Tag: maths

Questions Related to maths

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

Which of the following expressions is true?

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

  1. $2940000=$$\displaystyle 2\cdot 94\times 10^{5}$

  2. $502000=$$\displaystyle 5\cdot 02\times 10^{5}$

  3. $3683000=$$\displaystyle 3\cdot 683\times 10^{5}$

  4. $40404000=$$\displaystyle 4\cdot 0404\times 10^{5}$

Show answer
Correct Option: B
Explanation:

$\displaystyle 502000= 5\cdot 02\times 10^{5}$

Therefore, option B is correct.

When $70, 000$ is written as $7.0\times10^n$, what is the value of $n$?

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

  1. $1$

  2. $2$

  3. $3$

  4. $4$

  5. $5$

Show answer
Correct Option: D
Explanation:

Given that $70,000$ is written as $7.0$ $\times $ ${10}^{n}$

From this, we can write
$70,000$ $=$ $7.0$ $\times$ ${10}^{n}$
$\Rightarrow {10}^{n}$ $=$ $\dfrac {70,000}{7}$
$\Rightarrow {10}^{n}$ $=$ $10,000$
$\Rightarrow {10}^{n}$ $=$ ${10}^{4}$
$\Rightarrow n$ $=$ $\log _{10}$ ${10}^{4}$
$\Rightarrow n$ $=$ $4$ $\log _{10}$ $10$
$\Rightarrow $ $=$ $4$
Therefore, the value of $n$ is $'4'$.

The standard form of $15240000$ is __________.

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

  1. $1.524\times 10^{7}$

  2. $1.524\times 10^{6}$

  3. $15.24\times 10^{7}$

  4. $1.524\times 10^{8}$

Show answer
Correct Option: A
Explanation:

$15240000 = 1524\times 10000$

                   $= 1.524 \times 1000 \times 10000$
                   $= 1.524 \times 10^{7}$

Which of the following is equivalent to $ 7.7 \times 10^{-6}$?

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

  1. $0.00000077$

  2. $0.0000077$

  3. $0.000077$

  4. $0.00077$

Show answer
Correct Option: B
Explanation:

$7.7 \times 10^{-6}=\dfrac{7.7}{1000000}=0.0000077$

The number $3.02 \times10^{-6}$ can be expressed in decimal form as:

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

  1. $0.0000302$

  2. $0.00000302$

  3. $0.000302$

  4. $0.00302$

Show answer
Correct Option: B
Explanation:

$3.02 \times10^{-6}$ = $\dfrac{3.02}{1000000}$ $= 0.00000302$

The number $3\times10^{-8}$ can also be expressed as:

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

  1. $0.000003$

  2. $0.00003$

  3. $0.00000003$

  4. $0.0003$

Show answer
Correct Option: C
Explanation:

$3\times10^{-8}$ $=$ $\dfrac{3}{100000000}$ $=$ ${0.00000003}$