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Chapter 8: Problem 16

Estimate \(32 \%\) of 14.88 .

Short Answer

Expert verified
32% of 14.88 is approximately 4.76.

Step by step solution

01

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: \(32\% = 0.32\).
02

Multiply to find the percentage

Now, multiply the converted decimal by the given number to find 32% of 14.88: \(0.32 \times 14.88\).
03

Calculate the product

Perform the multiplication: \(0.32 \times 14.88 = 4.7616\).
04

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.

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Key Concepts

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

Decimal Conversion
When you see a percentage, it鈥檚 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.

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Most popular questions from this chapter

Estimate each value using the method of rounding. After you have made an estimate, find the exact value. Compare the exact and estimated values. Results may vary. $$ 33,712 \div 112 $$

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Compute each product using the distributive property. \(95 \cdot 11\)

Estimate each value using the method of rounding. After you have made an estimate, find the exact value. Compare the exact and estimated values. Results may vary. $$ 51,492 \div 514 $$

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