Question

practice exercises
exercise 1: scientists use the micron as a unit of length for very small objects. a micron is one-millionth of a meter, or \\(0.000001\text{ m}\\). write the number of meters in a micron in scientific notation.
exercise 2: a mountains elevation above sea level is \\(9.8 \times 10^3\text{ m}\\). write the elevation in standard notation.
exercise 3: a rectangular lake has a width of \\(6.0 \times 10^3\text{ m}\\) and a length of \\(1.2 \times 10^4\text{ m}\\). what is the area of the lake in scientific notation?
exercise 4: a rectangular piece of land with an area of \\(260,000\text{ m}^2\\) is \\(2,000\text{ m}\\) long. write the area and length in scientific notation, and then find the width.
exercise 5: one surface of a cut gemstone is rectangular in shape. it is \\(0.0002\text{ m}\\) wide and has an area of \\(0.000006\text{ m}^2\\). how long is the surface? do your work in scientific notation.

Explanation:

Convert micron measurement to scientific notation

$$ 0.000001\text{ m} = 1 \times 10^{-6}\text{ m} $$

Convert mountain elevation to standard notation

$$ 9.8 \times 10^3\text{ m} = 9,800\text{ m} $$

Calculate rectangular lake area in scientific notation

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Convert land measurements and find width

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Calculate gemstone length using scientific notation

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$$

Answer:

Question 1

\(1 \times 10^{-6}\text{ m}\)

Question 2

\(9,800\text{ m}\)

Question 3

\(7.2 \times 10^7\text{ m}^2\)

Question 4

Area: \(2.6 \times 10^5\text{ m}^2\)
Length: \(2 \times 10^3\text{ m}\)
Width: \(130\text{ m}\) (or \(1.3 \times 10^2\text{ m}\))

Question 5

\(3 \times 10^{-2}\text{ m}\) (or \(0.03\text{ m}\))