Problem 61 - Algebra A Combined Function

Question

Write each percent as \(a\) decimal. $$ 3.1 \% $$

Step-by-Step Solution

Answer

3.1% as a decimal is 0.031.

Step 1: Understand the Concept of Percentages

Percent means per hundred. So when we have a percentage, we are essentially talking about parts per hundred.

Step 2: Convert Percent to Decimal

To convert a percentage to a decimal, divide the percentage by 100. For example, to convert 1% to a decimal, you would write 1% as \( \frac{1}{100} = 0.01 \).

Step 3: Application to 3.1%

Convert 3.1% into a decimal by dividing by 100. So, \( 3.1 \% \) becomes \( \frac{3.1}{100} = 0.031 \).

Key Concepts

Percentages

A percentage is a way to express a number as a fraction of 100. It's crucial in our daily life for calculating discounts, interest rates, and even scores. When you say "percent," it literally means "per hundred." This unit is helpful because it allows for easy comparison of quantities with different denominators. For instance, 25% indicates 25 parts out of 100.

Understanding percentages can simplify complex calculations by standardizing them to a familiar range between 0 and 100. Remember, whenever you are dealing with percentages, it's like discussing sections of a whole pie divided into 100 slices.

Decimals

Decimals are a method of representing fractions using a base 10 system. In essence, they are another way to express numbers that fall between whole numbers. Decimals are crucial because they allow for more precise measurements than whole numbers alone. For example, the number 0.5 represents half, which can also be written as the fraction \(\frac{1}{2}\).

Decimals are represented with a decimal point, separating the whole number part from the fractional part. This standard allows for precise expressions of numbers beyond integers. In terms of conversion, decimals help transition percentages into a universally understandable format.

Mathematical Conversion Steps

The conversion from a percentage to a decimal is straightforward once you understand the core principle. The key here is realizing that a percentage is out of 100.

• First, take your percentage value.
• Then, divide this number by 100.
• This action effectively shifts the decimal point two places to the left.

For example, to convert 3.1% into a decimal, divide 3.1 by 100. In mathematical terms, this is written as \(\frac{3.1}{100} = 0.031\). This conversion is pivotal because it translates the percentage into a format suitable for more calculations, removing the percentage sign and thus contextualizing the number into a decimal.