Problem 286 - Intermediate Algebra

Question

In the following exercises, convert each percent to \(a\) decimal. $$ 7.8 \% $$

Step-by-Step Solution

Answer

0.078

Step 1 - Understand the Concept of Percent

A percent represents a part per hundred. To convert a percent to a decimal, you need to divide the number by 100.

Step 2 - Apply the Division

Take the given percent, 7.8%, and divide it by 100.

Step 3 - Perform the Calculation

Perform the division: \(7.8 \div 100 = 0.078\)

Key Concepts

percent

A percent represents a value out of 100. Whenever you encounter a percent, imagine it's a fraction where the denominator is 100. For example, 50% means 50 out of 100, or simply 0.50 in decimal form.

When you are asked to convert a percent to some other form like a decimal, you're essentially changing how the number is expressed without altering its value. This concept is fundamental in many areas of math and everyday life, like calculating discounts during shopping or understanding statistics.

decimal conversion

Decimal conversion is the process of changing a number from one form to its decimal form. When converting a percent to a decimal, you are making the number more convenient to use in arithmetic and algebraic calculations.

In most cases, you can convert a percent to a decimal by simply moving the decimal point two places to the left and removing the percent sign. For instance, 25% becomes 0.25. This method works because moving the decimal point two places to the left is equivalent to dividing by 100.

division

Division is one of the four fundamental operations of arithmetic. In the context of percent to decimal conversion, you often need to divide by 100. This is because 'percent' literally means 'per hundred.'

To understand this better, consider the percent 7.8%. When you perform the division 7.8 by 100, you are finding how many parts of 7.8 there are in 100, which equals 0.078. This is why dividing helps convert to a decimal. You can always visualize this process by imagining shifting the decimal point two positions to the left.

basic algebra

Basic algebra involves manipulating numbers and symbols to solve equations or evaluate expressions. Understanding percent to decimal conversion is crucial in algebra because it simplifies many problems.

Consider this scenario: If you need to solve for x in an equation like 7.8% of x = 15, converting 7.8% to a decimal turns it into 0.078. Now, the equation is 0.078x = 15, which is easier to solve by simple division. This makes it clear how important and helpful knowing how to convert between forms can be in algebra.