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Chapter 6: Problem 78

In the following exercises, convert each fraction to a percent. $$\frac{6}{7}$$

Short Answer

Expert verified
85.71%

Step by step solution

01

- Understand the Concept

To convert a fraction to a percent, multiply the fraction by 100. This is because percent means 'per hundred'.
02

- Set Up the Multiplication

Multiply the fraction \( \frac{6}{7} \) by 100. Set up the equation as follows: \[ \frac{6}{7} \times 100 \]
03

- Perform the Multiplication

Carry out the multiplication: \[ \frac{6}{7} \times 100 = \frac{6 \times 100}{7} = \frac{600}{7} \]
04

- Simplify the Result

Divide 600 by 7 to get a decimal value: \[ \frac{600}{7} \approx 85.71 \] (rounded to two decimal places)
05

- Convert to Percent

The decimal value 85.71 represents the percentage. Therefore, \( \frac{6}{7} \) as a percent is approximately 85.71%.

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Key Concepts

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

Percent Conversion
Converting a fraction to a percent is an essential skill in mathematics. It helps you understand the portion of one whole something equivalent to. To convert a fraction to a percent, you multiply the fraction by 100. This is because 'percent' means 'per hundred'.

For example, to convert \(\frac{6}{7}\) to a percent:
  • First, multiply the fraction by 100: \[\frac{6}{7} \times 100\]
Following these steps converts the fraction to a percentage, making it easier to understand in everyday terms.
Fraction Multiplication
Multiplying fractions is straightforward. You simply need to multiply the numerator (top part of the fraction) and the denominator (bottom part of the fraction) separately.

For our problem, \(\frac{6}{7}\), we multiply this fraction by 100, focusing on the numerator and keeping the denominator the same initially:
  • Set up the multiplication: \[\frac{6}{7} \times 100 = \frac{6 \times 100}{7} = \frac{600}{7}\].
This technique simplifies converting fractions into percentages, offering a clear method to follow each time.
Decimal Approximation
Often, when you divide the numerator by the denominator, the result isn't a whole number, and you get a decimal. In our example, converting \(\frac{600}{7}\) results in a repeating decimal. Therefore, we approximate to make the result more understandable.

To simplify \(\frac{600}{7}\):
  • Perform the division: 600 梅 7 鈮� 85.71 (rounded to two decimal places).
The decimal approximation step is vital. It ensures your percentage conversion is usable and understandable, especially in real-life scenarios where precision matters.

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Most popular questions from this chapter

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