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
If (\frac{p}{q}) is in lowest form and (q=2^8\cdot 5^3), after exactly how many decimal places will the decimal expansion terminate?After reducing (\frac{198}{2^2\cdot 3^2\cdot 5^5\cdot 11}) to lowest form, after how many decimal places will its decimal expansion terminate?If (n) is the smallest positive integer for which (\frac{n}{2^5\cdot 3^2\cdot 5^3\cdot 7^2}) has a terminating decimal, what is (n)?When (0.2\overline{54}) is written as (\frac{p}{q}) in lowest form, what is (q)?Which is the lowest fraction form of (0.2\overline{54})?What type of decimal expansion will (\frac{147}{2\cdot 3\cdot 5^4\cdot 7^2}) have?Which reduced denominator will give exactly (7) decimal places?If \(\dfrac{29}{2^a5^b}\) terminates exactly after 8 decimal places and \(a>b\), what is the value of \(a\)?Which is the lowest fraction form of (0.00096)?What is the denominator when (0.00096) is written as a fraction in lowest form?In (\frac{1}{2^2\cdot 5^5\cdot 13}), how many non-repeating decimal digits appear before the recurring part starts?Assertion: (\frac{121}{2^3\cdot 5^2\cdot 11^2}) 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 a terminating decimal?After how many decimal places will (\frac{5^4\cdot 7}{2^6\cdot 5^7\cdot 7}) terminate?If (\frac{p}{q}) is in lowest form and (q) divides (10^9) but does not divide (10^7), what is certain about its decimal places?What is the denominator when (0.00\overline{63}) is written as a fraction in lowest form?Which is the lowest fraction form of (0.00\overline{63})?After how many decimal places will (\frac{2^4\cdot 5^3}{2^9\cdot 5^5}) terminate?Which statement is always correct when (\frac{p}{q}) is in lowest form?What is (0.37999\ldots) equal to?