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Subjects

Mathematics

Decimal expansion of rational numbers

परिमेय संख्याओं का दशमलव प्रसार

In Class 10 Mathematics, this topic from the Real Numbers chapter explains how rational numbers are represented in decimal form. Students learn to distinguish terminating decimals from non-terminating recurring decimals and determine the type of expansion by reducing a fraction to its simplest form and examining the prime factors of its denominator. The topic also develops accuracy in long division, fraction-to-decimal conversion, and understanding the relationship between rational numbers and their decimal representations.

Practice questions

Which option shows a rational but non-terminating recurring decimal?After how many places will the decimal expansion of (\frac{18}{225}) terminate?Which of the following fractions will have a non-terminating recurring decimal expansion?Which statement is correct about (0.48) and (0.\overline{48})?What type of decimal expansion will (\frac{5}{2^3\times3\times5^2}) have?After how many places will the decimal expansion of (\frac{3}{2^5\times5^3}) terminate?Which option shows the correct decimal expansion of (\frac{7}{80})?Read the assertion and reason: Assertion: The decimal expansion of (\frac{27}{375}) is terminating. Reason: Its denominator in lowest form is (125). Choose the correct option.If (x=0.\overline{27}), what is the simplest fraction form of (x)?After how many places will the decimal expansion of (\frac{16}{1250}) terminate?What will be the decimal form of (\frac{77}{308})?Which statement is correct about the decimal expansion of (\frac{23}{2^2\times5^3})?Which decimal has (\frac{7}{20}) as its simplest fraction form?If (\frac{n}{36}) is in lowest form and (n) has no common factor with (36), what type of decimal expansion will it have?Which option correctly shows the simplest fraction form of (0.0125)?After how many places will the decimal expansion of (\frac{125}{2^4\times5^5}) terminate?Which option will not have a terminating decimal expansion?After how many decimal places will (\frac{17}{6250}) terminate?Which statement is correct about the decimal expansions of (\frac{3}{14}) and (\frac{9}{28})?Write (0.12\overline{3}) as a fraction in simplest form.