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Subjects

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 is the correct decimal form of (\frac{3}{20})?What is the decimal form of (\frac{7}{25})?Which is the decimal expansion of (\frac{1}{3})?Which is the decimal expansion of (\frac{2}{11})?If a fixed block of digits repeats again and again in a decimal, what type of number is it?What type of decimal expansion will a fraction have if its denominator in lowest form is (14)?If the denominator of a fraction in lowest form is (250), after at most how many decimal places will its decimal expansion terminate?What type of decimal expansion will (\frac{45}{8}) have?Choose the correct option for the decimal expansion of (\frac{1}{7}).What is the simplest fractional form of (0.6)?What type of decimal expansion will (\frac{9}{80}) have?After reducing (\frac{12}{30}), what will be its decimal expansion type?For which value of (q) will (\frac{17}{q}) have a terminating decimal expansion?For which value of (q) will (\frac{5}{q}) have a non-terminating recurring decimal expansion?Which rational form represents (0.125)?What is the simplest fractional form of (0.04)?Which fraction will give a terminating decimal with exactly two decimal places?After how many decimal places will (\frac{13}{3125}) terminate?If a factor (3) remains in the denominator in lowest form, what type of decimal expansion will the rational number have?What type of decimal expansion will (\frac{121}{500}) have, and within how many places will it terminate at most?