Problem 16 - Fundamentals of Mathematics

Question

Estimate \(32 \%\) of 14.88 .

Step-by-Step Solution

Answer

32% of 14.88 is approximately 4.76.

Step 1: Convert percentage to a decimal

To find a percentage of a number, we first convert the percentage into a decimal. For 32%, divide 32 by 100: \(32\% = 0.32\).

Step 2: Multiply to find the percentage

Now, multiply the converted decimal by the given number to find 32% of 14.88: \(0.32 \times 14.88\).

Step 3: Calculate the product

Perform the multiplication: \(0.32 \times 14.88 = 4.7616\).

Step 4: Round the result

Since the problem asks for an estimate, we can round the result to a reasonable precision. Here, round 4.7616 to 4.76.

Key Concepts

Decimal Conversion

When you see a percentage, it’s essentially telling you how many parts out of 100 you are dealing with. To use percentages in calculations, like finding how much 32% of a number is, you need to convert the percentage into a decimal format. This process involves a simple division step. You have to divide the percentage value by 100. For example, to convert 32% into a decimal, you calculate \( \frac{32}{100} = 0.32 \).
This conversion allows you to use the percentage in mathematical operations, such as multiplication, to find a part of a whole.

Multiplication

Once you have converted the percentage to a decimal, the next step is multiplication. Multiplication lets you find out what the percentage (now in decimal form) of a certain number is. In our example, you would multiply 0.32 by 14.88 to see what 32% of 14.88 equates to. This is written as:
\( 0.32 \times 14.88 \).

• This multiplication tells you the size of 32 parts out of 100 of the number 14.88.
• It is important to perform the multiplication carefully to get the most accurate result before rounding.

Hence, the multiplication step helps you directly calculate a portion of the original number.

Rounding Numbers

After performing your multiplication, you'll usually get a result with several decimal places. Rounding is a process to simplify that number. It's particularly useful when you are providing an estimate or when excessive precision is unnecessary.
In our example, the multiplication of \(0.32 \times 14.88 = 4.7616\), is accurate but can be cumbersome. Typically, you would round this to two decimal places for simplicity. Thus, 4.7616 becomes 4.76.

• When rounding, if the digit right after your rounding place is 5 or higher, you increase the number in your rounding place by one.
• In contrast, if it is less than 5, you keep the rounding place number the same and drop the rest.

This rounding technique aids in generating a neat and manageable answer that still retains reasonable accuracy.