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
How many decimal places will the decimal expansion of (\frac{3^2\cdot 5}{2^6\cdot 3^2\cdot 5^4}) have?If a decimal has a fixed repeating block like (0.357357357\ldots), what type of number is it?In which option is the decimal expansion of (\frac{p}{q}) certainly terminating when the fraction is in lowest form?What denominator remains after reducing (\frac{27}{2^3\cdot 3^3\cdot 5^2})?If (0.00\overline{45}) is written as (\frac{p}{q}) in lowest form, what is (q)?If (0.00\overline{45}) is written as (\frac{p}{q}) in lowest form, which is the correct (q)?What type of decimal expansion will (\frac{18}{999}) have?A reduced fraction terminates exactly after (2) decimal places. Which denominator is not possible?After reducing (\frac{45}{2^5\cdot 3^2\cdot 5^4}) to lowest form, after how many decimal places will its decimal expansion terminate?When (0.02\overline{7}) is written as (\frac{p}{q}) in lowest form, what is (q)?If (\frac{p}{q}) is in lowest form and (q=2^4\cdot 5^7), after exactly how many decimal places will the decimal expansion terminate?After reducing (\frac{84}{2^3\cdot 3\cdot 5^2\cdot 7}), after how many decimal places will its decimal expansion terminate?If (n) is the smallest positive integer for which (\frac{n}{2^2\cdot 3^4\cdot 5\cdot 13}) has a terminating decimal, what is (n)?When (0.3\overline{18}) is written as (\frac{p}{q}) in lowest form, what is (q)?What is the denominator when (0.3\overline{18}) is converted to lowest fraction form?What type of decimal expansion will (\frac{125}{2^8\cdot 5^6\cdot 11}) have?Which denominator in a reduced fraction will give exactly (6) decimal places?If \(\frac{17}{2^a5^b}\) has a decimal expansion that terminates exactly after 9 places and \(a<b\), what is the value of \(b\)?What is the denominator when (0.00072) is written as a fraction in lowest form?Which is the lowest fraction form of (0.00072)?