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Chapter 7: Problem 18

Change the percent to a simplified fraction or mixed number. $$5.2 \%$$

Short Answer

Expert verified
\(5.2\% = \frac{13}{250}\)

Step by step solution

01

- Understanding Percent

The given number is a percent. Recall that percent means per hundred. Therefore, 5.2% can be written as \(\frac{5.2}{100}\).
02

- Simplify the Fraction

To simplify \(\frac{5.2}{100}\), first convert the decimal into a fraction. \(5.2\) can be written as \(\frac{52}{10}\), so \(\frac{5.2}{100} = \frac{52}{1000}\).
03

- Reducing the Fraction

Now simplify \(\frac{52}{1000}\) by dividing the numerator and denominator by their greatest common divisor, which is 4. \(\frac{52 \div 4}{1000 \div 4} = \frac{13}{250}\).

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Key Concepts

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

Simplifying Fractions
Simplifying fractions involves reducing a fraction to its simplest form. This means rewriting the fraction so that the numerator (top number) and the denominator (bottom number) are as small as possible while still representing the same value. For example, in the exercise, we had to simplify the fraction \(\frac{52}{1000}\).
Here's a simple process to simplify a fraction:
  • Find the greatest common divisor (GCD) of the numerator and the denominator.
  • Divide both the numerator and the denominator by their GCD.
For instance, the GCD of 52 and 1000 is 4. When we divide both by 4, we get \(\frac{52 \div 4}{1000 \div 4} = \frac{13}{250}\). So, \(\frac{52}{1000}\) simplifies to \(\frac{13}{250}\).
Decimal to Fraction
When converting a decimal to a fraction, it's essential to understand place value. Every decimal can be represented as a fraction with a power of 10 in the denominator. For example, to convert 5.2 into a fraction:
  • First, recognize that 5.2 is the same as 5.2/1.
  • Shift the decimal point to the right to turn it into a whole number. Here, we multiply by 10 to get 52, doing the same for the denominator, which becomes 10.
  • This results in the fraction \(\frac{52}{10}\).
Next, in the provided exercise, this intermediate step gave us \(\frac{52}{1000}\) after including the \(\frac{5.2}{100}\) from the percent conversion. Always simplify the fraction if possible, like we saw above.
Reducing Fractions
Reducing fractions is the process of making sure a fraction is in its simplest form. This makes the fraction easier to understand and compare with other fractions. The key steps are:
  • Determine the GCD of the numerator and the denominator.
  • Divide both the numerator and the denominator by the GCD.
For example, in the given exercise with \(\frac{52}{1000}\), we found the GCD to be 4. By dividing both 52 and 1000 by 4, we obtained the reduced fraction \(\frac{13}{250}\). Thus, reducing fractions helps in representing the simplest and the most understandable form.

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Most popular questions from this chapter

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