Example 12 from Algebra and Trigonometry, 1.2 Exponents and Scientific Notation

Using Scientific Notation

Perform the operations and write the answer in scientific notation.

ⓐ $(8.14 \times 10^{−7}) (6.5 \times 10^{10})$
ⓑ $(4 \times 10^{5}) \div (−1.52 \times 10^{9})$
ⓒ $(2.7 \times 10^{5}) (6.04 \times 10^{13})$
ⓓ $(1.2 \times 10^{8}) \div (9.6 \times 10^{5})$
ⓔ $(3.33 \times 10^{4}) (−1.05 \times 10^{7}) (5.62 \times 10^{5})$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
1. ⓐ
  $\begin{matrix} (8.14 \times 10^{−7}) (6.5 \times 10^{10}) & = & (8.14 \times 6.5) (10^{−7} \times 10^{10}) & \begin{array}{l} Commutative and associative \\ properties of multiplication \end{array} \\ = & (52.91) (10^{3}) & Product rule of exponents \\ = & 5.291 \times 10^{4} & Scientific notation \end{matrix}$
2. ⓑ
  $\begin{matrix} (4 \times 10^{5}) \div (−1.52 \times 10^{9}) & = & (\frac{4}{−1.52}) (\frac{10^{5}}{10^{9}}) & \begin{array}{l} Commutative and associative \\ properties of multiplication \end{array} \\ \approx & (−2.63) (10^{−4}) & Quotient rule of exponents \\ = & −2.63 \times 10^{−4} & Scientific notation \end{matrix}$
3. ⓒ
  $\begin{matrix} (2.7 \times 10^{5}) (6.04 \times 10^{13}) & = & (2.7 \times 6.04) (10^{5} \times 10^{13}) & \begin{array}{l} Commutative and associative \\ properties of multiplication \end{array} \\ = & (16.308) (10^{18}) & Product rule of exponents \\ = & 1.6308 \times 10^{19} & Scientific notation \end{matrix}$
4. ⓓ
  $\begin{matrix} (1.2 \times 10^{8}) \div (9.6 \times 10^{5}) & = & (\frac{1.2}{9.6}) (\frac{10^{8}}{10^{5}}) & \begin{array}{l} Commutative and associative \\ properties of multiplication \end{array} \\ = & (0.125) (10^{3}) & Quotient rule of exponents \\ = & 1.25 \times 10^{2} & Scientific notation \end{matrix}$
5. ⓔ
  $\begin{matrix} (3.33 \times 10^{4}) (−1.05 \times 10^{7}) (5.62 \times 10^{5}) & = & [3.33 \times (−1.05) \times 5.62] (10^{4} \times 10^{7} \times 10^{5}) \\ \approx & (−19.65) (10^{16}) \\ = & −1.965 \times 10^{17} \end{matrix}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Perform the operations and write the answer in scientific notation.

ⓐ $(−7.5 \times 10^{8}) (1.13 \times 10^{−2})$
ⓑ $(1.24 \times 10^{11}) \div (1.55 \times 10^{18})$
ⓒ $(3.72 \times 10^{9}) (8 \times 10^{3})$
ⓓ $(9.933 \times 10^{23}) \div (- 2.31 \times 10^{17})$
ⓔ $(−6.04 \times 10^{9}) (7.3 \times 10^{2}) (−2.81 \times 10^{2})$

How did it go?

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Perform the operations and write the answer in scientific notation.

ⓐ $(−7.5 \times 10^{8}) (1.13 \times 10^{−2})$
ⓑ $(1.24 \times 10^{11}) \div (1.55 \times 10^{18})$
ⓓ $(9.933 \times 10^{23}) \div (- 2.31 \times 10^{17})$
ⓔ $(−6.04 \times 10^{9}) (7.3 \times 10^{2}) (−2.81 \times 10^{2})$

Solution

Your turn

Solution

Your turn