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 fractional form of (0.1\overline{6})?When (6.375) is written as a fraction in lowest form, what will its denominator be like?Choose the correct statement about the decimal expansion (12.004).Which of the following statements is incorrect?Which statement is correct about a non-terminating recurring decimal?After how many places will the decimal expansion of (\frac{1}{2^6}) terminate?After reducing (\frac{27}{216}), after how many places will its decimal expansion terminate?What is the decimal form of (\frac{7}{1250})?After how many places will the decimal expansion of (\frac{43}{400}) terminate?After simplifying (\frac{63}{175}), what type of decimal expansion will it have?Why will the decimal expansion of (\frac{65}{104}) terminate?After simplifying (\frac{169}{338}), after how many places will the decimal expansion terminate?If the reduced denominator contains the factor (17), what type of decimal expansion will occur?What should (2^6\times5^2) be multiplied by to make it a power of (10)?If (\frac{b}{180}) reduces to a fraction with denominator (20), what type of decimal expansion will it have?After how many places will the decimal expansion of (\frac{55}{88}) terminate?After reducing (\frac{14}{63}), what type of decimal expansion will it have?If a decimal repeats a fixed block like (0.\overline{142857}), what type of number is it?Which of the following decimals does not represent a rational number?The denominator of a rational number in lowest form is (2^3 \times 5^2 \times 7). Choose the correct statement about its decimal expansion.