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Chapter 0: Problem 128

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

Short Answer

Expert verified
The steps to convert a decimal number to scientific notation are: 1) identify the coefficient by moving the decimal after the first non-zero digit, 2) count how many places the decimal has moved (this will be the exponent, which will be positive if the original number was more than 1, and negative if it was less), and 3) write the coefficient multiplied by 10 raised to the power of the exponent. For example, 300 in scientific notation is \(3 \times 10^{2}\).

Step by step solution

01

Definition of Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. In scientific notation, numbers are written as a product of two numbers: a coefficient and 10 raised to a power.
02

Identify the Coefficient

The first step is to identify the coefficient for the scientific notation. This is done by placing a decimal point after the first non-zero digit in the number.
03

Count the Number of Places Moved

Next, count the number of places the decimal moved from its original place in the number. If the original number is less than 1, then the exponent is negative. If the original number is greater than 1, then the exponent is positive.
04

Write the number in Scientific Notation

Write down the coefficient from step 1 and multiply it by 10 raised to the power equal to the number of places you counted in step 2. This is your scientific notation.
05

Example of Decimal to Scientific Notation

For instance, the number 300 can be written in scientific notation as \(3 \times 10^{2}\), because the decimal is moved two places to the left to find the coefficient 3, and the original number is greater than 1, so the exponent is 2

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