Problem 89 - Algebra A Combined Function

Question

Write the percent from the circle graph as a decimal and a fraction. Africa: \(14.2 \%\)

Step-by-Step Solution

Answer

Decimal: 0.142; Fraction: \( \frac{71}{500} \).

Step 1: Convert Percentage to Decimal

To convert a percentage to a decimal, divide by 100. For Africa, which is given as 14.2%, we divide by 100 to get:\[ 14.2\% = \frac{14.2}{100} = 0.142 \]

Step 2: Convert Percentage to Fraction

To convert a percentage to a fraction, place the percentage number over 100 and simplify if possible. For 14.2%, write it as:\[ \frac{14.2}{100} \]To remove the decimal, multiply the numerator and denominator by 10:\[ \frac{14.2 \times 10}{100 \times 10} = \frac{142}{1000} \]Simplifying gives the fraction:\[ \frac{71}{500} \]

Key Concepts

Decimal Conversion

Converting a percentage to a decimal is a straightforward process. It involves two primary steps. First, take the percentage and divide it by 100. This division is because a percent symbol (%) means "out of 100." For instance, if you have 14.2%, you convert it to a decimal by doing the calculation: \[ 14.2 \div 100 = 0.142 \]Remember, moving a decimal point two places to the left is equivalent to dividing by 100, which is why 14.2% becomes 0.142. By understanding this, you can easily convert any percentage to a decimal in no time.

Fraction Conversion

Transforming a percentage into a fraction is another useful skill. To do this, place the percentage value over 100. In the case of 14.2%, it initially becomes:\[ \frac{14.2}{100} \]However, fractions are often easier to work with when there are no decimals involved. To remove the decimal, multiply both the numerator and the denominator by 10, turning 14.2% into:\[ \frac{142}{1000} \]By doing this, we have shifted the decimal one place to the right, making it easier to handle. Once in this form, the fraction might still need to be simplified, which we will discuss next.

Simplifying Fractions

The process of simplifying fractions is about making a fraction as simple as possible for easy understanding and computation. After obtaining our fraction from the earlier step \( \frac{142}{1000} \), simplification involves finding the greatest common divisor (GCD) of both the numerator and denominator.1. Break down both numbers into their prime factors, if needed.2. Identify the largest shared factor.3. Divide both the numerator and the denominator by this factor.For \( \frac{142}{1000} \), the GCD is 2.\[ \frac{142 \div 2}{1000 \div 2} = \frac{71}{500} \]The fraction \( \frac{71}{500} \) represents the simplest form since 71 is a prime number and has no common divisors with 500. This process ensures the fraction is as reduced as possible, aiding both interpretation and computation.