\(625\times16=10000\), so \( \frac{43}{625}=\frac{688}{10000}=0.0688 \). Making the denominator a power of (10) is the safest method.
Step 2
Why this answer is correct
The correct answer is A. (0.0688). \(625\times16=10000\), so \( \frac{43}{625}=\frac{688}{10000}=0.0688 \). Making the denominator a power of (10) is the safest method.
Step 3
Exam Tip
\(625\times16=10000\), इसलिए \( \frac{43}{625}=\frac{688}{10000}=0.0688 \) है। हर को (10) की घात बनाना सबसे सुरक्षित तरीका है।
\(0.003125=\frac{3125}{1000000}=\frac{1}{320}\). Count decimal places to write the denominator and then simplify.
Step 2
Why this answer is correct
The correct answer is B. \( \frac{1}{320} \). \(0.003125=\frac{3125}{1000000}=\frac{1}{320}\). Count decimal places to write the denominator and then simplify.
Step 3
Exam Tip
\(0.003125=\frac{3125}{1000000}=\frac{1}{320}\) है। दशमलव स्थान गिनकर हर लिखें और फिर सरल करें।
The denominator has (7), a factor other than (2) and (5). So the rational number will have a non-terminating recurring decimal.
Step 2
Why this answer is correct
The correct answer is C. असांत आवर्ती / Non-terminating recurring. The denominator has (7), a factor other than (2) and (5). So the rational number will have a non-terminating recurring decimal.
Step 3
Exam Tip
हर में (7) है, जो (2) और (5) के अलावा गुणनखंड है। इसलिए परिमेय संख्या का दशमलव असांत आवर्ती होगा।
\( \frac{91}{140}=\frac{13}{20} \) and \(20=2^2\times5\). Therefore, the decimal expansion will be terminating.
Step 2
Why this answer is correct
The correct answer is A. सांत / Terminating. \( \frac{91}{140}=\frac{13}{20} \) and \(20=2^2\times5\). Therefore, the decimal expansion will be terminating.
Step 3
Exam Tip
\( \frac{91}{140}=\frac{13}{20} \) और \(20=2^2\times5\) है। इसलिए दशमलव प्रसार सांत होगा।
The bar is only over (18), so after (3), (18) repeats. In bar notation, the barred part repeats continuously.
Step 2
Why this answer is correct
The correct answer is A. \(0.3181818\ldots\). The bar is only over (18), so after (3), (18) repeats. In bar notation, the barred part repeats continuously.
Step 3
Exam Tip
बार केवल (18) पर है, इसलिए (3) के बाद (18) बार-बार आएगा। बार संकेतन में बार वाले भाग को लगातार दोहराते हैं।
The tenths and hundredths digits are equal, so the thousandths digit must satisfy (a>6). Hence the smallest value is (7).
Step 2
Why this answer is correct
The correct answer is C. (7). The tenths and hundredths digits are equal, so the thousandths digit must satisfy (a>6). Hence the smallest value is (7).
Step 3
Exam Tip
दसवें और सौवें स्थान समान हैं, इसलिए हजारवें स्थान पर (a>6) होना चाहिए। अतः सबसे छोटा मान (7) है।
The number of zeros keeps changing, so there is no fixed recurring part. Such a decimal is non-terminating non-recurring.
Step 2
Why this answer is correct
The correct answer is C. असांत अनावर्ती / Non-terminating non-recurring. The number of zeros keeps changing, so there is no fixed recurring part. Such a decimal is non-terminating non-recurring.
Step 3
Exam Tip
इसमें शून्यों की संख्या बदलती रहती है, इसलिए कोई निश्चित आवर्ती भाग नहीं है। ऐसा दशमलव असांत अनावर्ती होता है।
\(64\times15625=1000000\), so \( \frac{7}{64}=0.109375 \). A denominator that is a power of (2) can be converted to a power of (10).
Step 2
Why this answer is correct
The correct answer is A. (0.109375). \(64\times15625=1000000\), so \( \frac{7}{64}=0.109375 \). A denominator that is a power of (2) can be converted to a power of (10).
Step 3
Exam Tip
\(64\times15625=1000000\), इसलिए \( \frac{7}{64}=0.109375 \) है। (2) की घात वाले हर को (10) की घात में बदला जा सकता है।
C. सांत क्योंकि सरल रूप \( \frac{2}{5} \) है/Terminating because the simplest form is \( \frac{2}{5} \)
Step 1
Concept
\( \frac{18}{45}=\frac{2}{5} \), and (5) has only factor (5). It is necessary to simplify the fraction first.
Step 2
Why this answer is correct
The correct answer is C. सांत क्योंकि सरल रूप \( \frac{2}{5} \) है / Terminating because the simplest form is \( \frac{2}{5} \). \( \frac{18}{45}=\frac{2}{5} \), and (5) has only factor (5). It is necessary to simplify the fraction first.
