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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

Choose the correct option for the decimal expansion of (\frac{1}{11}).Which block of digits repeats in (0.464646\ldots)?Which fraction is equal to (0.\overline{7})?Which terminating decimal is equal to (\frac{3}{5})?Which fraction is equal to (0.75)?If the denominator of a fraction in lowest form is (250), after how many places will its decimal expansion terminate?If a fraction is in lowest form, which denominator will give a non-terminating recurring decimal?Read the assertion and reason: Assertion: The decimal expansion of (\frac{1}{125}) is terminating. Reason: (125=5^3). Choose the correct option.Choose the correct option about the decimal expansion of (\frac{45}{120}).If the denominator of a fraction in lowest form is (2^2\times5^4), after at most how many decimal places will the decimal expansion terminate?Choose the correct conclusion about the decimal expansion of (\frac{27}{150}).What type of decimal expansion will (\frac{56}{180}) have?If the denominator of a fraction in lowest form is (2^3\times5^5), after at most how many decimal places will its decimal expansion terminate?After how many decimal places will the decimal expansion of (\frac{39}{520}) terminate?By which least natural number should (\frac{7}{24}) be multiplied so that the resulting fraction has a terminating decimal expansion?After how many places will the decimal expansion of (\frac{11}{2^4\times5^2}) terminate?Which statement is correct about the decimal expansion of (\frac{65}{312})?Which decimal is equal to (\frac{7}{16})?Write (0.3125) as a fraction in simplest form.If (\frac{a}{40}) is in lowest form, after at most how many decimal places can its decimal expansion terminate?