Problem 20 - Algebra 1

Question

Solve the percent problem. What distance is \(24 \%\) of 710 miles?

Step-by-Step Solution

Answer

The distance that represents \(24 \%\) of 710 miles is 170.4 miles.

Step 1: Convert the Percentage into a Decimal

We convert \(24 \%\) into a decimal by dividing 24 by 100. It would be written as \(0.24\).

Step 2: Calculate the Distance

Now, to find \(24 \%\) of 710 miles, we multiply 710 by the decimal equivalent of 24%. \(710 * 0.24 = 170.4\).

Key Concepts

percent to decimal conversion

When you see a percentage, like 24%, it’s simply another way of expressing a part of 100. The process of converting a percentage into a decimal is straightforward. You move the decimal point two places to the left or divide the number by 100. This is because "percent" literally means "per hundred." For example, to convert 24% into a decimal, you simply divide 24 by 100, resulting in 0.24.

Remember:

• Move the decimal two spots to the left.
• Or divide the number by 100.

Both these methods will get you to the same result: converting percentages into a decimal form you can use to perform all sorts of mathematical operations easily.

multiplying decimals

Multiplying decimals might seem a bit daunting, but it follows the same basic principles as multiplying whole numbers. Let’s break it down using the example from our problem, where we need to multiply 710 by 0.24 to find out 24% of 710 miles.

• First, ignore the decimal point and multiply the numbers as if they are whole numbers. So multiply 710 by 24, which would be 17040.
• Next, count the total number of digits to the right of the decimal points in the original numbers. Here, 0.24 has two decimal places.
• Place the decimal point in the resulting product so that there are the same number of digits to the right of the decimal point. Thus, 17040 becomes 170.40.

Hold on to these steps, practice with different numbers, and soon multiplying decimals will feel as easy as any other multiplication you do every day.

real-world application of percentages

Percentages are everywhere in our daily lives. From calculating discounts during a sale to determining interest rates on loans, and even when splitting bills. The particular exercise of finding a percent of a distance, like 24% of 710 miles, can relate to real-world scenarios such as calculating a portion of a journey you have traveled or estimating distances for travel plans.

• The concept helps in knowing how much of a total you are dealing with in tasks such as budgeting and resource allocation.
• Percentages allow for easy comparisons between different values, making it easier to understand proportions and deliver better decision-making in finance and time management.
• In professions like engineering, understanding percentages is crucial in assessing tolerances and performance criteria with a very high precision.

The real magic lies in the fact that once you understand how to work with percentages and convert them into a decimal for calculations, it opens up an easier approach to handling many of life’s mathematical necessities.