Problem 127 - Algebra and Trigonometry

Question

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

Step-by-Step Solution

Answer

To convert from scientific notation to decimal notation, move the decimal point in the number as per the exponent of 10 (right if the exponent is positive or left if it's negative). For instance, \(3.2 × 10^4\) in decimal notation becomes 32000.

Step 1: Understanding Scientific Notation

In scientific notation, numbers are written as a simple decimal number multiplied by a power of 10. For example, the scientific notation for 1500 can be represented as \(1.5 × 10^3\). The integer value in the exponent shows the number of places the decimal point is to be moved.

Step 2: Conversion to Decimal Notation

To convert from scientific notation to decimal notation, the decimal point in the decimal number is moved to the right if the exponent of 10 is positive or left if the exponent is negative. The number of places to be moved is equal to the absolute value of the exponent.

Step 3: Example of Conversion

Let's take an example to understand how to convert from scientific notation to decimal notation. Suppose we want to convert the number \(3.2 × 10^4\) to decimal notation. The exponent of 10 is 4, which is positive, so we move the decimal point in the decimal number four places to the right. So, \(3.2 × 10^4\) is equal to 32000 in decimal notation.