Tag: number names, numerals and place values

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Questions Related to number names, numerals and place values

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

The value of ${\left( {{{27}^{\tfrac{{ - 2}}{3}}}} \right)^{\tfrac{1}{2}}} \times {\left( {{{64}^{\tfrac{1}{3}}}} \right)^2} \times {\left( {{{81}^{\tfrac{{ - 3}}{2}}}} \right)^{\tfrac{1}{6}}}$

  1. $\dfrac{1}{9}$
  2. $\dfrac{16}{9}$
  3. $\dfrac{2}{9}$
  4. $-\dfrac{16}{9}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
${\left( {{{27}^{\tfrac{{ - 2}}{3}}}} \right)^{\tfrac{1}{2}}} \times {\left( {{{64}^{\tfrac{1}{3}}}} \right)^2} \times {\left( {{{81}^{\tfrac{{ - 3}}{2}}}} \right)^{\tfrac{1}{6}}}$

$\displaystyle =\left(\dfrac{1}{(27)^{\tfrac{2}{3}}}\right)^{\tfrac{1}{2}}\times (4^{3\times \tfrac{1}{3}})^{2}\times \left(\dfrac{1}{(81)^{\frac{3}{2}}}\right)^{\tfrac{1}{6}}$

$\displaystyle =\left(\dfrac{1}{27}\right)^{\tfrac{2}{3}\times \tfrac{1}{2}}\times (4)^{2}\times \left(\dfrac{1}{81}\right)^{\tfrac{3}{2}\times \tfrac{1}{6}}$

$\displaystyle =\left(\dfrac{1}{3^{3}}\right)^{\tfrac{1}{3}}\times (4)^{2}\times \left(\dfrac{1}{3^{4}}\right)^{\tfrac{1}{4}}$

$\displaystyle =\frac{1}{3}\times 16\times \frac{1}{3}$

$=\dfrac{16}{9}$
Multiple choice maths numbers and place value many forms of ten thousand standard form of numbers number names, numerals and place values

The distance of the earth from the sun is 149,000,000 km. In scientific notation the distance is:

  1. $\displaystyle 149\times 10^{6}$ km
  2. $\displaystyle 14.9\times 10^{7}$ km
  3. $\displaystyle 1.49\times 10^{8}$ km
  4. $\displaystyle 0.149\times 10^{9}$ km
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\displaystyle 149,000,000 km=149\times1000000=1.49\times100000000=1.49\times 10^{8}km$

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

Solve:

$ \displaystyle 9^{\dfrac{3}{2}\div (243)^{-\dfrac{2}{3}}} $  simplifies to

  1. $ \displaystyle 3^{\dfrac{10}{3}} $
  2. <p><span lang="EN-US">${{3}^{{{3}^{\dfrac{13}{3}}}}} $</p>
  3. $ \displaystyle 3^{\dfrac{1}{3}} $
  4. $ \displaystyle 3^{19} $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Consider the given expression,


  $ \Rightarrow {{9}^{\dfrac{3}{2}\div {{\left( 243 \right)}^{-\,\dfrac{2}{3}}}}}={{9}^{\dfrac{3}{2}\times {{\left( 243 \right)}^{\dfrac{2}{3}}}}} $

 $ ={{9}^{\dfrac{3}{2}\times {{\left( {{3}^{5}} \right)}^{\dfrac{2}{3}}}}}={{9}^{\dfrac{3}{2}\times {{3}^{\dfrac{10}{3}}}}} $

 $ ={{\left( {{3}^{2}} \right)}^{\dfrac{3}{2}\times {{3}^{\dfrac{10}{3}}}}}={{\left( 3 \right)}^{3\times {{3}^{\dfrac{10}{3}}}}} $

 $ ={{3}^{{{3}^{1+\dfrac{10}{3}}}}}={{3}^{{{3}^{\dfrac{13}{3}}}}} $


Hence, this is the answer. 

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

The standard form of $0.000000000000487$ is ______

  1. $\displaystyle 4\cdot 87\times 10^{-13}$
  2. $\displaystyle 4\cdot 87\times 10^{-14}$
  3. $\displaystyle 4\cdot 87\times 10^{-15}$
  4. $\displaystyle 4\cdot 87\times 10^{-12}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$0.000000000000487=\displaystyle \frac{487}{1000000000000000}$

=$ \dfrac{487}{10^{15}}$ =$\displaystyle \frac{4\cdot 87\times 10^{2}}{10^{15}}$
=$\displaystyle 4\cdot 87\times 10^{-13}$

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

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:

  1. $\displaystyle 1< k< 10$
  2. $\displaystyle 1< k\leqslant 10$
  3. $\displaystyle 1\leqslant k< 10$
  4. $\displaystyle 1\leqslant k\leqslant 10$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$k\times10^n$


If $n$ is an integer, then $k$ should lie between $1$ and $10$.

Lets consider the equalties, $k$ cannot be equal to $10$, if it is then we can update $k = 1$ and increment $n$ by $1$.

So, $1\leq k <10$

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

If $0.00044=$$\displaystyle 4\cdot 4\times 10^{n}$ then, find the value of $ n$.

  1. $4$
  2. $5$
  3. $-4$
  4. $-5$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\displaystyle 0\cdot 00044= \frac{44}{100000}= \frac{4\cdot 4\times10^{1}}{10^{5}}$
$=\displaystyle 4\cdot 4\times 10^{-4}$
Now
$\displaystyle 4\cdot 4\times 10^{-4}=4\cdot 4\times 10^{n}$
$\displaystyle \therefore n=-4$