\(0.\overline{216}=\frac{216}{999}=\frac{8}{37}\). For a purely recurring decimal, first use a denominator of (9)'s and then reduce fully.
Step 2
Why this answer is correct
The correct answer is A. (37). \(0.\overline{216}=\frac{216}{999}=\frac{8}{37}\). For a purely recurring decimal, first use a denominator of (9)'s and then reduce fully.
Step 3
Exam Tip
\(0.\overline{216}=\frac{216}{999}=\frac{8}{37}\) है। पूर्ण आवर्ती दशमलव में पहले (9) वाला हर बनाएं और फिर पूरा सरल करें।
\(0.00015625=\frac{15625}{100000000}\), and reducing by (15625) gives \(\frac{1}{6400}\). Do not forget to cancel common factors in large denominators.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{6400}\). \(0.00015625=\frac{15625}{100000000}\), and reducing by (15625) gives \(\frac{1}{6400}\). Do not forget to cancel common factors in large denominators.
Step 3
Exam Tip
\(0.00015625=\frac{15625}{100000000}\) है और (15625) से सरल करने पर \(\frac{1}{6400}\) मिलता है। बड़े हर में समान गुणनखंड काटना न भूलें।
\(0.015625=\frac{15625}{1000000}=\frac{1}{64}\). Convert a terminating decimal to a fraction and reduce the denominator.
Step 2
Why this answer is correct
The correct answer is B. (64). \(0.015625=\frac{15625}{1000000}=\frac{1}{64}\). Convert a terminating decimal to a fraction and reduce the denominator.
Step 3
Exam Tip
\(0.015625=\frac{15625}{1000000}=\frac{1}{64}\) है। सांत दशमलव को भिन्न में बदलकर हर को सरलतम रूप में देखें।
\(0.046875=\frac{46875}{1000000}\), and reducing gives \(\frac{3}{64}\). Convert the decimal to a fraction and reduce fully.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{3}{64}\). \(0.046875=\frac{46875}{1000000}\), and reducing gives \(\frac{3}{64}\). Convert the decimal to a fraction and reduce fully.
Step 3
Exam Tip
\(0.046875=\frac{46875}{1000000}\) है और सरल करने पर \(\frac{3}{64}\) मिलता है। दशमलव से भिन्न बनाकर अंतिम रूप तक सरल करें।
\(0.\overline{063}=\frac{63}{999}\), and reducing by (9) gives \(\frac{7}{111}\). An initial zero inside the repeating block is also counted as a digit.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{7}{111}\). \(0.\overline{063}=\frac{63}{999}\), and reducing by (9) gives \(\frac{7}{111}\). An initial zero inside the repeating block is also counted as a digit.
Step 3
Exam Tip
\(0.\overline{063}=\frac{63}{999}\) और (9) से सरल करने पर \(\frac{7}{111}\) मिलता है। आवर्ती भाग में आरंभिक शून्य को भी अंक माना जाता है।
Two non-repeating zeros and two repeating digits give \(\frac{54}{9900}\). Reducing it gives \(\frac{3}{550}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{3}{550}\). Two non-repeating zeros and two repeating digits give \(\frac{54}{9900}\). Reducing it gives \(\frac{3}{550}\).
Step 3
Exam Tip
दो अनावर्ती शून्य और दो आवर्ती अंकों से \(\frac{54}{9900}\) बनता है। इसे सरल करने पर \(\frac{3}{550}\) मिलता है।
\(0.00084=\frac{84}{100000}\), and reducing by (4) gives \(\frac{21}{25000}\). Even for small decimals, check the greatest common factor carefully.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{21}{25000}\). \(0.00084=\frac{84}{100000}\), and reducing by (4) gives \(\frac{21}{25000}\). Even for small decimals, check the greatest common factor carefully.
Step 3
Exam Tip
\(0.00084=\frac{84}{100000}\) है और (4) से सरल करने पर \(\frac{21}{25000}\) मिलता है। छोटे दशमलव में भी महत्तम सामान्य गुणनखंड ध्यान से देखें।
\(0.\overline{108}=\frac{108}{999}=\frac{4}{37}\). First form the denominator with (9)'s according to the repeating digits and then reduce.
Step 2
Why this answer is correct
The correct answer is B. (37). \(0.\overline{108}=\frac{108}{999}=\frac{4}{37}\). First form the denominator with (9)'s according to the repeating digits and then reduce.
