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
Choose the correct conclusion about the decimal expansion of (\frac{96}{450}).After how many places will the decimal expansion of (\frac{144}{320}) terminate?If the denominator of a fraction in lowest form is (2^5\times5^3), after at most how many places will the decimal expansion terminate?Choose the correct option for the decimal expansion of (\frac{221}{650}).Choose the correct statement about the set {x ∈ ℚ : x has a terminating decimal expansion}.Without doing long division, what type of decimal expansion will the rational number (\frac{13}{8}) have?Choose the correct statement about the decimal expansion of the rational number (\frac{7}{45}).After reducing (\frac{39}{312}), what is the correct type of its decimal expansion?If a fraction in lowest form has denominator (200), after at most how many decimal places will its decimal expansion terminate?After how many decimal places will the decimal expansion of (\frac{27}{125}) terminate?Which conclusion is correct for (\frac{14}{35})?Why will the decimal expansion of (\frac{9}{28}) not terminate?When (0.375) is written as a fraction in lowest form, which statement about the denominator's prime factors is correct?What type of number is represented by (0.\overline{6})?Choose the correct statement about (0.101001000100001\ldots).If the denominator of a fraction in lowest form is (2^n\times5^3) and its decimal terminates exactly after (4) places, what is the value of (n)?After simplifying (\frac{64}{4000}), after how many decimal places will its decimal expansion terminate?After how many decimal places will the decimal expansion of (\frac{3}{2^4\times5}) terminate?What type of decimal expansion will (\frac{6}{15}) have?Statement: If a fraction (\frac{p}{q}) in lowest form has (q=2^a5^b), then its decimal expansion will terminate. Choose the correct option.