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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 is the decimal form of (\frac{9}{250})?EasyLevel 20What type of decimal expansion will (\frac{8}{33}) have?EasyLevel 20If the simplest form of a fraction is (\frac{a}{1000}), what type of decimal expansion will it have?EasyLevel 20Which number is rational because its decimal expansion terminates?EasyLevel 20After reducing (\frac{36}{150}), what will be the type of its decimal expansion?EasyLevel 20Which statement is correct about the decimal expansion of (\frac{13}{54})?EasyLevel 20What is the simplest fractional form of (2.04)?EasyLevel 20For which value of (q) will (\frac{11}{q}) have a terminating decimal expansion?EasyLevel 20What type of decimal expansion will (\frac{10}{27}) have?EasyLevel 20A student says (\frac{15}{60}) is non-terminating recurring because (60) contains (3). What is the correct conclusion?EasyLevel 20What is the simplest fractional form of (0.0008)?EasyLevel 20After how many decimal places will (\frac{3}{2^5\times5^5}) terminate?EasyLevel 20What type of decimal expansion will (\frac{41}{90}) have?EasyLevel 20After at most how many decimal places will (\frac{13}{5000}) terminate?EasyLevel 20What is the nature of the decimal (0.2\overline{3})?EasyLevel 20Which is the decimal expansion of (\frac{6}{11})?EasyLevel 20If a fraction has decimal form (0.625), what is it equal to?EasyLevel 20In which option will the denominator make the decimal expansion non-terminating recurring?EasyLevel 20Assertion: If (\frac{p}{q}) is in lowest form and (q) has a factor (7), the decimal will not terminate. Reason: For a terminating decimal, the denominator in lowest form must be made only of (2) and (5). Choose the correct option.EasyLevel 20Which fraction is equal to the decimal (0.0125)?EasyLevel 20