Step 3
Exam Tip
\(0.\overline{108}=\frac{108}{999}=\frac{4}{37}\) है। आवर्ती अंकों की संख्या के अनुसार पहले (9) वाला हर बनाएं फिर सरल करें।
\(0.0003125=\frac{3125}{10000000}\), and reducing by (3125) gives \(\frac{1}{3200}\). Do not forget to cancel common factors in large denominators.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{3200}\). \(0.0003125=\frac{3125}{10000000}\), and reducing by (3125) gives \(\frac{1}{3200}\). Do not forget to cancel common factors in large denominators.
Step 3
Exam Tip
\(0.0003125=\frac{3125}{10000000}\) है और (3125) से सरल करने पर \(\frac{1}{3200}\) मिलता है। बड़े हर में समान गुणनखंड काटना न भूलें।
\(0.01875=\frac{1875}{100000}\), and dividing by (625) gives \(\frac{3}{160}\). Convert the decimal to a fraction and reduce fully.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{3}{160}\). \(0.01875=\frac{1875}{100000}\), and dividing by (625) gives \(\frac{3}{160}\). Convert the decimal to a fraction and reduce fully.
Step 3
Exam Tip
\(0.01875=\frac{1875}{100000}\) है और (625) से भाग देने पर \(\frac{3}{160}\) मिलता है। दशमलव से भिन्न बनाकर अंतिम रूप तक सरल करें।
\(0.01875=\frac{1875}{100000}=\frac{3}{160}\), and \(160=2^5\cdot 5\). The correct prime factorisation is \(2^5\cdot 5\), so complete the calculation before choosing.
Step 2
Why this answer is correct
The correct answer is A. \(2^4\cdot 5\). \(0.01875=\frac{1875}{100000}=\frac{3}{160}\), and \(160=2^5\cdot 5\). The correct prime factorisation is \(2^5\cdot 5\), so complete the calculation before choosing.
Step 3
Exam Tip
\(0.01875=\frac{1875}{100000}=\frac{3}{160}\) और \(160=2^5\cdot 5\) है। सही अभाज्य रूप \(2^5\cdot 5\) है इसलिए गणना पूरी करके विकल्प चुनें।
\(0.\overline{045}=\frac{45}{999}\), and reducing by (9) gives \(\frac{5}{111}\). First form the denominator with (9)'s according to the repeating digits.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{5}{111}\). \(0.\overline{045}=\frac{45}{999}\), and reducing by (9) gives \(\frac{5}{111}\). First form the denominator with (9)'s according to the repeating digits.
Step 3
Exam Tip
\(0.\overline{045}=\frac{45}{999}\) और (9) से सरल करने पर \(\frac{5}{111}\) मिलता है। आवर्ती अंकों की संख्या के अनुसार पहले (9) वाला हर बनाएं।
\(0.\overline{045}=\frac{45}{999}=\frac{5}{111}\), so the denominator is (111). An initial zero inside the repeating block is also counted as a digit.
Step 2
Why this answer is correct
The correct answer is A. (37). \(0.\overline{045}=\frac{45}{999}=\frac{5}{111}\), so the denominator is (111). An initial zero inside the repeating block is also counted as a digit.
Step 3
Exam Tip
\(0.\overline{045}=\frac{45}{999}=\frac{5}{111}\) है इसलिए हर (111) है। आवर्ती भाग में आरंभिक शून्य को भी अंक माना जाता है।
Two non-repeating zeros and two repeating digits give \(\frac{63}{9900}\). Reducing it gives \(\frac{7}{1100}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{7}{1100}\). Two non-repeating zeros and two repeating digits give \(\frac{63}{9900}\). Reducing it gives \(\frac{7}{1100}\).
Step 3
Exam Tip
दो अनावर्ती शून्य और दो आवर्ती अंकों से \(\frac{63}{9900}\) बनता है। इसे सरल करने पर \(\frac{7}{1100}\) मिलता है।
\(0.00096=\frac{96}{100000}\), and reducing by (32) gives \(\frac{3}{3125}\). Even for small decimals, check the greatest common factor carefully.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{3}{3125}\). \(0.00096=\frac{96}{100000}\), and reducing by (32) gives \(\frac{3}{3125}\). Even for small decimals, check the greatest common factor carefully.
Step 3
Exam Tip
\(0.00096=\frac{96}{100000}\) है और (32) से सरल करने पर \(\frac{3}{3125}\) मिलता है। छोटे दशमलव में भी महत्तम सामान्य गुणनखंड ध्यान से देखें।
The non-repeating part (2) and repeating part (54) give \(\frac{252}{990}\), which reduces to \(\frac{14}{55}\). In exams, identify repeating and non-repeating digits separately.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{14}{55}\). The non-repeating part (2) and repeating part (54) give \(\frac{252}{990}\), which reduces to \(\frac{14}{55}\). In exams, identify repeating and non-repeating digits separately.
