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
A rational number has decimal expansion (5.27000\ldots). Which statement is correct?What type of decimal expansion will (\frac{2^4\cdot 3}{2^7\cdot 3^2\cdot 5^2}) have?Which decimal is equal to (\frac{13}{99})?What type of decimal expansion will (\frac{6}{375}) have after reducing it to lowest form?If (\frac{a}{2^2\cdot 3\cdot 5\cdot 19}) is to have a terminating decimal, what factor must (a) contain at minimum?When (0.0075) is written as a fraction in lowest form, what is the prime factorisation of the denominator?What is the denominator when (0.0075) is written as a fraction in lowest form?In which fraction will exactly two non-repeating decimal digits appear before the recurring part begins?After how many decimal places will (\frac{625}{2^8\cdot 5^6}) terminate?If (q) is a divisor of (10^5) and (\frac{p}{q}) is in lowest form, which conclusion about the decimal expansion is certain?What type of decimal will the sum of (0.\overline{81}) and (0.\overline{18}) give?Which reduced denominator will give exactly (4) decimal places?Which denominator will not give exactly (4) decimal places if the fraction is in lowest form?What is the denominator when (2.4\overline{6}) is written as a fraction in lowest form?What type of decimal expansion will (\frac{98}{2\cdot 5\cdot 7^3}) have?Which option is the lowest fraction form of (0.0008)?Among (\frac{1}{18}), (\frac{1}{45}), (\frac{1}{72}), and (\frac{1}{90}), which has the most non-repeating digits before the recurring part?If (\frac{p}{q}) has a terminating decimal and is in lowest form, what can be said about the prime factors of (q^2)?What is (0.24999\ldots) equal to?Which denominator in a reduced fraction will give a non-terminating recurring decimal?