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
When (0.4\overline{7}) is written as a fraction (\frac{p}{q}) in lowest form, what is (q)?If the denominator of a reduced fraction is (2^a5^b), (a<b), and its decimal terminates exactly after (4) places, what is the correct conclusion?Which of the following fractions has a non-terminating recurring decimal expansion?To write (\frac{1}{2^r5^s}) as a fraction with denominator (10^8) and an integer numerator, which condition is necessary?Which of the following fractions will have the greatest number of decimal places in its decimal expansion?What is the denominator when (0.000125) is written as a fraction in lowest form?After how many decimal places will the decimal expansion of (\frac{18}{2^2\cdot 3^2\cdot 5^4}) terminate?Which denominator (q) can give a reduced fraction (\frac{p}{q}) whose decimal terminates exactly after (5) places?Assertion: (\frac{17}{200}) has a terminating decimal expansion. Reason: (200=2^3\cdot 5^2). Choose the correct option.When (0.125) is written as (\frac{p}{q}) in lowest form, what is the prime factorisation of (q)?Which decimal cannot be rational?If the denominator in lowest form is (2^5\cdot 5^3\cdot 7^0), what type of decimal expansion will it have?What type of decimal expansion will (\frac{55}{2\cdot 5^2\cdot 11^2}) have?What type of decimal expansion will (0.\overline{6}+0.\overline{3}) have?After reducing (\frac{126}{1575}) to lowest form, after how many decimal places will its decimal expansion terminate?What is the least value of (k) for (\frac{5^k}{2^3\cdot 5^8}) to terminate exactly after (3) decimal places?In which fraction will the repeating part start immediately after the decimal point?What is the denominator when (0.3125) is written as a fraction in lowest form?If (\frac{p}{q}) is in lowest form and (q=2^m5^n\cdot 13), what is the correct statement about its decimal expansion?Which fraction in lowest form is equal to (0.048)?