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
For (\frac{p}{q}) in lowest form, (q=2^7\cdot 5^2). After how many decimal places will the decimal expansion terminate?What type of decimal expansion will (\frac{154}{2\cdot 5^3\cdot 7\cdot 11}) have?If (n) is the smallest positive integer for which (\frac{n}{2^4\cdot 3^3\cdot 5^2\cdot 11}) has a terminating decimal expansion, what is (n)?When (0.1\overline{24}) is written as (\frac{p}{q}) in lowest form, what is (q)?After how many decimal places will (\frac{42}{2^2\cdot 3\cdot 5^4\cdot 7}) terminate?A reduced fraction has denominator (2^a5^b), and its decimal terminates exactly after (8) places. Which statement must be true?Which fraction will not have a terminating decimal expansion?What is the denominator when (0.00064) is written as a fraction in lowest form?If (\frac{p}{q}) is in lowest form and (q=2^3\cdot 5^2\cdot 17), what type of decimal expansion will it have?By what should the denominator of (\frac{1}{2^5\cdot 5^8}) be multiplied to make it (10^8)?What is the denominator when (0.\overline{36}) is written in lowest form?Which option gives a number that is rational but not a terminating decimal?After how many decimal places will (\frac{225}{2^4\cdot 3^2\cdot 5^5}) terminate?If (\frac{x}{540}) has a terminating decimal expansion, what factor must (x) contain at minimum?What is the correct conclusion about the decimal (0.12122122212222\ldots)?If (\frac{31}{2^a5^b}) terminates exactly after (6) decimal places and (a>b), what is the value of (a)?If (\frac{7}{2^3\cdot 5^5}) is written as (\frac{N}{10^5}), what is (N)?Which fraction has a decimal expansion terminating exactly after (6) places?After how many decimal places will the decimal expansion of (\frac{9}{15625}) terminate?Assertion: The decimal expansion of (\frac{35}{280}) is terminating. Reason: (\frac{35}{280}=\frac{1}{8}). Choose the correct option.