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
Which fraction has a terminating decimal even though the given denominator contains (31)?What type of decimal is the sum of (0.\overline{36}) and (0.\overline{63})?Which statement is correct about (\frac{1}{2^4\cdot 5^4\cdot 17})?If (\frac{p}{q}) has a terminating decimal and is in lowest form, what is correct about the prime factors of (q^4)?What type of decimal expansion will (\frac{2^5\cdot 17}{2^9\cdot 5^2\cdot 17^2}) have?What is the denominator when (0.015625) is written in lowest fraction form?Which option is the lowest fraction form of (0.00015625)?Among (\frac{1}{192}), (\frac{1}{225}), (\frac{1}{448}), and (\frac{1}{350}), which has the most non-repeating digits before the recurring part?When \(\frac{11}{2^8\cdot 5^5}\) is converted into \(\frac{N}{10^8}\), what is N?Which denominator will not give exactly (3) decimal places if the fraction is in lowest form?What is (0.00999\ldots) equal to?If the reduced denominator is q = 2^5 × 5^5 × 7^0, what is certain about the decimal expansion?If (\frac{a}{2^6\cdot 3\cdot 5^4\cdot 7\cdot 13}) is to have a terminating decimal, what factor must (a) contain at minimum?After reducing (\frac{750}{2^6\cdot 3\cdot 5^5}) to lowest form, after how many decimal places will its decimal expansion terminate?When (0.12\overline{45}) is written as (\frac{p}{q}) in lowest form, what is (q)?If (n) is the smallest positive integer for which (\frac{n}{2^4\cdot 5\cdot 7^3\cdot 11}) has a terminating decimal, what is (n)?In the decimal expansion of (\frac{1}{2^3\cdot 5^4\cdot 19^2}), how many non-repeating digits appear before the recurring part?Which denominator will not give exactly (6) decimal places in a reduced fraction?If \(\frac{23}{2^5\cdot 5^9}\) is written as \(\frac{N}{10^9}\), what is \(N\)?What is the denominator when (0.\overline{216}) is written in lowest fraction form?