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Chapter 0: Problem 127

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

Short Answer

Expert verified
To convert from scientific to decimal notation, move the decimal point in the base to the right if the exponent is positive, or to the left if the exponent is negative for the number of places equal to the absolute value of the exponent. For \(3.5 \times 10^2\), it becomes 350. For \(8.6 \times 10^{-3}\), it becomes 0.0086.

Step by step solution

01

Understanding Scientific Notation

Scientific notation is written as \(a \times 10^n\), where \(a\) is a real number such that \(1 \leq |a| < 10\) and \(n\) is an integer.
02

Conversion to Decimal Notation

To convert from scientific notation to decimal notation, you first look at the exponent \(n\) in the scientific notation. If \(n\) is positive, you would move the decimal point in \(a\) to the right \(n\) places. If \(n\) is negative, you would move the decimal point in \(a\) to the left \(n\) places. If there are not enough numbers, you would add zeroes.
03

Example of Conversion

For instance, given \(3.5 \times 10^2\) in scientific notation, since 2 is positive, you move the decimal 2 places to the right in 3.5, resulting in 350. For another instance, given \(8.6 \times 10^{-3}\), since -3 is negative, you move the decimal 3 places to left in 8.6, resulting in 0.0086.

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