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 a terminating decimal is written as (\frac{p}{q}) in lowest form and has at most (4) decimal places, which statement about (q) is correct?In (\frac{1}{2^a5^b3^c}), (c>0). What type of decimal expansion will this fraction have?What is the denominator when (0.00\overline{3}) is written as a fraction in lowest form?Which pair of equations is most suitable for converting (2.37\overline{5}) into a fraction?Which fraction reduces to a denominator of (2^4)?For (\frac{a}{2310}) to have a terminating decimal expansion, what factor must (a) contain at minimum?After how many decimal places will the decimal expansion of (\frac{1}{640}) terminate?If the denominator in lowest form is (20), after how many decimal places will the decimal expansion terminate?Which decimal is equal to (\frac{7}{90})?If (\frac{p}{q}) is in lowest form and the decimal terminates exactly after (3) places, which of these cannot be (q)?If (\frac{17}{2^2\cdot 5^6}) is written as (\frac{N}{10^6}), what is (N)?Which statement is correct about (0.0999\ldots)?Which decimal is not equal to a terminating decimal?If the denominator of a reduced fraction is (2^4\cdot 5^2), how many decimal places will its decimal expansion have?What type of decimal expansion will (\frac{13}{2^2\cdot 5^2\cdot 13^2}) have?By what should numerator and denominator of (\frac{1}{2^4\cdot 5^6}) be multiplied to make the denominator (10^6)?Which statement is correct for the decimal expansion of (\frac{p}{q}), when (\frac{p}{q}) is in lowest form?Which fraction will have a decimal expansion terminating exactly after (5) places?What is the most suitable classification of the decimal (0.123456789101112\ldots)?If (n) is the smallest positive integer for which the decimal expansion of (\frac{n}{2^3\cdot 3^2\cdot 5\cdot 7}) becomes terminating, what is the value of (n)?