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Class 9 Maths: The World of Numbers, 8 practice questions with answers

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These are 8 practice questions on Chapter 3, The World of Numbers, of the new NCERT Class 9 Maths textbook, Ganita Manjari, Part I (First Edition, April 2026). Each has a worked answer and the textbook page it comes from. They cover telling rational numbers from irrational ones, the distance between two numbers on the number line, finding a rational number between two others, deciding without dividing whether a decimal ends, and turning a decimal back into a fraction. Try each one on paper before you open the answer. Earlier Class 8 number sets are A Square and A Cube and Power Play (Exponents).

These questions are our own, drafted with AI help. Every number was re-computed by a test script, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Manjari: Mathematics, Textbook for Grade 9, Part I, Chapter 3, printed pages 41 to 67):

Rational or irrational

Question 1. Which one of these numbers is irrational: −7, 0.25, 22/7, √10?

Answer: √10. −7 = −7/1, 0.25 = 1/4 and 22/7 are all ratios of integers, so they are rational. √10 cannot be written as a ratio of integers; the textbook's summary names it as an irrational number, beside √2 and π. (Rational numbers, page 47; irrational numbers, page 53; summary, page 63.)

Question 2. How far apart are −3/4 and 5/4 on the number line?

Answer: 2. The distance is |a − b| = |−3/4 − 5/4| = |−8/4| = |−2| = 2. (Distance on the number line, page 52.)

Question 3. Find a rational number between 1/3 and 1/2 by taking their average.

Answer: 5/12. (1/3 + 1/2) ÷ 2 = (2/6 + 3/6) ÷ 2 = (5/6) ÷ 2 = 5/12. Check: 1/3 = 4/12 and 1/2 = 6/12, and 5/12 lies between them. (The density of rational numbers, page 52.)

Terminating or repeating

Question 4. Without long division, decide whether 13/40 has a terminating decimal, and if it does, write it.

Answer: it terminates; 13/40 = 0.325. 13/40 is in lowest terms and 40 = 2 × 2 × 2 × 5 has no prime factors other than 2 and 5, so the decimal terminates. Multiply the top and the bottom by 25 to make the denominator 1000: 13/40 = 325/1000 = 0.325. (The 2-and-5 test and making a power of 10, page 58.)

Question 5. Does 7/12 have a terminating decimal?

Answer: no, it repeats. 7/12 is in lowest terms and 12 = 2 × 2 × 3 has the prime factor 3, so the decimal cannot terminate. It repeats: 7/12 = 0.58333…, with the 3 repeating. (Page 58; a rational number's decimal either terminates or repeats, page 57.)

Decimals back to fractions

Question 6. Write 0.272727… (the block 27 repeating) as a fraction in lowest terms.

Answer: 3/11. Let x = 0.2727… Two digits repeat, so multiply by 100: 100x = 27.2727… Subtract: 100x − x = 27, so 99x = 27 and x = 27/99 = 3/11. (Pure repeating decimals, page 59.)

Question 7. Write 0.8333… (only the 3 repeating) as a fraction in lowest terms.

Answer: 5/6. Let x = 0.8333… One digit (8) does not repeat, so 10x = 8.333… One digit repeats, so multiply by 10 again: 100x = 83.333… Subtract: 100x − 10x = 83.333… − 8.333… = 75, so 90x = 75 and x = 75/90 = 5/6. (General repeating decimals, pages 59-60.)

Question 8. Write 0.625 as a fraction in lowest terms.

Answer: 5/8. 0.625 = 625/1000. Divide the top and the bottom by 125: 5/8. Check: 8 = 2 × 2 × 2, so 5/8 is exactly the kind of fraction whose decimal terminates. (Terminating decimals back to p/q, Case 1 and Example 4, pages 58-59.)

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Sources

All opened and read on 21 October 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 40.

The definitions and methods are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.