Tag: scientific notation

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Questions Related to scientific notation

Multiple choice maths square and square root scientific notation use of exponents power of 10

Which of the following options is INCORRECT?

  1. The number $48693$ rounded off to nearest hundred is $48700$

  2. LXXV is greater than LXXIV
  3. One million is equal to $10$ crore
  4. Place value of a digit $=$(face value of the digit)$\times$ (Value of the place)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Option A: For rounding to the nearest hundred, If tens digit is 0,1,2,3,4

, then round down to the previous hundred and If tens digit is 5,6,7,8,9, then round up to the next hundred.
Following the above rule, as 6 is present in the hundredth place, we will round up it to $700$.

Hence $48693$ $\rightarrow$ $48700$.

Option B: LXXV $\rightarrow$ $75$
                 LXXIV $\rightarrow$ $74$
So, LXXV $>$ LXXIV

Option C: 1 million $\rightarrow$ 10,00,000 $\rightarrow$ 10lakh

Option D: Face value is the value of the digit itself.
Value of place if the position of the digit in the number
Hence, Place value $\rightarrow$ face value $\times$ Value of place

Hence Option C is incorrect.





Multiple choice maths square and square root scientific notation use of exponents power of 10

In scientific notation, $670,000,000 + 700,000,000 =$?

  1. $1.37 \times {10}^{-9}$
  2. $1.37 \times {10}^{7}$
  3. $1.37 \times {10}^{8}$
  4. $1.37 \times {10}^{9}$
  5. $137 \times {10}^{15}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$670,000,000+700,000,000=1,370,000,000$

$\therefore 1,370,000,000=1.37\times 10^9$
Ans-Option $D$.

Multiple choice maths square and square root scientific notation use of exponents power of 10

Choose the correct answer from the alternatives given.
Select the correct combination of mathematical signs to replace * signs and to balance the following equation.
7*5*5*4* 10

  1. + $\div$ - =
  2. $\times $ - = $\times $
  3. $\times $ + = $\times$
  4. + $\times \div $ =
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Given,

$7**5*4* 10$

Now, we have

$7 \times5 + 5 = 4 \times 10$

$35+5=4 \times 10$

$40 =40$
Multiple choice maths square and square root scientific notation use of exponents power of 10

If $x$ and $y$ are any two positive real numbers, then $x > y$ implies

  1. $- x > - y$
  2. $- x < - y$
  3. $\frac{1}{x} > \frac{1}{y}$
  4. $-\frac{1}{x} > \frac{1}{y}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$ Given\quad that\quad x\quad and\quad y\quad are\quad positive\quad number\quad and\quad x>y.\ We\quad may\quad calculate\ (a)\quad on\quad the\quad positive\quad side\quad of\quad number\quad line\quad x\quad will\quad be\ \quad \quad to\quad the\quad right\quad of\quad y\quad and\quad \ (b)\quad on\quad the\quad negative\quad side\quad of\quad the\quad number\quad line\quad x\quad will\ \quad \quad be\quad to\quad the\quad left\quad of\quad y.\ Statement\quad A\longrightarrow -x>-y\quad i.e\quad -x\quad to\quad the\quad right\quad side\quad of\quad -y\ which\quad is\quad not\quad complying\quad with\quad (b).\quad So\quad it\quad is\quad not\quad true.\ Statement\quad B\longrightarrow -x<-y\quad i.e\quad -x\quad lies\quad to\quad the\quad left\quad of\quad -y.\ This\quad complies\quad with\quad (b).\quad So\quad the\quad statement\quad is\quad true.\ Statement\quad C\longrightarrow \frac { 1 }{ x } >\frac { 1 }{ y } .\quad Here\quad the\quad numerators\quad of\quad the\ two\quad fractions\quad are\quad equal.\quad But\quad the\quad denominator\quad of\quad \frac { 1 }{ x } \ is\quad greater\quad than\quad that\quad of\quad \frac { 1 }{ y } .\ So\quad this\quad statement\quad is\quad not\quad true.\ Statement\quad D\longrightarrow -\frac { 1 }{ x } >\frac { 1 }{ y } ,\ -\frac { 1 }{ x } is\quad a\quad negative\quad number\quad so\quad it\quad will\quad always\quad be\quad smaller\ than\quad a\quad positive\quad number.\ \therefore \quad -\frac { 1 }{ x } \ngtr \frac { 1 }{ y } .\quad So\quad this\quad statement\quad is\quad not\quad true.\ Answer-\quad Statement\quad B\quad is\quad correct.\  $

Multiple choice maths square and square root scientific notation use of exponents power of 10

Which one of the following statements is correct?

  1. There can be a real number which is both rational and irrational.

  2. The sum of two irrational numbers is always irrational.
  3. For any real numbers x and y, $x < y \Rightarrow x^{2} < y^{2}$

  4. Every integer is a rational number.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Every integer can be expressed as a rational number by dividing itself by 1.
Now, it becomes a rational number with the numerator the number itself and denominator 1.

Multiple choice maths square and square root scientific notation use of exponents power of 10

The $p/q$ form of $0.5\bar {6}$ is 

  1. $56/100$
  2. $56/99$
  3. $59/90$
  4. $51/90$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\begin{array}{l} x=0.566\ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _  \ 10x=5.666\ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ (i) \ 100x=56.6666\ _ \ _ \ _ \ _ \ _ \ _ (ii) \ (ii)-(i) \ 90x=51 \ x=\frac { { 51 } }{ { 90 } }  \end{array}$