Question

Arrange the following numbers in an ascending order:
$3.65\times {10}^{-7},$
$5.78\times {10}^{-6},$
$2.39\times {10}^{-9},$ and
$8.16\times {10}^{-6}$

• A. $3.65\times {10}^{-7}$
  $5.78\times {10}^{-6}$
  $2.39\times {10}^{-9}$
  $8.16\times {10}^{-6}$
• B. $2.39\times {10}^{-9}$
  $3.65\times {10}^{-7}$
  $8.16\times {10}^{-6}$
  $5.78\times {10}^{-6}$
• C. $2.39\times {10}^{-9}$
  $3.65\times {10}^{-7}$
  $5.78\times {10}^{-6}$
  $8.16\times {10}^{-6}$
• D. $3.65\times {10}^{-7}$
  $2.39\times {10}^{-9}$
  $5.78\times {10}^{-6}$
  $8.16\times {10}^{-6}$

Answer 1

The correct option is C $2.39\times {10}^{-9}$

$3.65\times {10}^{-7}$
$5.78\times {10}^{-6}$
$8.16\times {10}^{-6}$
$\underset{–}{\text{First Method:}}$

Step 1:
Write the given numbers in scientific notations. Here, the given numbers $3.65\times {10}^{-7}$, $5.78\times {10}^{-6}$, $2.39\times {10}^{-9}$ and $8.16\times {10}^{-6}$ are already written in scientific notations.

Step 2:

• Compare the exponents of numbers. The larger the exponent, the greater the number.
• When the exponents of two numbers are the same, the coefficient of those numbers should be considered. Larger is the coefficient, greater is the number.

Here, $5.78\times {10}^{-6}$ and $8.16\times {10}^{-6}$ have same exponents as $-6.$ So, their coefficient should be compared.
$\because 5.78<8.16$
$\Rightarrow 5.78\times {10}^{-6}<8.16\times {10}^{-6}$

Finally, as $-9<-7<-6$
$⟹2.39\times {10}^{-9}<3.65\times {10}^{-7}<5.78\times {10}^{-6}<8.16\times {10}^{-6}$

Therefore, option (c.) is the correct one.