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
What type of decimal expansion will the rational number (\frac{3}{8}) have?What type of decimal expansion does (\frac{5}{6}) have?Under what condition does (\frac{p}{q}) have a terminating decimal expansion when the fraction is in lowest form?After reducing (\frac{15}{40}), what type of decimal expansion will it have?After at most how many decimal places will the decimal expansion of (\frac{7}{16}) terminate?Choose the correct statement about the decimal expansion of (\frac{11}{45}).Which of the following fractions will give a terminating decimal?Which of the following fractions will give a non-terminating recurring decimal?When (0.75) is written as a rational number, which form is obtained?If the denominator of a fraction in lowest form is (2^3\times5^2), after at most how many decimal places will its decimal expansion terminate?After how many decimal places will the decimal expansion of (\frac{13}{125}) terminate?What type of decimal expansion does (\frac{22}{7}) have?Every terminating decimal can be written as which type of number?Which of the following decimals is not the decimal expansion of a rational number?What type of decimal expansion will (\frac{64}{455}) have?After reducing (\frac{35}{50}), what will be the type of its decimal expansion?After reducing (\frac{77}{210}), what type of decimal expansion will it have?Choose the correct option about the decimal expansion of (\frac{6}{15}).In lowest form, what form should the denominator (q) of a rational number have for the decimal to terminate?After how many decimal places does (\frac{1}{40}) terminate?