Let’s multiply and divide with scientific notation to answer questions about animals, careers, and planets.
Multiplying numbers in scientific notation extends what we do when we multiply regular decimal numbers. For example, one way to find (80)(60) is to view 80 as 8 tens and to view 60 as 6 tens. The product (80)(60) is 48 hundreds or 4,800. Using scientific notation, we can write this calculation as
(8 × 101)(6 × 101) = 48 × 102
To express the product in scientific notation, we would rewrite it as 4.8 × 103.
Calculating using scientific notation is especially useful when dealing with very large or very small numbers. For example, there are about 39 million or 3.9 × 107 residents in California. Each Californian uses about 180 gallons of water a day. To find how many gallons of water Californians use in a day, we can find the product (180)(3.9 × 107) = 702 × 107, which is equal to 7.02 × 109. That’s about 7 billion gallons of water each day!
Comparing very large or very small numbers by estimation also becomes easier with scientific notation. For example, how many ants are there for every human? There are 5 × 1016 ants and 7 × 109 humans. To find the number of ants per human, look at (5 × 1016)/(7 × 109). Rewriting the numerator to have the number 50 instead of 5, we get (50 × 1015)/(7 × 109). This gives us 50/7 × 106. Since 50/7 is roughly equal to 7, there are about 7 × 106 or 7 million ants per person!
Is each equation true or false? Explain your reasoning.
Use the table to answer questions about different creatures on the planet. Be prepared to explain your reasoning.
Use the table to answer questions about the Sun and the planets of the solar system (sorry, Pluto).
Answer the following questions about celestial objects in the solar system. Express each answer in scientific notation and as a decimal number.
Choose two celestial objects and create a scale image of them in the applet below.
Plot a point for the center of each circle. Select the Circle with Center and Radius tool and click on a point. When the dialog box opens, enter the radius.
Use the table to answer questions about professions in the United States as of 2012.
Answer the following questions about professions in the United States. Express each answer in scientific notation.
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
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