Problem 87 - Algebra A Combined Function

Question

In Exercises 87 through 90 , write the percent from the circle graph as a decimal and a fraction. Australia: \(0.5 \%\)

Step-by-Step Solution

Answer

Decimal: 0.005; Fraction: \( \frac{1}{200} \).

Step 1: Understanding Percentage

Before converting, recognize that "0.5%" is read as "zero point five percent," meaning "0.5 out of 100."

Step 2: Converting Percent to Decimal

To convert a percentage to a decimal, divide the percentage by 100 or simply move the decimal point two places to the left. For "0.5%," move the decimal two places to the left: 0.5 becomes 0.005.

Step 3: Converting Percent to Fraction

To convert a percentage to a fraction, write the percentage as the numerator with 100 as the denominator, then simplify the fraction. For "0.5%," write it as \( \frac{0.5}{100} \). To simplify, multiply by 10 to eliminate the decimal: \( \frac{0.5 \times 10}{100 \times 10} = \frac{5}{1000} \). Simplifying \( \frac{5}{1000} \) gives \( \frac{1}{200} \).

Key Concepts

Decimal Conversion

In understanding decimal conversion from a percentage, it’s important to first grasp what a percentage represents. A percentage is a way of expressing a number as a fraction of 100. For instance, 0.5% means 0.5 out of 100. The conversion of a percentage into a decimal format is straightforward and follows a simple rule.

To convert a percentage to a decimal, you divide the percentage by 100. This is the same as moving the decimal point two places to the left. For instance, converting 0.5% to a decimal involves shifting the decimal two spots to the left, resulting in 0.005. This transformation helps in interpreting the value on a linear scale without the percent sign.

This concept is not only essential in academics but also in real-world applications like calculating interest rates or understanding data charts. By converting percentages into decimals, you facilitate easier calculations and interpretations.

Fraction Conversion

Converting a percentage into a fraction is another method to express the same value in a different way, often shedding light on its inherent ratio. When you have a percentage, like 0.5%, you need to express it as a fraction with a denominator of 100 first.

With 0.5%, you write this as a fraction:

• 0.5 becomes the numerator after converting it to a fraction form, 0.5/100.

However, fractions do not usually include decimals, so the next step involves clearing the decimal by multiplying both the numerator and the denominator by 10, resulting in 5/1000.

This intermediate fraction needs simplification to reflect its simplest form, which brings us to the next key concept in conversion.

Simplifying Fractions

Simplifying fractions involves reducing them to their simplest form, where the numerator and the denominator have no common factors other than 1. This process makes understanding and comparing fractions much easier and is a crucial step in accurate conversion.

Once you have a fraction like 5/1000, the task is to find the greatest common divisor (GCD). Here, the GCD of 5 and 1000 is 5. By dividing both the numerator and the denominator by this GCD, you reduce the fraction:

• The simplified form of 5/1000 becomes 1/200 after dividing both terms by 5.

This simplification expresses the fraction in its simplest terms, making it easier to use in calculations or to interpret. Through simplification, you can achieve a more straightforward and concise representation of fractional values.