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
Which statement is most correct about the decimal expansion of (\frac{1}{2^2\cdot 5^2\cdot 7})?A fraction in lowest form is (\frac{p}{2^3\cdot 5^5}). If it is written as (\frac{N}{10^5}), what is (N)?What type of decimal expansion will (\frac{35}{2^2\cdot 5\cdot 7^2}) have?What is the denominator when (0.0048) is written as a fraction in lowest form?If a rational number has a non-terminating recurring decimal expansion, which statement about its denominator in lowest form is correct?Which option correctly gives the number of decimal places in (\frac{1}{2^a5^b}), when the fraction is in lowest form?What type of decimal expansion will (\frac{44}{2^3\cdot 5\cdot 11}) have?What is the correct conclusion about the decimal expansion of (\frac{44}{2^3\cdot 5\cdot 11})?What type of number is (0.125\overline{6})?After how many decimal places will the decimal expansion of (\frac{81}{2^4\cdot 3^4\cdot 5^2}) terminate?For (\frac{p}{q}) in lowest form, (q=2^6\cdot 5^4). What is the maximum number of decimal places in its decimal expansion?After how many decimal places will the decimal expansion of (\frac{75}{2^3\cdot 3\cdot 5^2}) terminate?If the decimal expansion of (\frac{11}{2^4\cdot 5^n}) terminates exactly after (7) decimal places, what is the value of (n)?After reducing (\frac{39}{2600}) to lowest form, after how many decimal places will its decimal expansion terminate?When (0.00\overline{27}) is written as a fraction (\frac{p}{q}) in lowest form, what is (q)?Which fraction will have a terminating decimal expansion even though the given denominator shows a factor (13)?If (\frac{m}{735}) has a terminating decimal expansion, what factor must (m) contain at minimum?In lowest form, the denominator of a rational number is (2^2\cdot 5\cdot 9). What type of decimal expansion will it have?What is the correct classification of the decimal (0.101001000100001\ldots)?What is the denominator when (0.\overline{09}) is written as a fraction in lowest form?