Rhode Island is the smallest state in the United States. Its land area is about 2.9 x 10^10 square feet. Alaska, the largest state, is about 5.5 x 10^

Maiclubk 2021-05-12 Answered
Rhode Island is the smallest state in the United States. Its land area is about 2.9 x 10^10 square feet. Alaska, the largest state, is about 5.5 x 10^2 times as large as Rhode Island. What is the land are of Alaska in square feet? Write you answer in scientific notation.

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Expert Answer

Bertha Stark
Answered 2021-05-13 Author has 12923 answers

When multiplying two numbers in scientific notation, you should group the significands (the fancy word for the number in front of the power of ten) and the powers of ten. Hence
\(2.9×10^{10}×5.5×10^2=(2.9×5.5)×(10^{10}×10^2) =15.95×10^{10}+2 =15.95×10^{12}\)
Then we need to make sure that the significand is between 11 and 1010 so we need to move the decimal place one place to the left. That will mean we should increase the power of ten by one. So we get
\(\displaystyle={1.595}×{10}^{{13}}\)
At this point, we should look at how many significant figures our starting numbers had. They both had 2 in this case. So our result should too. So we need to round so that this number has only two digits.
\(\displaystyle={1.6}×{10}^{{13}}\)
And that's it! We're done! ​

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