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}) has a terminating decimal and is in lowest form, what is correct about the prime factors of (q^3)?What type of decimal expansion will (\frac{2^4\cdot 13}{2^7\cdot 5^3\cdot 13^2}) have?What is the denominator when (0.03125) is written in lowest fraction form?Which option is the lowest fraction form of (0.0003125)?Among (\frac{1}{96}), (\frac{1}{175}), (\frac{1}{224}), and (\frac{1}{250}), which has the most non-repeating digits before the recurring part?If \(\frac{7}{2^6\cdot 5^4}\) is written as \(\frac{N}{10^6}\), what is \(N\)?After reducing (\frac{2^3\cdot 3^2\cdot 11}{2^6\cdot 3^3\cdot 5^4\cdot 11^2}) to lowest form, what type of decimal expansion will it have?If (\frac{19}{2^5\cdot 5^2}) is written as (\frac{N}{10^5}), what is (N)?When (0.0\overline{125}) is written as (\frac{p}{q}) in lowest form, what is (q)?If (\frac{p}{q}) is in lowest form, (q) divides (10^6) but does not divide (10^5), what is certain about the decimal expansion?If (\frac{p}{q}) is in lowest form and (q=2^9\cdot 5^4), after exactly how many decimal places will the decimal expansion terminate?After reducing (\frac{484}{2^4\cdot 5^3\cdot 11^2}) to lowest form, after how many decimal places will its decimal expansion terminate?If (n) is the smallest positive integer for which (\frac{n}{2^3\cdot 3^2\cdot 5^4\cdot 17^2}) has a terminating decimal, what is (n)?When (0.4\overline{27}) is written as (\frac{p}{q}) in lowest form, what is (q)?What is the denominator when (0.\overline{108}) is written in lowest fraction form?What type of decimal expansion will (\frac{55}{2^2\cdot 5^3\cdot 11^2}) have?Which reduced denominator will give exactly (8) decimal places?If \(\dfrac{31}{2^a5^b}\) terminates exactly after 10 decimal places and \(b>a\), what is the value of \(b\)?Which is the lowest fraction form of (0.00084)?In (\frac{1}{2^4\cdot 5^6\cdot 17}), how many non-repeating decimal digits appear before the recurring part starts?