Problem 68
Question
If 2 out of 200 people own a gerbil, find the percent of the people that own a gerbil.
Step-by-Step Solution
Verified Answer
1%
1Step 1: Identify the ratio
Given that 2 out of 200 people own a gerbil, the ratio of people who own a gerbil to the total number of people is \(\frac{2}{200} \).
2Step 2: Convert the ratio to a fraction
Divide the numerator by the denominator: \(\frac{2}{200} = 0.01 \).
3Step 3: Convert the fraction to a percentage
Multiply the result by 100 to get the percentage: \(0.01 \times 100 = 1\text{\%} \).
Key Concepts
Understanding RatiosFractions and Their SimplificationsConversions: Fraction to Percentage
Understanding Ratios
A ratio is a comparison between two quantities. It tells us how much of one thing there is compared to another. In this exercise, we need to find out how many people own a gerbil compared to the total number of people. The ratio given is \(\frac{2}{200}\). This means that for every 200 people, 2 people have a gerbil.
Ratios can be simplified just like fractions. Although not necessary here, always make sure the ratio presents the smallest numbers possible for easier calculations.
For example, the ratio \(\frac{2}{200}\) simplifies to \(\frac{1}{100}\) by dividing both the numerator and the denominator by 2.
Understanding these comparisons helps us make sense of data and relationships between quantities.
Ratios can be simplified just like fractions. Although not necessary here, always make sure the ratio presents the smallest numbers possible for easier calculations.
For example, the ratio \(\frac{2}{200}\) simplifies to \(\frac{1}{100}\) by dividing both the numerator and the denominator by 2.
Understanding these comparisons helps us make sense of data and relationships between quantities.
Fractions and Their Simplifications
Fractions represent part of a whole. Here, the fraction is derived from the ratio of gerbil owners to the total population: \(\frac{2}{200}\). This fraction signifies that out of every 200 people, 2 own a gerbil.
We simplify fractions to make calculations easier. To simplify \(\frac{2}{200}\), divide the numerator and the denominator by their greatest common divisor, which is 2 in this case, yielding \(\frac{1}{100}\).
Simplifying helps us convert the fraction more easily in the next steps. Remember, any fraction representing part of a whole can be converted into a percentage by further calculations.
We simplify fractions to make calculations easier. To simplify \(\frac{2}{200}\), divide the numerator and the denominator by their greatest common divisor, which is 2 in this case, yielding \(\frac{1}{100}\).
Simplifying helps us convert the fraction more easily in the next steps. Remember, any fraction representing part of a whole can be converted into a percentage by further calculations.
Conversions: Fraction to Percentage
To convert a fraction to a percentage, multiply the fraction by 100. In this scenario, we're converting \(\frac{0.01}\) to a percentage.
Calculation: \(0.01 \times 100 = 1\)
So, \(1\)\text{%} of the people in this scenario own a gerbil.
Percentages are useful because they express ratios as parts of 100, which are easier for people to understand and compare.
Regular conversions between fractions and percentages are helpful in everyday maths and understanding data in a clear and meaningful way.
Calculation: \(0.01 \times 100 = 1\)
So, \(1\)\text{%} of the people in this scenario own a gerbil.
Percentages are useful because they express ratios as parts of 100, which are easier for people to understand and compare.
Regular conversions between fractions and percentages are helpful in everyday maths and understanding data in a clear and meaningful way.
Other exercises in this chapter
Problem 67
For exercises \(23-74\), evaluate. $$ -\frac{1}{6}-\frac{1}{6} $$
View solution Problem 67
For exercises 1-80, evaluate. $$ \frac{(9-1)^{2}-64}{2^{3}} $$
View solution Problem 68
For exercises \(23-74\), evaluate. $$ -\frac{1}{10}-\frac{1}{10} $$
View solution Problem 68
For exercises 15-100, evaluate. $$ -3^{2}-17(-1) $$
View solution