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Exercises Expressions, exponents and radicals

Example 10 from Algebra and Trigonometry, 1.2 Exponents and Scientific Notation

Converting Standard Notation to Scientific Notation

Write each number in scientific notation.

ⓐDistance to Andromeda Galaxy from Earth: 24,000,000,000,000,000,000,000 m

ⓑDiameter of Andromeda Galaxy: 1,300,000,000,000,000,000,000 m

ⓒNumber of stars in Andromeda Galaxy: 1,000,000,000,000

ⓓDiameter of electron: 0.00000000000094 m

ⓔProbability of being struck by lightning in any single year: 0.00000143

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.

Solution
ⓐ
$\begin{array}{l} 24,000,000,000,000,000,000,000 m \\ \underset{\leftarrow 22 places}{\underset{}{24,000,000,000,000,000,000,000 m}} \\ 2.4 \times 10^{22} m \end{array}$

ⓑ
$\begin{array}{l} 1,300,000,000,000,000,000,000 m \\ \underset{\leftarrow 21 places}{\underset{}{1,300,000,000,000,000,000,000 m}} \\ 1.3 \times 10^{21} m \end{array}$

ⓒ
$\begin{array}{l} 1,000,000,000,000 \\ \underset{\leftarrow 12 places}{\underset{}{1,000,000,000,000}} \\ 1 \times 10^{12} \end{array}$

ⓓ
$\begin{array}{l} 0.00000000000094 m \\ \underset{\to 13 places}{\underset{}{0.00000000000094 m}} \\ 9.4 \times 10^{−13} m \end{array}$

ⓔ
$\begin{array}{l} 0.00000143 \\ \underset{\to 6 places}{\underset{}{0.00000143}} \\ 1.43 \times 10^{−6} \end{array}$

Your turn

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

Write each number in scientific notation.

ⓐU.S. national debt per taxpayer (April 2014): $152,000
ⓑWorld population (April 2014): 7,158,000,000
ⓒWorld gross national income (April 2014): $85,500,000,000,000
ⓓTime for light to travel 1 m: 0.00000000334 s
ⓔProbability of winning lottery (match 6 of 49 possible numbers): 0.0000000715

How did it go?

PreviousSimplifying Exponential Expressions Next Converting Scientific Notation to Standard Notation

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 1.2, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.