Step 3
Exam Tip
\( \frac{18}{45}=\frac{2}{5} \) और (5) केवल (5) का गुणनखंड है। पहले भिन्न को सरल रूप में बदलना जरूरी है।
The first (5) is in tenths and the last (5) is in ten-thousandths. Zero-value places need not be written separately.
Step 2
Why this answer is correct
The correct answer is B. \(2+\frac{5}{10}+\frac{5}{10000}\). The first (5) is in tenths and the last (5) is in ten-thousandths. Zero-value places need not be written separately.
Step 3
Exam Tip
पहला (5) दसवें और अंतिम (5) दस हजारवें स्थान पर है। शून्य वाले स्थानों का मान अलग से लिखना आवश्यक नहीं होता।
Multiplying both by (10000) gives \(1250\div5=250\). Multiplying both parts of a division by the same number does not change the quotient.
Step 2
Why this answer is correct
The correct answer is B. (250). Multiplying both by (10000) gives \(1250\div5=250\). Multiplying both parts of a division by the same number does not change the quotient.
Step 3
Exam Tip
दोनों को (10000) से गुणा करने पर \(1250\div5=250\) मिलता है। दशमलव भाग में समान गुणा करने से भागफल नहीं बदलता।
\(0.999\ldots=1\) is a standard recurring decimal result. In exams, treat \(0.\overline{9}\) as equal to (1).
Step 2
Why this answer is correct
The correct answer is C. \(0.999\ldots=1\). \(0.999\ldots=1\) is a standard recurring decimal result. In exams, treat \(0.\overline{9}\) as equal to (1).
Step 3
Exam Tip
\(0.999\ldots=1\) एक मानक आवर्ती दशमलव परिणाम है। परीक्षा में \(0.\overline{9}\) को (1) के बराबर मानें।
\( \frac{11}{20}=0.55 \) and \( \frac{5}{9}=0.555\ldots \), so (0.554) lies between them. Convert the boundaries into decimals.
Step 2
Why this answer is correct
The correct answer is C. (0.554). \( \frac{11}{20}=0.55 \) and \( \frac{5}{9}=0.555\ldots \), so (0.554) lies between them. Convert the boundaries into decimals.
Step 3
Exam Tip
\( \frac{11}{20}=0.55 \) और \( \frac{5}{9}=0.555\ldots \), इसलिए (0.554) इनके बीच है। सीमाओं को दशमलव में बदलें।
\(48=2^4\times3\) has (3), and the fraction is in simplest form. Therefore, the decimal will be non-terminating recurring.
Step 2
Why this answer is correct
The correct answer is B. असांत आवर्ती / Non-terminating recurring. \(48=2^4\times3\) has (3), and the fraction is in simplest form. Therefore, the decimal will be non-terminating recurring.
Step 3
Exam Tip
\(48=2^4\times3\) में (3) है और भिन्न सरल रूप में है। इसलिए दशमलव असांत आवर्ती होगा।
\(0.\overline{27}\) is non-terminating recurring, so it is rational but not terminating. Recurring decimals are always rational.
Step 2
Why this answer is correct
The correct answer is C. \(0.\overline{27}\). \(0.\overline{27}\) is non-terminating recurring, so it is rational but not terminating. Recurring decimals are always rational.
Step 3
Exam Tip
\(0.\overline{27}\) असांत आवर्ती है, इसलिए परिमेय है लेकिन सांत नहीं है। आवर्ती दशमलव हमेशा परिमेय होते हैं।
It is non-terminating and has no fixed repetition. Such a decimal can be the form of an irrational number.
Step 2
Why this answer is correct
The correct answer is C. अपरिमेय / Irrational. It is non-terminating and has no fixed repetition. Such a decimal can be the form of an irrational number.
Step 3
Exam Tip
यह असांत है और इसमें निश्चित दोहराव नहीं है। ऐसा दशमलव अपरिमेय संख्या का रूप हो सकता है।
The decimal places are equal, so compare from left to right. The smallest is (4.006) and the greatest is (4.600).
Step 2
Why this answer is correct
The correct answer is A. (4.006<4.060<4.066<4.600). The decimal places are equal, so compare from left to right. The smallest is (4.006) and the greatest is (4.600).
Step 3
Exam Tip
दशमलव स्थान समान हैं, इसलिए बाएं से दाएं तुलना करें। सबसे छोटा (4.006) और सबसे बड़ा (4.600) है।
C. \(0.20200200020000\ldots\) बिना निश्चित दोहराव/\(0.20200200020000\ldots\) without fixed repetition
Step 1
Concept
A non-terminating decimal without fixed repetition is irrational. Terminating and recurring decimals are rational.
Step 2
Why this answer is correct
The correct answer is C. \(0.20200200020000\ldots\) बिना निश्चित दोहराव / \(0.20200200020000\ldots\) without fixed repetition. A non-terminating decimal without fixed repetition is irrational. Terminating and recurring decimals are rational.
Step 3
Exam Tip
बिना निश्चित दोहराव वाला असांत दशमलव अपरिमेय होता है। सांत और आवर्ती दशमलव परिमेय होते हैं।
\(1600\times625=1000000\), so \( \frac{29}{1600}=0.018125 \). Even a large denominator can be converted into a power of (10).
