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 does (\frac{18}{45}) have?What is the correct decimal conclusion for (\frac{22}{55})?After how many decimal places will (\frac{3}{80}) terminate?Which decimal is an example of a non-terminating recurring rational number?If the denominator of a fraction in lowest form is (2^3\times5^2), after at most how many decimal places will it terminate?If the denominator of a fraction in lowest form is (2^4), after how many decimal places will the decimal expansion terminate?If the denominator of a fraction in lowest form is (5^3), after how many decimal places will the decimal expansion terminate?Choose the correct option about the decimal expansion of (\frac{11}{30}).After how many decimal places will (\frac{27}{1250}) terminate?What lowest form is obtained before converting (\frac{14}{35}) into a decimal?Why does the decimal expansion of (\frac{35}{70}) terminate?Write (0.2) in fraction form.Which fraction is equal to (0.05)?What will be the decimal form of (\frac{3}{40})?Which case cannot occur in the decimal expansion of a rational number?If a decimal is non-terminating but a fixed block of digits repeats, what type of number is it?After how many places will the decimal expansion of (\frac{17}{200}) terminate?Why will the decimal expansion of (\frac{7}{64}) terminate?What type of decimal expansion does (\frac{8}{15}) have?What is the decimal form of (\frac{15}{75})?