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
After how many places will the decimal expansion of (\frac{23}{500}) terminate?After reducing (\frac{81}{90}), what type of decimal expansion will it have?Why will the decimal expansion of (\frac{37}{74}) terminate?After simplifying (\frac{121}{242}), after how many places will the decimal expansion terminate?If the reduced denominator contains the factor (11), what is the correct conclusion about the decimal expansion?For a lowest-form fraction with denominator (2^3\times5^5), what should be multiplied to make the denominator a power of (10)?What type of decimal expansion will (\frac{21}{56}) have in lowest form?Choose the correct option about the decimal expansion of (\frac{13}{75}).If the denominator of a fraction in lowest form is (2^4\times5^6), after how many places will its decimal expansion terminate?Which statement is correct about (0.04\overline{7})?Without doing division, after how many places will the decimal expansion of (\frac{19}{80}) terminate?Choose the correct statement about the decimal expansion of (\frac{23}{90}).After reducing (\frac{36}{144}), what type of decimal expansion will it have?If a fraction in lowest form has denominator (320), after at most how many places will its decimal expansion terminate?After how many places will the decimal expansion of (\frac{11}{6250}) terminate?Which conclusion is correct for (\frac{18}{42})?After simplifying (\frac{49}{140}), what type of decimal expansion will it have?When (0.0625) is written as a fraction in lowest form, what will be the denominator?What is the simplest fractional form of (0.\overline{18})?Which statement is correct about (0.01001000100001\ldots)?