Exponents and Standard Form - Class VIII
Working with exponents, powers, and standard/scientific notation
Questions
In standard from, the number 829030000 is written as $K\times { 10 }^{ 8 }$ where K is equal to
- 82903
- 829.03
- 82.903
- 8.2903
The sum of the powers of the prime factors in $108 \times 192$ is
- $5$
- $7$
- $8$
- $12$
The value of $\displaystyle (243)^{\frac{-2}{5}}$ is---
- $\displaystyle \frac{1}{9}$
- $\displaystyle \frac{2}{9}$
- 9
- None of these
Find the value of $\displaystyle (64)^{-2/3}$---
- 16
- $\displaystyle \frac{1}{16}$
- $\displaystyle -\frac{1}{16}$
- None of these
The value of $[(-3)^{(-2)}]^{(-3)}$ is---
- 243
- 27
- 729
- None of these
Charge of an electron is $0.00000000000000000016$ coulomb. This number can also be written in standard form as:
- $\displaystyle 1\cdot 6\times 10^{19}$
- $\displaystyle 1\cdot 6\times 10^{-20}$
- $\displaystyle 1\cdot 6\times 10^{-19}$
- $\displaystyle 1\cdot 6\times 10^{18}$
The value of $(3^0 - 2^1) \times 4^2$ is---
- -16
- 32
- 64
- 0
Simplify $\displaystyle (27)^{\frac{-2}{3}} \div \displaystyle (64)^{\frac{-2}{3}}$ is---
- $\displaystyle \frac{9}{16}$
- 16
- $\displaystyle \frac{16}{9}$
- 9
Size of a bacteria is $\displaystyle 1.5\times 10^{-7}m$. This number can also be written as:
- $0.00000015$
- $0.0000015$
- $0.000000015$
- $15000000$
The usual form of $\displaystyle 6\cdot 8793\times 10^{4}$ is:
- $687930$
- $68793$
- $6879.3$
- $6879300$
Which of the following statement is false?
- $\displaystyle 4\cdot 59\times 10^{-3}=0.00459$
- $\displaystyle 7\times 10^{-5}=0.00007$
- $\displaystyle 1\cdot 03\times 10^{-3}=1030$
- $\displaystyle 8\cdot 8\times 10^{-4}=0.00088$
Which of the following expressions is true?
- $2940000=$$\displaystyle 2\cdot 94\times 10^{5}$
- $502000=$$\displaystyle 5\cdot 02\times 10^{5}$
- $3683000=$$\displaystyle 3\cdot 683\times 10^{5}$
- $40404000=$$\displaystyle 4\cdot 0404\times 10^{5}$
When $70, 000$ is written as $7.0\times10^n$, what is the value of $n$?
- $1$
- $2$
- $3$
- $4$
- $5$
The standard form of $15240000$ is __________.
- $1.524\times 10^{7}$
- $1.524\times 10^{6}$
- $15.24\times 10^{7}$
- $1.524\times 10^{8}$
Which of the following is equivalent to $ 7.7 \times 10^{-6}$?
- $0.00000077$
- $0.0000077$
- $0.000077$
- $0.00077$
The number $3.02 \times10^{-6}$ can be expressed in decimal form as:
- $0.0000302$
- $0.00000302$
- $0.000302$
- $0.00302$
The number $3\times10^{-8}$ can also be expressed as:
- $0.000003$
- $0.00003$
- $0.00000003$
- $0.0003$
The value of $\dfrac{(10^4+324)(22^4+324)(34^4+324)(46^4+324)(58^4+324)}{(4^4+324)(16^4+324)(28^4+324)(40^4+324)(52^4+324)}$ is?
- $324$
- $400$
- $373$
- $1024$
The value of ${\left( {{{27}^{\tfrac{{ - 2}}{3}}}} \right)^{\tfrac{1}{2}}} \times {\left( {{{64}^{\tfrac{1}{3}}}} \right)^2} \times {\left( {{{81}^{\tfrac{{ - 3}}{2}}}} \right)^{\tfrac{1}{6}}}$
- $\dfrac{1}{9}$
- $\dfrac{16}{9}$
- $\dfrac{2}{9}$
- $-\dfrac{16}{9}$
The distance of the earth from the sun is 149,000,000 km. In scientific notation the distance is:
- $\displaystyle 149\times 10^{6}$ km
- $\displaystyle 14.9\times 10^{7}$ km
- $\displaystyle 1.49\times 10^{8}$ km
- $\displaystyle 0.149\times 10^{9}$ km
The standard form of $0.000000000000487$ is ______
- $\displaystyle 4\cdot 87\times 10^{-13}$
- $\displaystyle 4\cdot 87\times 10^{-14}$
- $\displaystyle 4\cdot 87\times 10^{-15}$
- $\displaystyle 4\cdot 87\times 10^{-12}$
The standard form of $8,60,00,00,00,00,000$ is
- $\displaystyle 8\cdot 6\times 10^{13}$
- $\displaystyle 8\cdot 6\times 10^{-13}$
- $\displaystyle 8\cdot 6\times 10^{12}$
- $\displaystyle 8\cdot 6\times 10^{14}$
A number is said to be in the standard form when it is written as $\displaystyle k\times 10^{n}$ where $n$ is an integer and:
- $\displaystyle 1< k< 10$
- $\displaystyle 1< k\leqslant 10$
- $\displaystyle 1\leqslant k< 10$
- $\displaystyle 1\leqslant k\leqslant 10$
The usual form of $\displaystyle 5\times 10^{-8}$ is
- $0.000005$
- $0.00000005$
- $0.0000005$
- $0.000000005$
The usual form of $\displaystyle 4\cdot 56\times 10^{-5}$ is:
- $0.0000456$
- $0.00000456$
- $0.000456$
- $456000$
If $0.00044=$$\displaystyle 4\cdot 4\times 10^{n}$ then, find the value of $ n$.
- $4$
- $5$
- $-4$
- $-5$
Find the value of $n$ such that $502000000=$$\displaystyle 5\cdot 02\times 10^{n}$.
- $5$
- $7$
- $-8$
- $8$
The standard form of $\displaystyle \frac{1}{10000000}$ is:
- $\displaystyle 1\times 10^{-7}$
- $\displaystyle 0\cdot 1\times 10^{-7}$
- $\displaystyle 1\times 10^{7}$
- $\displaystyle 1\times 10^{-6}$
The distance of the sun from the earth is $1,49,60,00,00,000$ m. Express it in standard form.
- $\displaystyle 1\cdot 496\times 10^{-10}$
- $\displaystyle 1\cdot 496\times 10^{-11}$
- $\displaystyle 1\cdot 496\times 10^{10}$
- $\displaystyle 1\cdot 496\times 10^{11}$
The size of a plant cell is $0.00005473$ m. This number can also be written as
- $\displaystyle 5\cdot 473\times 10^{-3}$
- $\displaystyle 5\cdot 473\times 10^{-5}$
- $\displaystyle 5\cdot 473\times 10^{11}$
- $\displaystyle 5\cdot 473\times 10^{5}$
The usual form of $\displaystyle 2\cdot 73\times 10^{12}$ is:
- $273000000000$
- $2.730000000000$
- $2730000000000$
- $27300000000000$
The value of ${ \left( 256 \right) }^{ 0.16 }.{ \left( 256 \right) }^{ 0.09 }$ is:
- $4$
- $16$
- $64$
- $256.25$
- $-16$