The smallest number is farthest left, and (-1.8) is the smallest. For negative decimals, larger magnitude means farther left.
Step 2
Why this answer is correct
The correct answer is A. ( -1.8). The smallest number is farthest left, and (-1.8) is the smallest. For negative decimals, larger magnitude means farther left.
Step 3
Exam Tip
सबसे छोटी संख्या संख्या रेखा पर सबसे बाईं ओर होती है, और (-1.8) सबसे छोटी है। ऋणात्मक दशमलव में अधिक परिमाण का मतलब अधिक बायाँ होता है।
A. यह (-4) और (-3) के बीच है/It lies between (-4) and (-3)
Step 1
Concept
\( \frac{-13}{4}=-3.25\), which lies between (-4) and (-3). Place negative decimals to the left side.
Step 2
Why this answer is correct
The correct answer is A. यह (-4) और (-3) के बीच है / It lies between (-4) and (-3). \( \frac{-13}{4}=-3.25\), which lies between (-4) and (-3). Place negative decimals to the left side.
Step 3
Exam Tip
\( \frac{-13}{4}=-3.25\), जो (-4) और (-3) के बीच आता है। ऋणात्मक दशमलव को बाईं ओर रखें।
Since \(2<\sqrt{7}<3\), we have \(-3<-\sqrt{7}<-2\). For negative numbers, remember the order reverses.
Step 2
Why this answer is correct
The correct answer is A. ( -3) और (-2) / ( -3) and (-2). Since \(2<\sqrt{7}<3\), we have \(-3<-\sqrt{7}<-2\). For negative numbers, remember the order reverses.
Step 3
Exam Tip
क्योंकि \(2<\sqrt{7}<3\), इसलिए \(-3<-\sqrt{7}<-2\)। ऋणात्मक संख्या में क्रम उलटने पर ध्यान रखें।
The distance from (2.357) to (2.36) is (0.003), and to (2.35) is (0.007). The smaller distance gives the closer point.
Step 2
Why this answer is correct
The correct answer is B. (2.36). The distance from (2.357) to (2.36) is (0.003), and to (2.35) is (0.007). The smaller distance gives the closer point.
Step 3
Exam Tip
(2.357) की (2.36) से दूरी (0.003) और (2.35) से दूरी (0.007) है। छोटी दूरी वाला बिंदु अधिक निकट होता है।
\(\sqrt{5}\approx2.236\) and \(\sqrt{2}\approx1.414\), so the difference is about (0.822). Use short approximations to locate differences of irrationals.
Step 2
Why this answer is correct
The correct answer is A. ((0,1)). \(\sqrt{5}\approx2.236\) and \(\sqrt{2}\approx1.414\), so the difference is about (0.822). Use short approximations to locate differences of irrationals.
Step 3
Exam Tip
\(\sqrt{5}\approx2.236\) और \(\sqrt{2}\approx1.414\), इसलिए अंतर लगभग (0.822) है। अपरिमेयों के अंतर का स्थान निकालने के लिए छोटे अनुमान उपयोग करें।
Because \(4^2+1^2=17\), the hypotenuse will be \(\sqrt{17}\). Pythagoras theorem is useful for square-root construction on the number line.
Step 2
Why this answer is correct
The correct answer is A. (4) और (1) / (4) and (1). Because \(4^2+1^2=17\), the hypotenuse will be \(\sqrt{17}\). Pythagoras theorem is useful for square-root construction on the number line.
Step 3
Exam Tip
क्योंकि \(4^2+1^2=17\), इसलिए कर्ण \(\sqrt{17}\) होगा। संख्या रेखा पर वर्गमूल निर्माण में पाइथागोरस प्रमेय उपयोगी है।
\(\pi\approx3.14\) and \(\sqrt{10}\approx3.16\), so \(\pi<\sqrt{10}\). Good approximations help compare close irrationals.
Step 2
Why this answer is correct
The correct answer is A. \(\pi<\sqrt{10}\). \(\pi\approx3.14\) and \(\sqrt{10}\approx3.16\), so \(\pi<\sqrt{10}\). Good approximations help compare close irrationals.
Step 3
Exam Tip
\(\pi\approx3.14\) और \(\sqrt{10}\approx3.16\), इसलिए \(\pi<\sqrt{10}\)। निकट अपरिमेयों की तुलना में अच्छे अनुमान उपयोगी होते हैं।
A. -\(\frac{5}{6}\), \(-\frac{3}{4}\), \(-\frac{2}{3}\)
Step 1
Concept
For negative numbers, the one with larger magnitude is farther left, so \(-\frac{5}{6}<-\frac{3}{4}<-\frac{2}{3}\). Compare positive values first, then reverse the order.
