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
How many decimal places will the decimal expansion of (\frac{7}{80}) have?After at most how many decimal places will (\frac{49}{2^7\times5^2}) terminate?After how many decimal places will (\frac{23}{2^3\times5^3}) terminate?What type of decimal expansion will (\frac{29}{343}) have?What is the simplest fractional form of (0.0005)?Which of the following decimals is a terminating decimal?Which of the following is an example of a non-terminating non-recurring decimal?A student says (\frac{3}{50}) will be recurring because (3) is not exactly divisible by (50). What is the correct conclusion?Assertion: If the denominator of (\frac{p}{q}) in lowest form is (2^a5^b), the decimal expansion terminates. Reason: In this case, the denominator can be changed into the form (10^k). Choose the correct option.What type of decimal expansion will the rational number (-\frac{17}{200}) have?After how many decimal places will the decimal expansion of (\frac{19}{32}) terminate?Which is the decimal expansion of (\frac{4}{9})?After reducing (\frac{18}{48}), what type of decimal expansion will it have?What is the correct decimal form of (\frac{21}{28})?If the denominator of a fraction in lowest form is (2^2\times5^4), after at most how many decimal places will its decimal expansion terminate?Which of the following fractions will not give a terminating decimal?What is the simplest fractional form of (0.375)?Which option gives a decimal that is rational but not terminating?After how many decimal places will the decimal expansion of (\frac{37}{625}) terminate?What type of decimal expansion will the rational number (-\frac{9}{28}) have?