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Chapter 6: Problem 57

Find fraction notation. Simplify. $$ 0.0325 \% $$

Short Answer

Expert verified
\(\frac{13}{40000}\)

Step by step solution

01

Convert Percentage to Decimal

First, convert the given percentage to a decimal. Since 0.0325% means 0.0325 per 100, move the decimal point two places to the left: \[0.0325 \times \frac{1}{100} = 0.000325\]
02

Write as a Fraction

Next, express 0.000325 as a fraction by writing it over 1 and multiplying both the numerator and the denominator by 1000000 to eliminate the decimal: \[0.000325 = \frac{0.000325 \times 1000000}{1 \times 1000000} = \frac{325}{1000000}\]
03

Simplify the Fraction

Simplify the fraction by finding the greatest common divisor (GCD) of 325 and 1000000, which is 25. Divide both the numerator and the denominator by 25: \[\frac{325 \ \textcolor{red}{\thickapprox }}{25} = 13 \ \frac{1000000 \ \textcolor{red}{\thickapprox }}{25} = 40000\]Therefore, the simplified fraction is: \[\frac{13}{40000}\]

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Key Concepts

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

Convert percentage to decimal

When you have a percentage and want to convert it to a decimal, the key is understanding what a percentage actually represents. The term 'percent' means per hundred. Therefore, converting a percentage to a decimal involves moving the decimal point two spaces to the left.
For example, to convert \(0.0325\)% to a decimal:
  • Write the percentage as \(0.0325 \%\text{ or }\ 0.0325/100\)
  • Move the decimal point two places to the left: \(0.0325 \text{ becomes }\ 0.000325\)
This gives us the decimal form of the percentage: \(0.000325\).
Express decimal as fraction

Once you have a decimal, the next step to writing it as a fraction is to place it over 1 and then eliminate the decimal by multiplying both the numerator and the denominator by a power of 10 that matches the number of decimal places.
For example, converting \(0.000325\) to a fraction involves:
  • Writing \(0.000325\) as \(\frac{0.000325}{1}\)
  • Since there are 6 decimal places, multiply both the numerator and the denominator by \(10^6\text{ or } 1000000\):
    \(\frac{0.000325 \times 1000000}{1 \times 1000000}\text{ which simplifies to }\ \frac{325}{1000000}\)
This method effectively removes the decimal, giving you a fraction in its simplest form before any further simplification.
Greatest common divisor

To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that divides both numbers without leaving a remainder.
For example, to simplify \(\frac{325}{1000000}\):
  • Find the GCD of 325 and 1000000, which is 25.
  • Divide both the numerator and the denominator by 25:
    \(\frac{325 \div 25}{1000000 \div 25}\text{ equals }\ \frac{13}{40000}\)
The fraction is now in its simplest form: \(\frac{13}{40000}\).
Using the GCD is crucial because it ensures you have the simplest and most reduced form of a fraction.

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Most popular questions from this chapter

On a test of 80 items, Pedro got \(93 \%\) correct. (There was partial credit on some items.) How many items did he get correct? incorrect?

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