Problem 23 - Elementary Algebra

Question

For the following problems, convert each percent to a decimal. $$ 35 \% $$

Step-by-Step Solution

Answer

Question: Convert 35% into its decimal form. Answer: The decimal form of 35% is 0.35.

Step 1: Write the given percentage as a fraction with the denominator being 100

We are given that the percentage is 35%, so we can write it as a fraction like this: $$ \frac{35}{100} $$

Step 2: Divide the numerator by the denominator

Now, divide the numerator (35) by the denominator (100) to get the decimal form: $$ \frac{35}{100} = \frac{35 \div 1}{100 \div 1} = 0.35 $$

Step 3: Write the final answer

Now that we have divided the numerator by the denominator, we have the decimal form of the given percentage: $$ 35\% = 0.35 $$

Key Concepts

Fraction to Decimal Conversion

Converting fractions to decimals is an important skill in math that allows us to express numbers in a different form. Let’s explore this concept in detail. To convert a fraction to a decimal, we divide the numerator (the top number) by the denominator (the bottom number).

For example, if we have the fraction \(\frac{35}{100}\), we perform the division: 35 divided by 100. This results in 0.35.

• Write the fraction with its numerator and denominator.
• Perform the division of the numerator by the denominator.
• Express the result as a decimal number.

This process can be applied to any fraction, and it’s especially useful when dealing with percentages, as it helps to easily understand and compare values. By converting fractions to decimals, you’ll have a more intuitive grasp of numbers in various mathematical contexts.

Numerator and Denominator

Understanding the terms "numerator" and "denominator" is pivotal in math, especially when working with fractions. A fraction consists of two parts:

• Numerator: This is the number above the fraction line. It signifies the number of parts you have.
• Denominator: This is the number below the fraction line. It indicates the total number of equal parts into which the whole is divided.

For instance, in the fraction \(\frac{35}{100}\), 35 is the numerator, and 100 is the denominator. The numerator tells us how many parts we are considering, while the denominator tells us how many equal parts make up a whole.

When converting to a decimal, understanding these roles is crucial as the division process is essentially splitting the numerator into equal parts as defined by the denominator, transitioning the concept of part-whole into a decimal format.

Basic Arithmetic Operations

Basic arithmetic operations are the foundation of math and include addition, subtraction, multiplication, and division. In the context of converting fractions, division plays a key role. By dividing the numerator by the denominator, we perform one of these fundamental operations that translate a fraction into a decimal.

• Addition and Subtraction: Used for combining numbers or determining differences between them.
• Multiplication: Often used to scale numbers or distribute them over a set.
• Division: Essential in breaking down numbers into smaller units, particularly in fraction to decimal conversion.

In our exercise, the arithmetic operation we focus on is division. Dividing 35 (numerator) by 100 (denominator) is a straightforward application of this operation, resulting in the decimal 0.35. Mastery of these basic operations allows us to tackle more complex problems with ease.