2×5×5×5×5.

here we got 2⁴ × 5⁴ .

so we came to know that yes it is a terminating number as the prime factorisation of the denominator consists of only 2 and 5 but remember if if the denominator consist of 2,5,3and 7 (suppose). just look at the numerator if it is 21 as an example then take out the prime factorization of the numerator too so now what we observe that the prime factorization consists of 3 into 7 so 3 ×7 in the numerator cuts 3 into 7 in the denominator show the remaining factors are 2 into 5 the denominator likewise this just if you get factors except 2and5 just check it out if it divides then it maybe terminal if it doesn't then it is non terminal .

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