Question 2.5: Carry out the following mathematical operations involving nu......
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}}
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\quadMultiplication 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\quadThe 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