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Chapter 6: Problem 16

Write as a fraction and as a decimal. $$90 \%$$

Short Answer

Expert verified
As a fraction, 90% is \(\frac{9}{10}\). As a decimal, 90% is 0.9.

Step by step solution

01

Converting percent to fraction

Take the percentage number and place it over 100 to create a fraction. So, 90% becomes the fraction \(\frac{90}{100}\). Next, simplify the fraction by finding the greatest common divisor of the numerator and the denominator.
02

Simplifying the fraction

The greatest common divisor for 90 and 100 is 10. By dividing both numerator and denominator with 10, the fraction \(\frac{90}{100}\) simplifies to \(\frac{9}{10}\).
03

Converting percent to decimal

To convert 90% to a decimal, move the decimal point two places to the left. So, 90% becomes 0.90 or simply 0.9.

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Key Concepts

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

Fraction Conversion
When dealing with percentages, converting them into fractions is a straightforward process. A percentage represents a number out of 100. Therefore, to convert a percentage to a fraction:
  • Take the percentage value, for example, 90%.
  • Place this number over 100, which is the base of percentages.
So, 90% becomes \( \frac{90}{100} \). This conversion is helpful, especially when you need to perform further mathematical operations or comparisons. Understanding fraction conversion lays the foundation for simplifying fractions, which is another key concept to grasp.
Decimal Conversion
Converting percentages into decimals is another essential skill you will frequently use. To convert a percentage to a decimal, follow these simple steps:
  • Take the percentage number, like 90%, and understand initially, it means 90.0.
  • Move the decimal point two places to the left. This shifting represents division by 100.
For instance, moving the decimal point two places to the left in 90.0 results in 0.90, or simply 0.9. This is a quick way to transform percentages into a decimal form for various mathematical applications.
Simplification of Fractions
When you convert a percentage to a fraction, you'll frequently need to simplify it as much as possible. Simplifying fractions involves reducing them to their simplest form. Here's how you can simplify a fraction:
  • Identify the greatest common divisor (GCD) of the numerator and the denominator.
  • Divide both the numerator and the denominator by this GCD to achieve the simplest form.
For the fraction \( \frac{90}{100} \), the GCD of 90 and 100 is 10. By dividing both by 10, you simplify \( \frac{90}{100} \) to \( \frac{9}{10} \). Simplifying fractions makes calculations easier and results more precise, ensuring you understand the foundational math without unnecessary complexity.

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Most popular questions from this chapter

For \(\frac{1}{4} \%\), the percent ratio is the ratio \(\frac{\frac{1}{4}}{100}\). Which of the following fractions is equivalent to this ratio? (i) \(\frac{1}{25}\) (ii) \(\frac{1}{400}\) (iii) \(\frac{25}{1}\)

Solve. Use the proportion method. Find \(96 \%\) of 75

Solve. Use the basic percent equation. \(80 \%\) of 16.25 is what?

Solve. Use the proportion method. 37 is what percent of \(148 ?\)

Solve. Use the proportion method. What percent of 1500 is \(693 ?\)
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