Finding out what fraction 30/36000 represents and expressing it as a percentage is a straightforward math problem with practical applications in various fields. This article will guide you through the process step-by-step, explaining the concepts involved.
Simplifying the Fraction 30/36000
The fraction 30/36000 represents a part of a whole. To understand it better, we simplify it to its lowest terms. This means finding the greatest common divisor (GCD) of both the numerator (30) and the denominator (36000) and dividing both by it.
Finding the GCD:
The easiest way to find the GCD is to break down both numbers into their prime factors:
- 30 = 2 x 3 x 5
- 36000 = 26 x 32 x 53
The common prime factors are 2, 3, and 5. The lowest power of each common factor is 21, 31, and 51. Therefore, the GCD is 2 x 3 x 5 = 30.
Simplifying:
Dividing both the numerator and the denominator by the GCD (30):
30/30 = 1 36000/30 = 1200
Therefore, the simplified fraction is 1/1200.
Converting the Fraction to a Percentage
To express 1/1200 as a percentage, we perform the division and multiply the result by 100:
1 ÷ 1200 = 0.0008333...
0.0008333... x 100 = 0.08333...%
Rounding to two decimal places, we get 0.08%.
What does 0.08% mean?
0.08% means that 30 is a very small part of 36000. It represents less than one-tenth of one percent. To visualize this, imagine a pie chart; 30 out of 36000 would represent a tiny, almost invisible slice.
Practical Applications
Understanding how to simplify fractions and convert them to percentages is crucial in various situations, including:
- Finance: Calculating interest rates, returns on investment, or proportions of a budget.
- Statistics: Representing data in graphs and charts, analyzing survey results.
- Science: Expressing experimental results or concentrations of substances.
- Everyday life: Determining discounts, sales tax, or tips.
This article has shown you how to simplify the fraction 30/36000 to 1/1200 and convert it into a percentage of approximately 0.08%. Remember that understanding these basic mathematical concepts can significantly help you in various aspects of life.
