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
Assertion: (\frac{169}{2^3\cdot 5^4\cdot 13^2}) has a terminating decimal. Reason: After reducing, only (2) and (5) remain in the denominator. Choose the correct option.After how many decimal places will (\frac{3^4\cdot 5^2}{2^7\cdot 3^4\cdot 5^5}) terminate?If (\frac{p}{q}) is in lowest form and (q) divides (10^{10}) but does not divide (10^8), what is certain about its decimal places?Which is the lowest fraction form of (0.00\overline{54})?After how many decimal places will (\frac{2^5\cdot 5^2}{2^{10}\cdot 5^6}) terminate?What is (0.46999\ldots) equal to?If (\frac{a}{2^5\cdot 3^4\cdot 5^2\cdot 19}) is to have a terminating decimal, what factor must (a) contain at minimum?What type of decimal expansion will (\frac{245}{2^2\cdot 5^2\cdot 7^3}) have?What is the correct classification of the decimal (0.505000500005000005\ldots)?If \(\dfrac{37}{2^4\cdot 5^8}\) is written as \(\dfrac{N}{10^8}\), what is \(N\)?If the reduced denominator is (q=2^7\cdot 5^7), what is certain about the decimal expansion?What type of decimal expansion will 22/(2^2 × 5^4 × 11^2) have?After how many decimal places will (\frac{243}{2^5\cdot 3^5\cdot 5^4}) terminate?If a reduced fraction has a decimal terminating in at most (9) places, its denominator will be a divisor of which number?Which is the lowest fraction form of (0.\overline{063})?A fraction has reduced denominator (2^5\cdot 5^2\cdot 7^0\cdot 19^0). What type of decimal expansion will it have?In the decimal expansion of (\frac{1}{2^7\cdot 5^3\cdot 41}), how many non-repeating digits appear before the recurring part?Which is the lowest fraction form of (0.046875)?If p/q is in lowest form and q = 2^m × 5^n × 13^r, where r > 0, what type of decimal expansion will it have?What type of decimal expansion will (\frac{320}{2^7\cdot 5^3\cdot 11}) have?