Step 3
Exam Tip
सांत भाग (2) और आवर्ती भाग (54) से भिन्न \(\frac{252}{990}\) बनती है जो \(\frac{14}{55}\) तक सरल होती है। परीक्षा में आवर्ती और अनावर्ती अंकों को अलग पहचानें।
\(0.000625=\frac{625}{1000000}\), and reducing by (625) gives \(\frac{1}{1600}\). Do not fear large denominators; cancel common factors.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{1600}\). \(0.000625=\frac{625}{1000000}\), and reducing by (625) gives \(\frac{1}{1600}\). Do not fear large denominators; cancel common factors.
Step 3
Exam Tip
\(0.000625=\frac{625}{1000000}\), जिसे (625) से सरल करने पर \(\frac{1}{1600}\) मिलता है। बड़े हर से डरें नहीं, समान गुणनखंड काटें।
\(0.0625=\frac{625}{10000}=\frac{1}{16}\). Convert a terminating decimal to a fraction and always reduce the denominator.
Step 2
Why this answer is correct
The correct answer is B. (16). \(0.0625=\frac{625}{10000}=\frac{1}{16}\). Convert a terminating decimal to a fraction and always reduce the denominator.
Step 3
Exam Tip
\(0.0625=\frac{625}{10000}=\frac{1}{16}\)। सांत दशमलव को भिन्न में बदलकर हर को सरलतम रूप में अवश्य देखें।
\(0.0375=\frac{375}{10000}\), and dividing by (125) gives \(\frac{3}{80}\). Convert the decimal to a fraction and reduce fully.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{3}{80}\). \(0.0375=\frac{375}{10000}\), and dividing by (125) gives \(\frac{3}{80}\). Convert the decimal to a fraction and reduce fully.
Step 3
Exam Tip
\(0.0375=\frac{375}{10000}\) और (125) से भाग देने पर \(\frac{3}{80}\) मिलता है। दशमलव से भिन्न बनाकर अंतिम रूप तक सरल करें।
\(0.0375=\frac{375}{10000}=\frac{3}{80}\), and \(80=2^4\cdot 5\). The correct prime factorisation is \(2^4\cdot 5\).
Step 2
Why this answer is correct
The correct answer is A. \(2^3\cdot 5\). \(0.0375=\frac{375}{10000}=\frac{3}{80}\), and \(80=2^4\cdot 5\). The correct prime factorisation is \(2^4\cdot 5\).
Step 3
Exam Tip
\(0.0375=\frac{375}{10000}=\frac{3}{80}\) और \(80=2^4\cdot 5\)। सही अभाज्य रूप \(2^4\cdot 5\) है।
Two non-repeating zeros and two repeating digits give \(\frac{72}{9900}\). Reducing it gives \(\frac{2}{275}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{2}{275}\). Two non-repeating zeros and two repeating digits give \(\frac{72}{9900}\). Reducing it gives \(\frac{2}{275}\).
Step 3
Exam Tip
दो अनावर्ती शून्य और दो आवर्ती अंकों से \(\frac{72}{9900}\) बनता है। इसे सरल करने पर \(\frac{2}{275}\) मिलता है।
\(0.00072=\frac{72}{100000}\), and reducing by (8) gives \(\frac{9}{12500}\). First write the denominator as a power of (10), then reduce.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{9}{12500}\). \(0.00072=\frac{72}{100000}\), and reducing by (8) gives \(\frac{9}{12500}\). First write the denominator as a power of (10), then reduce.
Step 3
Exam Tip
\(0.00072=\frac{72}{100000}\), जिसे (8) से सरल करने पर \(\frac{9}{12500}\) मिलता है। पहले (10) की घात वाला हर बनाकर फिर भिन्न को सरल करें।
\(0.3\overline{18}=0.3181818\ldots=\frac{315}{990}=\frac{7}{22}\). Always reduce the final fraction in mixed recurring decimals.
Step 2
Why this answer is correct
The correct answer is A. (22). \(0.3\overline{18}=0.3181818\ldots=\frac{315}{990}=\frac{7}{22}\). Always reduce the final fraction in mixed recurring decimals.
Step 3
Exam Tip
\(0.3\overline{18}=0.3181818\ldots=\frac{315}{990}=\frac{7}{22}\)। मिश्रित आवर्ती दशमलव में अंतिम उत्तर हमेशा सरल करें।
First form the denominator as a power of (10), then reduce. चरण 1: \(0.0008=\frac{8}{10000}\) है। चरण 2: (8) से भाग देने पर \(\frac{1}{1250}\) मिलता है। चरण 3: दशमलव के स्थानों के अनुसार पहले (10) की घात वाला हर बनाइए, फिर सरल कीजिए।
