Tag: numbers and place value

Questions Related to numbers and place value

The sum of the powers of the prime factors in $108 \times 192$  is

maths numbers and place value many forms of ten thousand standard form of numbers number names, numerals and place values

  1. $5$

  2. $7$

  3. $8$

  4. $12$

Show answer
Correct Option: D
Explanation:

$\displaystyle 108=2\times 2\times  3\times 3\times 3=2^{2}\times 3^{3}$
$\displaystyle 192=2\times2\times2\times2\times2\times2\times3$
$\displaystyle =2^{6}\times 3^{1}$
$\displaystyle 108 \times 192=2^{2}\times 3^{3}\times 2^{6}\times 3^{1}$
$\displaystyle =2^{8}\times 3^{4}$
Sum of the powers = 8 + 4 = 12

The value of $\displaystyle (243)^{\frac{-2}{5}}$ is---

maths numbers and place value many forms of ten thousand standard form of numbers number names, numerals and place values

  1. $\displaystyle \frac{1}{9}$

  2. $\displaystyle \frac{2}{9}$

  3. 9

  4. None of these

Show answer
Correct Option: A
Explanation:

$\displaystyle (243)^{-2/5} =\displaystyle(3^5)^{-2/5}$
                $\displaystyle = 3^{-2} = \frac{1}{9}$

Find the value of $\displaystyle (64)^{-2/3}$---

maths numbers and place value many forms of ten thousand standard form of numbers number names, numerals and place values

  1. 16

  2. $\displaystyle \frac{1}{16}$

  3. $\displaystyle -\frac{1}{16}$

  4. None of these

Show answer
Correct Option: B
Explanation:

$\displaystyle (64)^{-2/3} = 4^3 \times 1^{-2/3} = 4^{-2}$
                 $\displaystyle = \frac{1}{4^2} = \frac{1}{16}$   

The value of $[(-3)^{(-2)}]^{(-3)}$ is---

maths numbers and place value many forms of ten thousand standard form of numbers number names, numerals and place values

  1. 243

  2. 27

  3. 729

  4. None of these

Show answer
Correct Option: C
Explanation:

$[(-3)^{(-2)}]^{(-3)} = (-3)^6$
                           = 729

Charge of an electron is $0.00000000000000000016$ coulomb. This number can also be written in standard form as:

maths numbers and place value many forms of ten thousand standard form of numbers number names, numerals and place values

  1. $\displaystyle 1\cdot 6\times 10^{19}$

  2. $\displaystyle 1\cdot 6\times 10^{-20}$

  3. $\displaystyle 1\cdot 6\times 10^{-19}$

  4. $\displaystyle 1\cdot 6\times 10^{18}$

Show answer
Correct Option: C
Explanation:

$0.0000000000000000000016=\displaystyle \frac{16}{100000000000000000000}$


=$\displaystyle \frac{1\cdot 6\times 10^{1}}{10^{20}}$

=$\displaystyle 1\cdot 6\times 10^{-19}$

The value of $(3^0 - 2^1) \times 4^2$ is---

maths numbers and place value many forms of ten thousand standard form of numbers number names, numerals and place values

  1. -16

  2. 32

  3. 64

  4. 0

Show answer
Correct Option: A
Explanation:

$(3^0 - 2^1) \times 4^2 = (1-2) \times 16$
                                         $= -1 \times 16 = -16$

Simplify $\displaystyle (27)^{\frac{-2}{3}} \div \displaystyle (64)^{\frac{-2}{3}}$ is---

maths numbers and place value many forms of ten thousand standard form of numbers number names, numerals and place values

  1. $\displaystyle \frac{9}{16}$

  2. 16

  3. $\displaystyle \frac{16}{9}$

  4. 9

Show answer
Correct Option: C
Explanation:

$\displaystyle \frac{(27)^{-2/3}}{ ( 64)^{-2/3}} = \frac{\displaystyle \frac{1}{9}}{ \displaystyle \frac{14}{16}} = \frac{16}{9}$

Size of a bacteria is $\displaystyle 1.5\times 10^{-7}m$. This number can also be written as:

maths numbers and place value many forms of ten thousand standard form of numbers number names, numerals and place values

  1. $0.00000015$

  2. $0.0000015$

  3. $0.000000015$

  4. $15000000$

Show answer
Correct Option: A
Explanation:
$a\times 10^{-k} = \dfrac{a}{10^k}$

$\displaystyle 1.5 \times 10^{-7}= \dfrac{1.5}{10^7} = 0.00000015$

The usual form of $\displaystyle 6\cdot 8793\times 10^{4}$ is:

maths numbers and place value many forms of ten thousand standard form of numbers number names, numerals and place values

  1. $687930$

  2. $68793$

  3. $6879.3$

  4. $6879300$

Show answer
Correct Option: B
Explanation:

$\displaystyle 6\cdot 8793\times 10^{4}=68,793$

Which of the following statement is false?

maths numbers and place value many forms of ten thousand standard form of numbers number names, numerals and place values

  1. $\displaystyle 4\cdot 59\times 10^{-3}=0.00459$

  2. $\displaystyle 7\times 10^{-5}=0.00007$

  3. $\displaystyle 1\cdot 03\times 10^{-3}=1030$

  4. $\displaystyle 8\cdot 8\times 10^{-4}=0.00088$

Show answer
Correct Option: C
Explanation:

$\displaystyle 1\cdot 03\times 10^{-3}= 0\cdot 00103$
$\displaystyle \therefore $ The given statement is false