The middle number between (0) and (1) is \(\frac{0+1}{2}=\frac{1}{2}\). In exams, use the average for the midpoint.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{2}\). The middle number between (0) and (1) is \(\frac{0+1}{2}=\frac{1}{2}\). In exams, use the average for the midpoint.
Step 3
Exam Tip
(0) और (1) के बीच की मध्य संख्या \(\frac{0+1}{2}=\frac{1}{2}\) है। परीक्षा में मध्य संख्या के लिए औसत लें।
\(-\frac{3}{2}=-1.5\), so it lies between (-2) and (-1). For negative numbers, values increase to the right.
Step 2
Why this answer is correct
The correct answer is A. \(-\frac{3}{2}\). \(-\frac{3}{2}=-1.5\), so it lies between (-2) and (-1). For negative numbers, values increase to the right.
Step 3
Exam Tip
\(-\frac{3}{2}=-1.5\) होता है, इसलिए यह (-2) और (-1) के बीच है। ऋणात्मक संख्याओं में दाईं ओर जाने पर मान बढ़ता है।
The denominator of \(\frac{3}{4}\) is (4), so divide (0) to (1) into (4) equal parts. The numerator tells you to move to the third mark.
Step 2
Why this answer is correct
The correct answer is A. (4). The denominator of \(\frac{3}{4}\) is (4), so divide (0) to (1) into (4) equal parts. The numerator tells you to move to the third mark.
Step 3
Exam Tip
\(\frac{3}{4}\) में हर (4) है, इसलिए (0) से (1) तक (4) बराबर भाग करें। अंश बताता है कि तीसरे निशान पर जाना है।
\(-\frac{7}{3}\approx -2.33\), so it lies between (-3) and (-2). Check the position of negative decimals carefully.
Step 2
Why this answer is correct
The correct answer is A. (-3) और (-2) / (-3) and (-2). \(-\frac{7}{3}\approx -2.33\), so it lies between (-3) and (-2). Check the position of negative decimals carefully.
Step 3
Exam Tip
\(-\frac{7}{3}\approx -2.33\) है, इसलिए यह (-3) और (-2) के बीच है। ऋणात्मक दशमलव की स्थिति ध्यान से देखें।
The integer part of (2.75) is (2), so it lies between (2) and (3). The integer part gives the first clue.
Step 2
Why this answer is correct
The correct answer is A. (2) और (3) / (2) and (3). The integer part of (2.75) is (2), so it lies between (2) and (3). The integer part gives the first clue.
Step 3
Exam Tip
(2.75) का पूर्णांक भाग (2) है, इसलिए यह (2) और (3) के बीच है। दशमलव का पूर्णांक भाग पहला संकेत देता है।
Since \(2^2=4\) and \(3^2=9\), \(\sqrt{5}\) lies between (2) and (3). Look at the nearest perfect squares.
Step 2
Why this answer is correct
The correct answer is A. (2) और (3) / (2) and (3). Since \(2^2=4\) and \(3^2=9\), \(\sqrt{5}\) lies between (2) and (3). Look at the nearest perfect squares.
Step 3
Exam Tip
क्योंकि \(2^2=4\) और \(3^2=9\), इसलिए \(\sqrt{5}\) (2) और (3) के बीच है। निकटतम पूर्ण वर्ग देखें।
Since \(3^2=9\) and \(4^2=16\), \(\sqrt{10}\) lies between (3) and (4). Use perfect squares to locate square roots.
Step 2
Why this answer is correct
The correct answer is A. (3) और (4) / (3) and (4). Since \(3^2=9\) and \(4^2=16\), \(\sqrt{10}\) lies between (3) and (4). Use perfect squares to locate square roots.
Step 3
Exam Tip
क्योंकि \(3^2=9\) और \(4^2=16\), इसलिए \(\sqrt{10}\) (3) और (4) के बीच है। वर्गमूल की स्थिति पूर्ण वर्गों से पहचानें।
\(-\sqrt{3}\) is negative, so it lies to the left of (0). Negative numbers are placed on the left side of the number line.
Step 2
Why this answer is correct
The correct answer is A. (0) के बाईं ओर / left of (0). \(-\sqrt{3}\) is negative, so it lies to the left of (0). Negative numbers are placed on the left side of the number line.
Step 3
Exam Tip
\(-\sqrt{3}\) ऋणात्मक संख्या है, इसलिए यह (0) के बाईं ओर होगी। ऋणात्मक संख्याएँ संख्या रेखा पर बाईं तरफ होती हैं।
A. न धनात्मक न ऋणात्मक/neither positive nor negative
Step 1
Concept
(0) is neither positive nor negative. It is treated as the origin on the number line.
Step 2
Why this answer is correct
The correct answer is A. न धनात्मक न ऋणात्मक / neither positive nor negative. (0) is neither positive nor negative. It is treated as the origin on the number line.
Step 3
Exam Tip
(0) न धनात्मक है और न ऋणात्मक। यह संख्या रेखा का मूल बिंदु माना जाता है।
A. वे (0) से बराबर दूरी पर हैं/they are equally far from (0)
Step 1
Concept
(2.4) and (-2.4) are opposite numbers, so they are equally far from (0). The sign tells the direction.
