Question A.SE.1: Perform each of the following operations, using your calcula...
Perform each of the following operations, using your calculator where possible:
(a) Write the number 0.0054 in standard exponential notation. (b) \left(5.0 \times 10^{-2}\right)+\left(4.7 \times 10^{-3}\right) (c) \left(5.98 \times 10^{12}\right)\left(2.77 \times 10^{-5}\right) (d) \sqrt[4]{1.75 \times 10^{-12}}
(a) Because we move the decimal point three places to the right to convert 0.0054 to 5.4, the exponent is -3:
5.4 × 10^{-3}
Scientific calculators are generally able to convert numbers to exponential notation using one or two keystrokes; frequently “SCI” for “scientific notation” will convert a number into exponential notation. Consult your instruction manual to see how this operation is accomplished on your calculator.
(b) To add these numbers longhand, we must convert them to the same exponent.
\left(5.0 \times 10^{-2}\right)+\left(0.47 \times 10^{-2}\right)=(5.0+0.47) \times 10^{-2}=5.5 \times 10^{-2}
(c) Performing this operation longhand, we have
(5.98 \times 2.77) \times 10^{12-5}=16.6 \times 10^7=1.66 \times 10^8
(d) To perform this operation on a calculator, we enter the number, press the \sqrt[x]{y} key (or the INV and y^x keys), enter 4, and press the = key. The result is 1.15 × 10^{-3}.