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
What is the denominator when (0.\overline{027}) is written in lowest fraction form?A fraction has reduced denominator (2^3\cdot 5^2\cdot 3^0\cdot 11^0). What type of decimal expansion will it have?In the decimal expansion of (\frac{1}{2^4\cdot 5^3\cdot 37}), how many non-repeating digits appear before the recurring part?When 0.0375 is written in lowest fraction form, what is the prime factorisation of the denominator?Which is the lowest fraction form of (0.0375)?If p/q is in lowest form and q = 2^m × 5^n × 7^r, where r > 0, what type of decimal expansion will it have?Which decimal can definitely be called a rational number?After how many decimal places will 72/(2^3 × 3^2 × 5^5) terminate?Which fraction has a terminating decimal even though the given denominator contains (19)?What type of decimal is the sum of (0.\overline{54}) and (0.\overline{45})?Which statement is correct about (\frac{1}{2^2\cdot 5^2\cdot 9})?If (\frac{p}{q}) has a non-terminating recurring decimal and is in lowest form, what is correct about (q)?What type of decimal expansion will (\frac{2^5\cdot 7}{2^8\cdot 5^2\cdot 7^2}) have?What is the denominator when (0.0625) is written in lowest fraction form?Which option is the lowest fraction form of (0.000625)?Among (\frac{1}{48}), (\frac{1}{75}), (\frac{1}{112}), and (\frac{1}{150}), which has the most non-repeating digits before the recurring part?If (q=2^r5^s) and (\frac{p}{q}) is in lowest form, what is the minimum (k) to write the decimal as (\frac{N}{10^k})?Which number is an example of a non-terminating non-recurring decimal?When \(\frac{3}{2^4\cdot 5^6}\) is written as \(\frac{N}{10^6}\), what is \(N\)?After reducing (\frac{242}{2^3\cdot 5^4\cdot 11^2}) to lowest form, after how many decimal places will its decimal expansion terminate?