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
In (\frac{1}{2^3\cdot 5^2\cdot 7^2}), how many non-repeating decimal digits will appear before the recurring part starts?Assertion: (\frac{63}{2^4\cdot 3^2\cdot 5^3\cdot 7}) has a terminating decimal. Reason: After reducing, only (2) and (5) remain in the denominator. Choose the correct option.Which decimal is rational but not equal to any terminating decimal?After how many decimal places will (\frac{3^5}{2^2\cdot 3^4\cdot 5^6}) terminate?If (\frac{p}{q}) is in lowest form and (q) divides (10^8) but does not divide (10^6), what is certain about its decimal places?What is the denominator when (0.00\overline{72}) is written as a fraction in lowest form?Which is the lowest fraction form of (0.00\overline{72})?After how many decimal places will (\frac{2^3\cdot 5^2}{2^7\cdot 5^5}) terminate?Which statement is always true when (\frac{p}{q}) is in lowest form?What is (0.124999\ldots) equal to?If (\frac{a}{2^3\cdot 3^2\cdot 5^4\cdot 17}) is to have a terminating decimal, what factor must (a) contain at minimum?What type of decimal expansion will (\frac{189}{2^2\cdot 3^3\cdot 5\cdot 7}) have?What is the correct classification of the decimal (0.202002000200002\ldots)?If (\frac{11}{2^6\cdot 5^2}) is written as (\frac{N}{10^6}), what is (N)?Choose the correct value of \(N\) when \(\frac{11}{2^6\cdot 5^2}\) is written as \(\frac{N}{10^6}\).If the reduced denominator is (q=2^5\cdot 5^5) and the numerator is not divisible by (10), what is certain about the decimal expansion?Which option will give a non-terminating recurring decimal?Which fraction will give a non-terminating recurring decimal?What type of decimal expansion will (\frac{14}{2\cdot 5^2\cdot 7^2}) have?If a reduced fraction has a decimal terminating in at most (5) places, its denominator will be a divisor of which number?