Chapter SR8, Problem 22P

Solution

To write the number $4\times {10}^{-2}$ in standard form.

  $0.04$

Given:

The number in scientific notation $4\times {10}^{-2}$ .

Concept Used:

To write a number in standard form from the scientific notation, if the exponent over 10 is positive then move the decimal to the right side as many digits as the number on the exponent and add 0’s to the right side after the last numeric digit.

If the exponent over 10 is negative then move the decimal point to the left side as many digits as the exponent number by adding 0’s before the first non-zero digit.

Calculation:

In order to write the number $4\times {10}^{-2}$ in standard form, note that the exponent is negative so move the decimal to 2 digits left side by adding 0’s before the first non-zero digit as shown below

  $\begin{array}{c}4\times {10}^{-2}=0.04\\ =0.04\end{array}$

Thus, the given number in standard form is $0.04$ .