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Chapter 5: Problem 149

Explain how to convert from scientific to decimal notation and give an example.

Short Answer

Expert verified
To convert from scientific notation to decimal notation, move the decimal point in the coefficient to the right if the exponent of 10 is positive (as many places as the value of the exponent), or to the left if the exponent of 10 is negative (as many places as the value of the exponent, ignoring the minus sign). So, \(2.3 \times 10^4\) becomes 23000, and \(7.5 \times 10^{-3}\) becomes 0.0075.

Step by step solution

01

Understand scientific notation

Scientific notation is a way of expressing very large or very small numbers. A number in scientific notation is written as the product of a coefficient (between 1 and 10) and 10 raised to a power. For example, \(2.3 \times 10^4\) is a number in scientific notation.
02

Conversion to decimal notation for positive exponent

When converting to decimal notation, you move the decimal point in the coefficient to the right if the exponent of 10 is positive. The number of places you move the decimal point is equal to the value of the exponent. Using the earlier example, \(2.3 \times 10^4\) is converted to decimal notation by moving the decimal point in 2.3 four places to the right. That gives us 23000.
03

Conversion to decimal notation for negative exponent

Conversely, if the exponent of 10 is negative, you move the decimal point in the coefficient to the left. The number of places to move is again equal to the value of the exponent (ignoring the minus sign). For example, \(7.5 \times 10^{-3}\) would be converted by moving the decimal point in 7.5 three places to the left, giving us 0.0075.

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