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
If the denominator of a fraction in lowest form is (2^7\times5^3), after how many places will the decimal expansion terminate?After simplifying (\frac{45}{360}), after how many places will its decimal expansion terminate?After how many places will the decimal expansion of (\frac{7}{2^2\times5^4}) terminate?What type of decimal expansion will (\frac{16}{28}) have?Statement: The decimal expansion of every rational number is either terminating or non-terminating recurring. Choose the correct option.If the reduced denominator has the factor (13), what is the correct conclusion about the decimal expansion?After how many places will the decimal expansion of (\frac{31}{250}) terminate?After how many decimal places will the decimal expansion of (\frac{9}{2000}) terminate?After how many places will the decimal expansion of (\frac{1}{128}) terminate?If the denominator of a fraction in lowest form is (3125), after how many places will the decimal expansion terminate?If the decimal expansion of (\frac{5}{2^x\times5^3}) terminates exactly after (6) places, what can be the value of (x)?Which denominator should be checked to decide whether a decimal expansion terminates or not?What is the correct type of decimal expansion of (\frac{52}{195})?Choose the correct option for (\frac{84}{210}).Which of the following numbers is rational but has a non-terminating recurring decimal?Which of the following fractions will not have a terminating decimal expansion?If a fraction (\frac{p}{q}) in lowest form has a non-terminating recurring decimal, what is correct about (q)?A terminating decimal with exactly (4) decimal places can be written as a fraction with which denominator?What is the simplest fractional form of (0.875)?Which is the simplest fractional form of (0.\overline{45})?