Problem 57 - Algebra 1

Question

Write the percent as a decimal. $$ 3 \% $$

Step-by-Step Solution

Answer

The decimal equivalent of 3% is 0.03.

Step 1: Identify the given percentage

The given percentage is 3%.

Step 2: Convert the percentage to a decimal

To convert a percentage into a decimal, divide the percentage by 100. This is done because 'percent' translates to 'per 100'. Therefore, divide 3 by 100 to get the decimal equivalent. The result is \( \frac{3}{100} = 0.03 \).

Key Concepts

Percent

A percent is a way to express a number as a part of a whole, specifically out of 100. The term 'percent' itself comes from the Latin phrase 'per centum', which means 'by the hundred'. For example, when we say 3%, we are saying three out of every hundred parts. Percentages are commonly used in day-to-day life, for instance, to describe discounts, interest rates, or statistical data.
Understanding the concept of percentage is crucial, as it allows you to compare quantities and understand proportions in a more intuitive way. By seeing a percentage value, you can easily grasp how big or small a particular number is in relation to 100.

Decimal

Decimals are another way of representing numbers that include fractions or parts of a whole. In our number system, decimals are represented with a dot (.) known as the decimal point. Numbers to the right of the decimal point indicate fractions, where each place value represents a fraction that is ten times smaller than the one to its left.
To convert a percentage into a decimal, the main thing to remember is that since 'percent' means 'per one hundred', you're effectively dealing with fractions having a denominator of 100. For example, 3% is the same as 3 per 100, or 0.03 when expressed as a decimal. This principle allows for a seamless transition between percentages and decimals, simplifying calculations and comparisons.

Division

Division is a fundamental mathematical operation used to split or distribute a number into equal parts. When converting a percentage to a decimal, division plays a key role. Here, you take the percentage number and divide it by 100. This operation is straightforward:

• It helps in understanding how much one part would be if the total is 100;
  
• It breaks down larger numbers into manageable decimal forms.
  

For instance, converting 3% into a decimal involves dividing 3 by 100, resulting in 0.03. This method of division helps convert percentages efficiently to a decimal format. Embracing division in this context allows for easy manipulation of numbers and enhances your ability to perform calculations without getting confused by the percentage format.