Q12. - Algebra 1

Question

Express each number in scientific notation.

$\mathbf{0}\mathbf{.0042}$

Step-by-Step Solution

Answer

The required notation is represented by $\mathbf{4}\mathbf{.2}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}$. 

Step 1. Change the position of the decimal.

The provided number contains 4 as its first value that is not zero so change the position of the decimal and put that just after the first value.

$0004.2$

Step 2. Calculate the value of n .

The required notation will be in the form of $a\times {10}^n$ in which a is representing the obtained number by changing the position of the decimal. The value of n is represented by the count associated with the numbers that are present before the final value. The value of n will be negative as the decimal travelled in the right direction. So, write the required value associated with n.

$n=-3$

Step 3. Write the required notation.

Substitute the obtained value of n into $a\times {10}^n$ without mentioning the zeros that are not required to write the required notation.

$4.2\times {10}^{-3}$