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
A rational number (\frac{p}{q}) is in lowest form and (q=2^3\cdot 5^2). Choose the correct statement about its decimal expansion.How many digits after the decimal point will appear in the decimal expansion of (\frac{7}{1250}) in lowest form?Identify the type of decimal expansion of (\frac{63}{140}).If the decimal expansion of (\frac{13}{2^a5^b}) terminates exactly after (6) decimal places, which condition on (a) and (b) is correct?Which option gives a number whose decimal expansion will not terminate?After reducing (\frac{18}{225}) to lowest form, which statement about its decimal expansion is correct?If (\frac{n}{180}) has a terminating decimal expansion and the fraction is not necessarily in lowest form, what factor must (n) contain at minimum?For (\frac{41}{2^2\cdot 5^3}), what is the minimum value of (k) to convert the denominator into (10^k)?Which of the following fractions has a terminating decimal expansion even though its given denominator appears to contain a factor other than (2) and (5)?If a rational number in lowest form has decimal expansion (0.00048), which statement about the highest powers of (2) and (5) in its denominator is correct?Among (\frac{1}{6}), (\frac{1}{12}), (\frac{1}{15}), and (\frac{1}{30}), which has the shortest terminating part before the recurring part starts?A rational number has reduced denominator (q=2^4\cdot 5^4). If its numerator is not divisible by (10), what is the most suitable conclusion about its decimal expansion?If (x=\frac{3}{2^m5^n}) and (m<n), by what should numerator and denominator be multiplied to write (x) as a terminating decimal?Which of the following statements is always true?What is the correct type of decimal expansion of (\frac{77}{2^3\cdot 5^2\cdot 7})?Which fraction has a non-terminating recurring decimal, though a student may wrongly think it terminates by looking quickly at the denominator?Which fraction has a non-terminating recurring decimal expansion?A fraction in lowest form is (\frac{p}{q}) and (q=72). What can be said about its decimal expansion?If (\frac{p}{q}) is in lowest form and (q=2^5\cdot 5^2\cdot 11), what will its decimal expansion be?When (0.\overline{27}) is written as a rational number, what will be the reduced denominator?