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Chapter 1: Problem 31

Express the following numbers in scientific notation: (a) 0.000000027 , (b) 356 (c) 47,764 (d) 0.096 .

Short Answer

Expert verified
(a) The number 0.000000027 in scientific notation is \(2.7 \times 10^{-8}\). (b) The number 356 in scientific notation is \(3.56 \times 10^{2}\). (c) The number 47,764 in scientific notation is \(4.7764 \times 10^{4}\). (d) The number 0.096 in scientific notation is \(9.6 \times 10^{-2}\).

Step by step solution

01

Express 0.000000027 in scientific notation

The number 0.000000027 is already between 1 and 10, but it needs to be multiplied by a power of 10. The decimal point should be moved 8 places to the right to get the number 2.7. Therefore, the number expressed in scientific notation is \(2.7 \times 10^{-8}\).
02

Express 356 in scientific notation

To express 356 in scientific notation, the decimal point should be moved 2 places to the left to form a number between 1 and 10, that is 3.56. Therefore, the number expressed in scientific notation is \(3.56 \times 10^{2}\).
03

Express 47,764 in scientific notation

To express the number 47,764 in scientific notation, the decimal point should be moved 4 places to the left to form a number between 1 and 10, that is 4.7764. Therefore, the number 47,764 in scientific notation is \(4.7764 \times 10^{4}\).
04

Express 0.096 in scientific notation

To write the number 0.096 in scientific notation, move the decimal point 2 places to the right to form a number between 1 and 10, that is 9.6. Therefore, the number 0.096 in scientific notation is \(9.6 \times 10^{-2}\).

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