Problem 90 - Algebra A Combined Function

Question

Write the percent from the circle graph as a decimal and a fraction. Asia: \(60.6 \%\)

Step-by-Step Solution

Answer

60.6% as a decimal is 0.606 and as a fraction is \(\frac{303}{500}\).

Step 1: Convert from Percent to Decimal

To convert a percentage into a decimal, we move the decimal point two places to the left. For example, for Asia's percentage of 60.6%, moving the decimal point two places left gives us 0.606. Therefore, Asia's percentage as a decimal is 0.606.

Step 2: Convert from Decimal to Fraction

Now, we need to convert the decimal (0.606) into a fraction.1. Identify how many decimal places there are. Since there are three decimal places, 0.606 is the same as saying 606/1000.2. Simplify the fraction by finding the greatest common divisor of 606 and 1000. The greatest common divisor (GCD) of 606 and 1000 is 2.3. Divide both the numerator and the denominator by their GCD:\[\frac{606}{1000} = \frac{606 \div 2}{1000 \div 2} = \frac{303}{500}\]So, the decimal 0.606 as a fraction is \(\frac{303}{500}\).

Key Concepts

Percent to Decimal Conversion

Converting a percentage into a decimal number is a simple process that helps in various mathematical calculations. The key thing to remember is to move the decimal point two places to the left. This is because percentages are a way of expressing numbers as parts of 100.
For example, let’s take the percentage from the circle graph for Asia, which is 60.6%. To convert 60.6% into a decimal:

• Move the decimal point from its position in the percentage two spots to the left.
• This includes moving past any digits and will result in the decimal 0.606.

This means Asia's percentage of 60.6% is equivalent to a decimal value of 0.606. This method works for all percentages and is a great way to turn percent values into decimals quickly and efficiently.

Decimal to Fraction Conversion

Once you have a number in decimal form, sometimes you need to convert it into a fraction because fractions provide a different perspective or ease of calculation in some scenarios. Let's look at how to convert the decimal 0.606 into a fraction.
First, you need to identify how many decimal places are present. Here, 0.606 has three decimal places.

• Write the decimal as a fraction with the decimal number as the numerator (606) and place a '1' followed by as many zeros as there were decimal places (1000) as the denominator. This results in the fraction \(\frac{606}{1000}\).
• This fraction can often be simplified to a smaller fraction equivalent. To do this, find the greatest common divisor (GCD) of the numerator and the denominator.

In this case, the GCD of 606 and 1000 is 2. By dividing both the numerator and the denominator by 2, you simplify the fraction to \(\frac{303}{500}\). Thus, the decimal 0.606 is expressed as the fraction \(\frac{303}{500}\).

Simplifying Fractions

Simplifying fractions is all about reducing them to their simplest form where the numerator and denominator have no common divisor other than 1. This often makes fractions easier to work with in further calculations or comparisons.
To simplify a fraction such as \(\frac{606}{1000}\), follow these easy steps:

• First, determine the greatest common divisor (GCD), which is the largest number that can divide both the numerator and the denominator without leaving a remainder.
• For \(\frac{606}{1000}\), the GCD is 2. Divide both the numerator (606) and the denominator (1000) by 2.

After this step, you get \(\frac{303}{500}\), which is the simplified version of our original fraction. Remember, a fraction is in its simplest form when the numerator and denominator no longer share any common factors except for 1. Simplifying fractions is a valuable skill because it helps ensure calculations are as straightforward as possible.