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 rational form is equal to (0.12\overline{3})?After reducing (\frac{5}{2^4\cdot 5^6}) to lowest form, after how many decimal places will it terminate?If (0.0\overline{6}) is written as (\frac{p}{q}) in lowest form, what is (q)?A number has decimal expansion (0.125000\ldots). Which statement is correct about it?For (\frac{a}{2^3\cdot 5^2\cdot 13}) to have a terminating decimal, what factor must (a) contain at minimum?If (\frac{7}{q}) has a terminating decimal expansion and is in lowest form, which option is possible for (q)?What type of decimal expansion will (\frac{99}{9900}) have after reducing it to lowest form?What type of decimal expansion does (\frac{27}{990}) have?If a rational number has reduced denominator (2^r5^s) and (r>s), how many decimal places will its decimal expansion have?What is the denominator when (0.375) is written as a fraction in lowest form?Which number is rational but does not have a terminating decimal expansion?If (\frac{m}{56}) has a terminating decimal expansion, which factor must (m) contain?How many decimal places will the decimal expansion of (\frac{13}{3125}) have?Which pair of equations is most suitable for converting (0.2\overline{18}) into a fraction?How many decimal places will the terminating decimal of (\frac{37}{2^6\cdot 5^3}) have?Which option is a non-terminating non-recurring decimal?If (\frac{p}{q}) is in lowest form and (q=2^2\cdot 5^3\cdot 3^0), what is the correct conclusion about the decimal expansion?Before reducing, what type of denominator is first obtained for the rational form of (0.\overline{142857})?After how many decimal places will the decimal expansion of (\frac{16}{2^7\cdot 5^4}) terminate?If a number has decimal expansion (4.1363636\ldots), which category does it belong to?