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Chapter 6: Problem 25

Find decimal notation. $$ 14 \frac{7}{8} \% $$

Short Answer

Expert verified
0.14875

Step by step solution

01

- Convert Mixed Number to Fraction

First, convert the mixed number to an improper fraction. Convert \(14 \frac{7}{8}\) to \(\frac{119}{8}\).
02

- Convert Fraction to Decimal

Divide the numerator by the denominator to convert the fraction \(\frac{119}{8}\) into a decimal. \(\frac{119}{8} = 14.875\).
03

- Convert Percentage to Decimal

To convert a percentage to a decimal, divide by 100. Therefore, \(14.875\%\) becomes \(0.14875\).

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Key Concepts

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

Converting Fractions
A fraction represents a part of a whole. It consists of a numerator (top number) and a denominator (bottom number). Converting fractions into decimal form is an essential skill in many math problems. To convert a fraction to a decimal, simply divide the numerator by the denominator.

This is what we did in the problem when we converted the fraction \(\frac{119}{8}\) into a decimal. We divided 119 by 8, which gave us 14.875. This step helps to simplify the problem and prepares it for the next conversion.
Improper Fractions
An improper fraction is a fraction where the numerator is greater than or equal to the denominator. Converting a mixed number (a whole number combined with a fraction) to an improper fraction is a crucial step before conversion to a decimal.

Let's see how to do this:
  • First, multiply the whole number by the denominator.
  • Next, add this result to the numerator.
  • The sum becomes the new numerator, while the denominator stays the same.
For our exercise, converting \14 \frac{7}{8}\ to an improper fraction involves:

\[14 \times 8 + 7 = 112 + 7 = 119\]

The improper fraction is \(\frac{119}{8}\). Once we have this, we can easily convert it to a decimal.
Percentage to Decimal Conversion
Converting a percentage to a decimal is straightforward. A percentage is essentially a fraction with a denominator of 100. To convert it to a decimal, divide the percentage by 100.

Here are the steps:
  • Write down the percentage.
  • Divide by 100.
For our given percentage, 14.875%, it becomes:

\[14.875 \div 100 = 0.14875\]

This conversion is essential as percentages are often easier to understand in decimal form when performing calculations or comparisons.

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