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Chapter 7: Problem 15

Write each percent as a decimal. $$ 2.8 \% $$

Short Answer

Expert verified
2.8% as a decimal is 0.028.

Step by step solution

01

Understanding Percent to Decimal Conversion

A percent is a way of expressing a number as a fraction of 100. Therefore, to convert a percent into a decimal, you need to divide the percentage by 100.
02

Convert 2.8% to a Decimal

To change 2.8% into a decimal, divide 2.8 by 100. This is done by moving the decimal point two places to the left.
03

Perform the Division

2.8 divided by 100 equals 0.028. Mathematically, this is shown as: \[2.8 \div 100 = 0.028\]
04

Write the Result

The decimal representation of 2.8% is 0.028.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Decimal Representation
When working with mathematics, the decimal representation of a number is often the most straightforward form to understand. Decimals are simply another way of showing fractions, where the numbers appear either to the left or right of the decimal point.
  • A number to the left represents whole units.
  • Numbers to the right of the decimal point represent fractional parts of those units.
For example, in the number 0.028, the '0' before the decimal point stands for zero whole units, while the numbers to the right represent parts of a whole. In this case, 28 parts of thousand, or 0.028.
Decimal representation is a universal method for expressing values, which makes it handy for all kinds of calculations, especially in more complex equations or financial math.
Dividing by 100
An essential step in converting a percent to a decimal is dividing by 100. This is because a percent literally means "per one hundred."
Understanding why we divide by 100 helps grasp the simplification process:
  • Percentages are another form of fractions, where the denominator is always 100.
  • Dividing by 100 converts this fraction into a decimal.
In practical terms, dividing by 100 shifts the decimal point two places to the left. For instance, when converting 2.8% to a decimal, you move the decimal point from 2.8 to 0.028.
This simple shift allows you to transition from percent form to a usable decimal format in equations and other mathematical operations.
Mathematical Notation
Mathematical notation is the universal language of math, providing a clear and standardized way to communicate equations and procedures. When converting a percentage to a decimal, notation plays a key role in keeping the process readable and correct.
In the notation used for the conversion of 2.8% to its decimal form, you write it as:
\[2.8 \div 100 = 0.028\]
This notation clearly illustrates the operation of dividing 2.8 by 100 to arrive at the decimal 0.028.
  • It uses symbols like \(\div\), which indicates division.
  • Furthermore, the equal sign \(=\) connects the process to its result.
Understanding this notation helps not only in completing the specific task at hand but also in developing fluency in reading and solving mathematical problems systematically and easily.

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