Question

Without actual division, find which of the following rational numbers have terminating decimal expansion. i) 21/35​

Answer 1

Answer:

No

Step-by-step explanation:

One easy trick to find if the decimal terminates is to  see if the denominator is a factor of 2, 5 or both only.

Here,

21/35 can be written as 21/7*5

Although it has a 5, it dosent have a 2, so it dosent terminate

Answer 2

21/35 has terminating decimal expansion as denominator gas only 5 as prime factor after reducing fraction in its simplest form.

Given:

• Rational number 21/35

To Find:

• whether 21/35 has terminating decimal expansion or not

Solution:

• ​Any number in the form of p/q  where p and q are co primes.
• if q has only prime factors of 2 and 5 then it is terminating decimal.
• if q has prime factors other than 2 and 5 also then its non terminating recurring decimal
• Rational numbers are terminating decimals or non terminating recurring decimal.
• Irrational numbers are non terminating non-recurring decimals

Step 1:

Reduce the fraction in simplest form

21/35

Divide numerator and denominator by 7

3/5

Step 2:

Check the prime factors of denominator

5 is the only prime factor

As 5 is the only prime factor  and there is no factor other than 2 or 5

hence 21/35 has terminating decimal expansion

Verification

3/5 = 0.6

Hence 21/35 = 0.6