Exercise 1.4: Decimal Expansions of Rational Numbers
You'll figure out whether a fraction gives a terminating or recurring decimal — without actually dividing. The trick is to check the prime factors of the denominator.
Extra Practice Questions
These questions cover the same concepts as Exercise 1.4. Try solving them to build confidence before or after the textbook exercise.
Without actually dividing, determine which of these will have a terminating decimal: 13/3125
The HCF of two prime numbers is always:
Find the HCF and LCM of 6, 72, and 120 using prime factorisation.
The prime factorisation of 56 is:
Find the HCF of 867 and 255 using Euclid's division algorithm.
Express 0.\overline{6} as a fraction in simplest form.
The number 6n, for any natural number n, can end with the digit:
Find the largest number that divides 2053 and 967 and leaves remainders 5 and 7 respectively.
Express 0.\overline{47} in the form p/q.
Use Euclid's division lemma to show that any positive odd integer is of the form 4q+1 or 4q+3.
Stuck on a question?
Paste any question from Exercise 1.4 into our AI Maths Solver and get a step-by-step solution instantly. It works for all NCERT questions.
Try AI Solver — FreeCommon Mistakes to Avoid
- ✗Forgetting to simplify the fraction to lowest terms before checking the denominator
- ✗Not remembering the rule: terminating only if denominator has factors of 2 and 5 only
- ✗Confusing non-terminating non-recurring (irrational) with non-terminating recurring (rational)
Other Exercises in Chapter 1
Frequently Asked Questions
How do you know if a decimal is terminating?
A rational number p/q (in lowest terms) has a terminating decimal if the prime factorisation of q contains only 2s and 5s. If q has any other prime factor, the decimal repeats.
How many questions are in Exercise 1.4?
Exercise 1.4 has 3 questions on determining whether rational numbers have terminating or non-terminating recurring decimal expansions.
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