Step 2
Why this answer is correct
The correct answer is A. वे (0) से बराबर दूरी पर हैं / they are equally far from (0). (2.4) and (-2.4) are opposite numbers, so they are equally far from (0). The sign tells the direction.
Step 3
Exam Tip
(2.4) और (-2.4) विपरीत संख्याएँ हैं, इसलिए वे (0) से बराबर दूरी पर हैं। चिह्न दिशा बताता है।
A. तीन बराबर भागों में पहला निशान/first mark among three equal parts
Step 1
Concept
For \(\frac{1}{3}\), divide (0) to (1) into (3) equal parts and take the first mark. The denominator tells the number of parts.
Step 2
Why this answer is correct
The correct answer is A. तीन बराबर भागों में पहला निशान / first mark among three equal parts. For \(\frac{1}{3}\), divide (0) to (1) into (3) equal parts and take the first mark. The denominator tells the number of parts.
Step 3
Exam Tip
\(\frac{1}{3}\) के लिए (0) से (1) तक (3) बराबर भाग करें और पहला निशान लें। हर भागों की संख्या बताता है।
\(-\frac{1}{4}=-0.25\), so it lies between (-1) and (0). Small negative fractions are close to (0) on the left.
Step 2
Why this answer is correct
The correct answer is A. (-1) और (0) के बीच / between (-1) and (0). \(-\frac{1}{4}=-0.25\), so it lies between (-1) and (0). Small negative fractions are close to (0) on the left.
Step 3
Exam Tip
\(-\frac{1}{4}=-0.25\), इसलिए यह (-1) और (0) के बीच है। छोटे ऋणात्मक भिन्न (0) के बाईं ओर पास होते हैं।
A. दोनों एक ही बिंदु पर होंगे/both are at the same point
Step 1
Concept
Since (4.0=4), both represent the same point. A zero after the decimal does not change the value.
Step 2
Why this answer is correct
The correct answer is A. दोनों एक ही बिंदु पर होंगे / both are at the same point. Since (4.0=4), both represent the same point. A zero after the decimal does not change the value.
Step 3
Exam Tip
(4.0=4), इसलिए दोनों एक ही बिंदु हैं। दशमलव शून्य मान नहीं बदलता।
Every point on the number line represents a real number. Between (1) and (2), both rational and irrational numbers can occur.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक संख्याएँ / real numbers. Every point on the number line represents a real number. Between (1) and (2), both rational and irrational numbers can occur.
Step 3
Exam Tip
संख्या रेखा का प्रत्येक बिंदु एक वास्तविक संख्या दिखाता है। (1) और (2) के बीच परिमेय और अपरिमेय दोनों हो सकते हैं।
A. दोनों एक ही बिंदु पर हैं/both are at the same point
Step 1
Concept
\(\sqrt{16}=4\), so both have the same position. Identify square roots of perfect squares directly.
Step 2
Why this answer is correct
The correct answer is A. दोनों एक ही बिंदु पर हैं / both are at the same point. \(\sqrt{16}=4\), so both have the same position. Identify square roots of perfect squares directly.
Step 3
Exam Tip
\(\sqrt{16}=4\), इसलिए दोनों की स्थिति समान है। पूर्ण वर्ग का वर्गमूल सीधे पहचानें।
\(2+\frac{1}{4}=\frac{8}{4}+\frac{1}{4}=\frac{9}{4}\). Convert the integer to a fraction with the same denominator.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{9}{4}\). \(2+\frac{1}{4}=\frac{8}{4}+\frac{1}{4}=\frac{9}{4}\). Convert the integer to a fraction with the same denominator.
Step 3
Exam Tip
\(2+\frac{1}{4}=\frac{8}{4}+\frac{1}{4}=\frac{9}{4}\) है। पूर्णांक को समान हर वाली भिन्न में बदलें।
\(-2+\frac{1}{2}=-\frac{4}{2}+\frac{1}{2}=-\frac{3}{2}\). Be careful with direction when adding a fraction to a negative integer.
Step 2
Why this answer is correct
The correct answer is A. \(-\frac{3}{2}\). \(-2+\frac{1}{2}=-\frac{4}{2}+\frac{1}{2}=-\frac{3}{2}\). Be careful with direction when adding a fraction to a negative integer.
Step 3
Exam Tip
\(-2+\frac{1}{2}=-\frac{4}{2}+\frac{1}{2}=-\frac{3}{2}\) है। ऋणात्मक पूर्णांक में भिन्न जोड़ते समय दिशा ध्यान रखें।
\(\frac{3}{2}=1.5\), so both show the same point. Identify equal values in decimal and fraction forms.
Step 2
Why this answer is correct
The correct answer is A. दोनों बराबर हैं / both are equal. \(\frac{3}{2}=1.5\), so both show the same point. Identify equal values in decimal and fraction forms.
