## Q. 2.5

Carry out the following mathematical operations involving numbers that are expressed in scientific notation.
a. $(2.33 × 10³) × (1.55 × 10^{4})$     b. $\frac{8.42\times 10^{6}}{3.02\times 10^{4}}$

## Verified Solution

a. Multiplying the two coefficients gives
$\quad\quad\quad\quad 2.33 × 1.55 = 3.6115 \quad\quad (calculator answer)\\\quad\quad\quad\quad\quad\quad\quad\quad\quad= 3.61 \quad\quad (correct answer)$
Remember that the coefficient obtained by multiplication can have only three significant figures in this case, the same number as in both input numbers for the multiplication.
$\quad\quad$Multiplication of the two powers of 10 to give the exponential term requires that we add the exponents.
$\quad\quad\quad\quad 10³ × 10^{4} = 10^{3+4} = 10^{7}$
Combining the new coefficient with the new exponential term gives the answer.
$\quad\quad\quad\quad 3.61 × 10^{7}$
b. Performing the indicated division of the coefficients gives
$\quad\quad\quad\quad \frac{8.42}{3.02}=2.7880794 \quad\quad (calculator answer)\\\quad\quad\quad\quad\quad\quad=2.79 \quad\quad (correct answer)$
Because both input numbers have three significant figures, the answer also has three significant figures.
$\quad\quad$The division of exponential terms requires that we subtract the exponents.
$\quad\quad\quad\quad\frac{10^{6}}{10^{4}}= 10^{(+6)-(+4)} = 10²$
Combining the new coefficient and the new exponential term gives
$\quad\quad\quad\quad 2.79 × 10²$