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Class 10MathematicsReal NumbersDecimal expansion of rational numbersHardLevel 20
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After reducing (\frac{126}{1575}) to lowest form, after how many decimal places will its decimal expansion terminate?

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Answer and explanation

Correct answer: (2)

Step 1: (126=2\cdot 3^2\cdot 7) and (1575=3^2\cdot 5^2\cdot 7). Step 2: After cancellation, we get (\frac{2}{25}). Since (25=5^2), the decimal terminates after (2) places. Step 3: Prime factorisation helps with larger numbers.

Related tags

Prime-FactorisationSimplificationDecimal-PlacesReal-Numbers

Frequently asked questions

What is the correct answer to this question?

(2)

Why is this the correct answer?

Step 1: (126=2\cdot 3^2\cdot 7) and (1575=3^2\cdot 5^2\cdot 7). Step 2: After cancellation, we get (\frac{2}{25}). Since (25=5^2), the decimal terminates after (2) places. Step 3: Prime factorisation helps with larger numbers.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Decimal expansion of rational numbers.

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  1. 1What type of decimal expansion will the rational number (\frac{3}{8}) have?
  2. 2What type of decimal expansion does (\frac{5}{6}) have?
  3. 3Under what condition does (\frac{p}{q}) have a terminating decimal expansion when the fraction is in lowest form?
  4. 4After reducing (\frac{15}{40}), what type of decimal expansion will it have?
  5. 5After at most how many decimal places will the decimal expansion of (\frac{7}{16}) terminate?
  6. 6Choose the correct statement about the decimal expansion of (\frac{11}{45}).
  7. 7Which of the following fractions will give a terminating decimal?
  8. 8Which of the following fractions will give a non-terminating recurring decimal?
  9. 9When (0.75) is written as a rational number, which form is obtained?
  10. 10If the denominator of a fraction in lowest form is (2^3\times5^2), after at most how many decimal places will its decimal expansion terminate?
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