Question

Which of the given options expresses $56,700$ in scientific notation?

• A. $567\times 100$
  
• B. $567\times {10}^2$
• C. $56.7\times {10}^3$
  
• D. $5.67\times {10}^4$
  

Answer 1

The correct option is D $5.67\times {10}^4$


Detailed step-by-step solution:
Expressing $56,700$ in scientific notation:
$\Rightarrow 56,700=567\times 100$
$\Rightarrow 56,700=567\times {10}^2$

$567\times {10}^2:$ It is in $a\times {10}^n$ form, but the factor $a=567$ does not lie between $1$ and $10$. Hence, the number is not in scientific notation.

$\Rightarrow 567=5.67\times 100$
$\Rightarrow 567=5.67\times {10}^2$
$\Rightarrow 56,700=5.67\times {10}^2\times {10}^2$

$\Rightarrow 56,700=5.67\times {10}^{2+2}$ (by using the product rule of powers, i.e., $am\times an=am+n)$

$\Rightarrow 56,700=5.67\times {10}^4$

The number which expresses $56,700$ in scientific notation is $5.67\times {10}^4$.