Step 2
Why this answer is correct
The correct answer is A. -\(\frac{5}{6}\), \(-\frac{3}{4}\), \(-\frac{2}{3}\). For negative numbers, the one with larger magnitude is farther left, so \(-\frac{5}{6}<-\frac{3}{4}<-\frac{2}{3}\). Compare positive values first, then reverse the order.
Step 3
Exam Tip
ऋणात्मक संख्याओं में अधिक परिमाण वाली संख्या अधिक बाएँ होती है, इसलिए क्रम \(-\frac{5}{6}<-\frac{3}{4}<-\frac{2}{3}\) है। पहले धनात्मक मानों की तुलना करें, फिर क्रम उलटें।
\(\sqrt{8}=2\sqrt{2}\), so the midpoint is \(\frac{\sqrt{2}+2\sqrt{2}}{2}=\frac{3\sqrt{2}}{2}\). Simplify first, then average.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{3\sqrt{2}}{2}\). \(\sqrt{8}=2\sqrt{2}\), so the midpoint is \(\frac{\sqrt{2}+2\sqrt{2}}{2}=\frac{3\sqrt{2}}{2}\). Simplify first, then average.
Step 3
Exam Tip
\(\sqrt{8}=2\sqrt{2}\), इसलिए मध्य बिंदु \(\frac{\sqrt{2}+2\sqrt{2}}{2}=\frac{3\sqrt{2}}{2}\) है। सरलीकरण के बाद औसत लें।
A. बाएँ \( \frac{7}{4} \) इकाई/Left \( \frac{7}{4} \) units
Step 1
Concept
A negative number lies to the left of (0), and its distance is its absolute value \(\frac{7}{4}\). Identify direction and distance separately.
Step 2
Why this answer is correct
The correct answer is A. बाएँ \( \frac{7}{4} \) इकाई / Left \( \frac{7}{4} \) units. A negative number lies to the left of (0), and its distance is its absolute value \(\frac{7}{4}\). Identify direction and distance separately.
Step 3
Exam Tip
ऋणात्मक संख्या (0) के बाएँ होती है और दूरी उसका निरपेक्ष मान \(\frac{7}{4}\) है। दिशा और दूरी को अलग-अलग पहचानें।
A. यह (0) और (1) के बीच अपरिमेय है/It is irrational between (0) and (1)
Step 1
Concept
This decimal is non-terminating and non-repeating, so it is irrational and lies between (0) and (1). Identify rationality by the decimal pattern.
Step 2
Why this answer is correct
The correct answer is A. यह (0) और (1) के बीच अपरिमेय है / It is irrational between (0) and (1). This decimal is non-terminating and non-repeating, so it is irrational and lies between (0) and (1). Identify rationality by the decimal pattern.
Step 3
Exam Tip
यह दशमलव अनावर्ती और असांत है, इसलिए अपरिमेय है और (0) से (1) के बीच है। दशमलव पैटर्न देखकर परिमेयता पहचानें।
(|x-2|=3) means (x) is (3) units away from (2), so (x=-1,5). Place the distance on both sides of the center.
Step 2
Why this answer is correct
The correct answer is A. (-1) और (5) / (-1) and (5). (|x-2|=3) means (x) is (3) units away from (2), so (x=-1,5). Place the distance on both sides of the center.
Step 3
Exam Tip
(|x-2|=3) का अर्थ है (x), (2) से (3) इकाई दूर है, इसलिए (x=-1,5)। केंद्र से दोनों ओर दूरी लगाएँ।
Because (11<13<15), \(\sqrt{11}<\sqrt{13}<\sqrt{15}\). For positive square roots, the order of radicands is preserved.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{13}\). Because (11<13<15), \(\sqrt{11}<\sqrt{13}<\sqrt{15}\). For positive square roots, the order of radicands is preserved.
Step 3
Exam Tip
क्योंकि (11<13<15), इसलिए \(\sqrt{11}<\sqrt{13}<\sqrt{15}\)। धनात्मक वर्गमूल में मूल संख्या का क्रम बना रहता है।
With common denominator (30), \(\frac{18}{30}<\frac{20}{30}<\frac{25}{30}\). Use a common denominator to order fractions.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{3}{5},\frac{2}{3},\frac{5}{6}\). With common denominator (30), \(\frac{18}{30}<\frac{20}{30}<\frac{25}{30}\). Use a common denominator to order fractions.
Step 3
Exam Tip
समान हर (30) लेने पर \(\frac{18}{30}<\frac{20}{30}<\frac{25}{30}\)। भिन्नों का क्रम निकालने के लिए समान हर लें।
