Problem 52 - Algebra 1: Concepts and Skills

Question

Write the percent as a decimal. $$ 90 \% $$

Step-by-Step Solution

Answer

The decimal form of 90% is 0.90.

Step 1: Understanding the conversion from percent to decimal

A percent is a value that represents a fraction of 100. Subsequently, in order to convert from percent to decimal, one needs to divide the given percentage by 100.

Step 2: Apply conversion

Divide 90 by 100, which gives \( \frac{90}{100} = 0.90 \).

Key Concepts

Percent

Percent is a way to express a number as a part of a whole, specifically out of 100. The word "percent" itself means "per hundred." It's a useful way to represent ratios and compare values easily.
For example, if you score 90% on a test, it means you answered 90 out of every 100 questions correctly. In practical terms, percentages are used in various areas of daily life, such as calculating discounts, interest rates, and statistical data.

• Percentages can be greater than 100 if the amount is more than the whole.
• They can also be negative, indicating a decrease or loss.

Understanding percentages can greatly aid in financial literacy and data interpretation.

Decimals

Decimals are another way of representing fractions, specifically those fractions with a denominator that is a power of ten. They help express fractions in a more versatile and manageable format.
For instance, the decimal 0.90 means a little less than 1, where the `0` before the decimal point represents the whole number, and the digits after the decimal point represent fractions of 10, 100, etc.
Decimals simplify arithmetic operations like addition, subtraction, multiplication, and division. They are commonplace in financial calculations and scientific measurements due to their precision.

• Decimals provide a clear visual representation of value.
• They are easy to compare and calculate in mathematical operations.

Understanding how to work with decimals is crucial for daily numerical tasks.

Fractions

Fractions denote parts of a whole and are expressed as a ratio of two numbers, the numerator over the denominator. In simple terms, the numerator tells us how many parts we have, while the denominator tells us how many parts make up a whole.
For example, the fraction \( \frac{90}{100} \) is equivalent to 90% and 0.90 when converted to a decimal. This fraction tells us that we have 90 out of 100 parts, illustrating the direct relationship between fractions, decimals, and percentages.
Fractions are used to represent quantities that are not whole numbers, such as in recipes or when splitting expenses. They are fundamental in algebra and help solve real-world problems efficiently.

• Fractions can be easily converted to decimals and percentages.
• They are ideal for exactly representing smaller or divisible quantities.

Understanding fractions and their conversions form the building blocks for more advanced mathematical concepts.