Tag: use of exponents

Questions Related to use of exponents

Convert $6.634\times 10^{-3}$ in decimal form.

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

  1. $6634$

  2. $0.006634$

  3. $0.006643$

  4. $0.0006634$

Show answer
Correct Option: B
Explanation:

$6.634\times 10^{-3}$ can be written as 

$=\dfrac{6.634}{1000}=0.006634$
Hence, option B is correct.

Write $1200\times 3200$ in scientific notation.

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

  1. $384000$

  2. $384\times 10^3$

  3. $3.84\times 10^6$

  4. $3840\times10^2$

Show answer
Correct Option: C
Explanation:

The value of $3200\times 1200$ is 

$=32\times12\times10^4\=384\times 10^4\=3.84\times 10^6$

Which of the following options is INCORRECT?

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

  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)

Show answer
Correct Option: C
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.





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

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

  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. $137 \times {10}^{15}$

Show answer
Correct Option: D
Explanation:

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

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

IX + XV + XX = _________.

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

  1. 45

  2. 35

  3. 44

  4. 76

Show answer
Correct Option: C
Explanation:

We have,

$IX+XV+XX$
$=9+15+20$
$=44$

Hence, this is the answer.

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

maths square and square root scientific notation use of exponents power of 10
    • $\div$ - =

  2. $\times $ - = $\times $

  3. $\times $ + = $\times$

    • $\times \div $ =
Show answer
Correct Option: C
Explanation:
Given,

$7**5*4* 10$

Now, we have

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

$35+5=4 \times 10$

$40 =40$

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

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

  1. $- x > - y$

  2. $- x < - y$

  3. $\frac{1}{x} > \frac{1}{y}$

  4. $-\frac{1}{x} > \frac{1}{y}$

Show answer
Correct Option: B
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.\  $

Which one of the following statements is correct?

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

  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.

Show answer
Correct Option: D
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.

The $p/q$ form of $0.5\bar {6}$ is 

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

  1. $56/100$

  2. $56/99$

  3. $59/90$

  4. $51/90$

Show answer
Correct Option: D
Explanation:

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

If the decimal number $\displaystyle 2^{111}$ is written in the octal system then what is its unit place digit?

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

  1. $0$

  2. $1$

  3. $2$

  4. $3$

Show answer
Correct Option: A
Explanation:

Here,$ 2^{111}$ = $2^{3\times27}$
which is divisible by $2^{3} = 8$
Hence, the digit in the unit place is 0