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Class 10MathematicsReal NumbersDecimal expansion of rational numbersHardLevel 19
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Which pair of equations is most suitable for converting (0.2\overline{18}) into a fraction?

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Answer and explanation

Correct answer: (10x=2.1818\ldots), (1000x=218.1818\ldots)

Step 1: In (x=0.21818\ldots), the non-repeating part is (2) and the repeating part is (18). Step 2: First use (10x=2.1818\ldots), then (1000x=218.1818\ldots) so the recurring parts align. Step 3: Choose powers of (10) based on the lengths of the non-repeating and repeating parts.

Related tags

Recurring-Decimal-MethodFraction-ConversionReal-NumbersAdvanced

Frequently asked questions

What is the correct answer to this question?

(10x=2.1818\ldots), (1000x=218.1818\ldots)

Why is this the correct answer?

Step 1: In (x=0.21818\ldots), the non-repeating part is (2) and the repeating part is (18). Step 2: First use (10x=2.1818\ldots), then (1000x=218.1818\ldots) so the recurring parts align. Step 3: Choose powers of (10) based on the lengths of the non-repeating and repeating parts.

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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10 more MCQs
  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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