Step 2
Why this answer is correct
The correct answer is A. (0.018125). \(1600\times625=1000000\), so \( \frac{29}{1600}=0.018125 \). Even a large denominator can be converted into a power of (10).
Step 3
Exam Tip
\(1600\times625=1000000\), इसलिए \( \frac{29}{1600}=0.018125 \) है। बड़े हर को भी (10) की घात में बदला जा सकता है।
\( \frac{56}{154}=\frac{4}{11} \), and the denominator has (11). So the decimal will be non-terminating recurring.
Step 2
Why this answer is correct
The correct answer is C. असांत आवर्ती / Non-terminating recurring. \( \frac{56}{154}=\frac{4}{11} \), and the denominator has (11). So the decimal will be non-terminating recurring.
Step 3
Exam Tip
\( \frac{56}{154}=\frac{4}{11} \) है और हर में (11) है। इसलिए दशमलव असांत आवर्ती होगा।
\( \frac{1}{15}=0.0666\ldots=0.06\overline{6} \), which is greater than (0.0625). Convert the fraction into decimal for comparison.
Step 2
Why this answer is correct
The correct answer is A. \(0.0625<\frac{1}{15}=0.06\overline{6}\). \( \frac{1}{15}=0.0666\ldots=0.06\overline{6} \), which is greater than (0.0625). Convert the fraction into decimal for comparison.
Step 3
Exam Tip
\( \frac{1}{15}=0.0666\ldots=0.06\overline{6} \), जो (0.0625) से बड़ा है। तुलना के लिए भिन्न को दशमलव में बदलें।
\( \frac{13}{125}=0.104 \) and \( \frac{7}{40}=0.175 \), so the sum is (0.279). First convert the fractions into decimals.
Step 2
Why this answer is correct
The correct answer is A. (0.279). \( \frac{13}{125}=0.104 \) and \( \frac{7}{40}=0.175 \), so the sum is (0.279). First convert the fractions into decimals.
Step 3
Exam Tip
\( \frac{13}{125}=0.104 \) और \( \frac{7}{40}=0.175 \), इसलिए योग (0.279) है। पहले भिन्नों को दशमलव में बदलें।
The number of zeros between (2)'s increases, so there is no fixed repetition. Such a decimal is non-terminating non-recurring.
Step 2
Why this answer is correct
The correct answer is C. असांत अनावर्ती / Non-terminating non-recurring. The number of zeros between (2)'s increases, so there is no fixed repetition. Such a decimal is non-terminating non-recurring.
Step 3
Exam Tip
इसमें (2) के बीच शून्यों की संख्या बढ़ती है, इसलिए निश्चित दोहराव नहीं है। ऐसा दशमलव असांत अनावर्ती होता है।
On multiplying by (100000), the decimal point moves five places to the right. Therefore, \(0.004096\times100000=409.6\).
Step 2
Why this answer is correct
The correct answer is B. (409.6). On multiplying by (100000), the decimal point moves five places to the right. Therefore, \(0.004096\times100000=409.6\).
Step 3
Exam Tip
(100000) से गुणा करने पर दशमलव बिंदु पांच स्थान दाईं ओर जाता है। इसलिए \(0.004096\times100000=409.6\) है।
\(0.59\overline{9}=0.6000\ldots\) and \( \frac{3}{5}=0.6 \). Identify repeating (9)'s correctly.
Step 2
Why this answer is correct
The correct answer is C. \(0.6=0.59\overline{9}=\frac{3}{5}\). \(0.59\overline{9}=0.6000\ldots\) and \( \frac{3}{5}=0.6 \). Identify repeating (9)'s correctly.
Step 3
Exam Tip
\(0.59\overline{9}=0.6000\ldots\) और \( \frac{3}{5}=0.6 \) है। दोहरते (9) को सही तरह पहचानें।
\( \frac{7}{8}=0.875 \), so (0.8735) is greater than (0.873) and less than (0.875). Convert boundary values into decimals.
Step 2
Why this answer is correct
The correct answer is B. (0.8735). \( \frac{7}{8}=0.875 \), so (0.8735) is greater than (0.873) and less than (0.875). Convert boundary values into decimals.
Step 3
Exam Tip
\( \frac{7}{8}=0.875 \), इसलिए (0.8735), (0.873) से बड़ा और (0.875) से छोटा है। सीमा मानों को दशमलव में बदलें।
\(128\times78125=10000000\), so \( \frac{37}{128}=0.2890625 \). A denominator that is a power of (2) gives a terminating decimal.
Step 2
Why this answer is correct
The correct answer is A. (0.2890625). \(128\times78125=10000000\), so \( \frac{37}{128}=0.2890625 \). A denominator that is a power of (2) gives a terminating decimal.
Step 3
Exam Tip
\(128\times78125=10000000\), इसलिए \( \frac{37}{128}=0.2890625 \) है। (2) की घात वाले हर का दशमलव सांत होता है।