Step 3
Exam Tip
\(\frac{3}{2}=1.5\), इसलिए दोनों एक ही बिंदु दिखाते हैं। दशमलव और भिन्न का समान मान पहचानें।
\(0.333\ldots=\frac{1}{3}\) is a recurring decimal. Recurring decimals also represent fixed points on the number line.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{3}\). \(0.333\ldots=\frac{1}{3}\) is a recurring decimal. Recurring decimals also represent fixed points on the number line.
Step 3
Exam Tip
\(0.333\ldots=\frac{1}{3}\) एक आवर्ती दशमलव है। आवर्ती दशमलव भी संख्या रेखा पर निश्चित बिंदु दिखाते हैं।
Since \(2^2=4\) and \(3^2=9\), \(\sqrt{7}\) lies between (2) and (3). Bound the number using nearby squares.
Step 2
Why this answer is correct
The correct answer is A. (2) और (3) / (2) and (3). Since \(2^2=4\) and \(3^2=9\), \(\sqrt{7}\) lies between (2) and (3). Bound the number using nearby squares.
Step 3
Exam Tip
क्योंकि \(2^2=4\) और \(3^2=9\), इसलिए \(\sqrt{7}\) (2) और (3) के बीच है। संख्या को निकट वर्गों से घेरें।
\(\sqrt{8}\) lies between (2) and (3), so \(-\sqrt{8}\) lies between (-3) and (-2). The negative sign changes the direction.
Step 2
Why this answer is correct
The correct answer is A. (-3) और (-2) / (-3) and (-2). \(\sqrt{8}\) lies between (2) and (3), so \(-\sqrt{8}\) lies between (-3) and (-2). The negative sign changes the direction.
Step 3
Exam Tip
\(\sqrt{8}\) (2) और (3) के बीच है, इसलिए \(-\sqrt{8}\) (-3) और (-2) के बीच होगा। ऋण चिह्न दिशा बदल देता है।
\(\frac{2}{5}=0.4\), \(\frac{1}{2}=0.5\), and \(\frac{3}{5}=0.6\), so \(\frac{1}{2}\) lies between them. Decimal form helps in comparison.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{2}\). \(\frac{2}{5}=0.4\), \(\frac{1}{2}=0.5\), and \(\frac{3}{5}=0.6\), so \(\frac{1}{2}\) lies between them. Decimal form helps in comparison.
Step 3
Exam Tip
\(\frac{2}{5}=0.4\), \(\frac{1}{2}=0.5\), और \(\frac{3}{5}=0.6\), इसलिए \(\frac{1}{2}\) बीच में है। तुलना के लिए दशमलव रूप उपयोगी है।
\(x\le 2\) means (2) or smaller numbers, so it is the left side including (2). The symbol \(\le\) includes the boundary point.
Step 2
Why this answer is correct
The correct answer is A. (2) सहित बाईं ओर / left side including (2). \(x\le 2\) means (2) or smaller numbers, so it is the left side including (2). The symbol \(\le\) includes the boundary point.
Step 3
Exam Tip
\(x\le 2\) का अर्थ (2) या उससे छोटी संख्याएँ हैं, इसलिए (2) सहित बाईं ओर होगा। \(\le\) में सीमा बिंदु शामिल होता है।
A. (-1) को छोड़कर दाईं ओर/right side excluding (-1)
Step 1
Concept
(x>-1) means numbers greater than (-1), so the region is to the right and (-1) is not included. The symbol (>) gives an open point.
Step 2
Why this answer is correct
The correct answer is A. (-1) को छोड़कर दाईं ओर / right side excluding (-1). (x>-1) means numbers greater than (-1), so the region is to the right and (-1) is not included. The symbol (>) gives an open point.
Step 3
Exam Tip
(x>-1) का अर्थ (-1) से बड़ी संख्याएँ हैं, इसलिए दाईं ओर क्षेत्र होगा और (-1) शामिल नहीं होगा। (>) में खुला बिंदु बनता है।
Since \(3^2=9\) and \(4^2=16\), \(\sqrt{13}\) lies between (3) and (4). Use nearby perfect squares to locate square roots.
Step 2
Why this answer is correct
The correct answer is A. (3) और (4) / (3) and (4). Since \(3^2=9\) and \(4^2=16\), \(\sqrt{13}\) lies between (3) and (4). Use nearby perfect squares to locate square roots.
Step 3
Exam Tip
क्योंकि \(3^2=9\) और \(4^2=16\), इसलिए \(\sqrt{13}\) (3) और (4) के बीच है। वर्गमूल की स्थिति के लिए निकट पूर्ण वर्ग देखें।
\(-\frac{9}{4}=-2.25\), so it lies between (-3) and (-2). Be careful with direction for negative fractions.
Step 2
Why this answer is correct
The correct answer is A. (-3) और (-2) / (-3) and (-2). \(-\frac{9}{4}=-2.25\), so it lies between (-3) and (-2). Be careful with direction for negative fractions.
Step 3
Exam Tip
\(-\frac{9}{4}=-2.25\), इसलिए यह (-3) और (-2) के बीच है। ऋणात्मक भिन्न में छोटी दिशा को ध्यान से समझें।
