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Chapter 5: Problem 150

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

Short Answer

Expert verified
The number 452.16 in scientific notation is written as \(4.5216 \times 10^{2}\).

Step by step solution

01

Understand Scientific Notation

Scientific notation is a way of writing numbers that accommodates values too large or small to be conveniently written in standard decimal notation. Scientific notation has two parts: 1) A number between 1 and 10; this is often referred to as the 'coefficient'. 2) A power of 10 written as '10 to the power of n', where 'n' is the 'exponent'.
02

Identify Coefficient

Identify the coefficient of the scientific notation. The coefficient is the decimal number in the original number, adjusted so that it is between 1 and 10. If we are given the number 452.16, the coefficient would be 4.5216.
03

Determine Exponent

Identify the location of the decimal point in the original number and determine its new location after making the number a coefficient. The count of place values to get from the new location of the point to the original location is the exponent. For 452.16, the original decimal point is between 2 and 1. In the coefficient 4.5216, the decimal point is between 4 and 5. The point has been moved 2 places to the left, so the exponent is 2.
04

State the Result in Scientific Notation

Now that we have our coefficient and our exponent, we can express our original number in scientific notation. The number 452.16 in scientific notation is written as \(4.5216 \times 10^{2}\).

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