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Without actual division, state whether the following have a terminating decimal. 19/75 - Mathematics

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Question

Without actual division, state whether the following have a terminating decimal.

`19/75`

Sum
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Solution

Step 1: Factor the denominator

75 = 3 × 5 × 5 = 3 × 52

Step 2: Check the prime factors

Only prime factor is 3

Step 3: Apply the rule

Denominator has only 5 → Non-terminating decimal

No, `19/75` has a non-terminating decimal.

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Chapter 1: Rational and Irrational Numbers - EXERCISE 1A [Page 5]

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B Nirmala Shastry Mathematics [English] Class 9 ICSE
Chapter 1 Rational and Irrational Numbers
EXERCISE 1A | Q 4. (ii) | Page 5
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