Problem 31 - Prealgebra

Question

Express each decimal or fraction as a percent. Round to the nearest tenth,if necessary. $$\frac{9}{40}$$

Step-by-Step Solution

Answer

\( \frac{9}{40} \) as a percent is \(22.5\%\).

Step 1: Understand the Problem

We are given the fraction \( \frac{9}{40} \) and we need to express it as a percent. A percent is a way of expressing a number as a fraction of 100.

Step 2: Convert the Fraction to a Decimal

To convert \( \frac{9}{40} \) to a decimal, divide the numerator by the denominator. \[\frac{9}{40} = 9 \div 40\]Calculating this gives:\[0.225\]

Step 3: Convert the Decimal to a Percent

To convert a decimal to a percent, multiply the decimal by 100.\( 0.225 \times 100 = 22.5 \%\).

Step 4: Round the Percent

The result from the previous step is already rounded to the nearest tenth, which is \(22.5\%\). Thus no further rounding is necessary.

Key Concepts

Fractions to Decimals

Converting fractions to decimals is a crucial skill in mathematics. A fraction like \( \frac{9}{40} \) can be converted to a decimal by dividing the numerator (the top number) by the denominator (the bottom number). Here’s how it works.

- Begin by dividing the number 9 by 40.- Using a calculator or long division method will yield a result of 0.225.
This process transforms the fraction into a decimal, making it easier to handle when using percentages or performing other calculations. It's a fundamental part of prealgebra, helping to build a strong mathematical foundation.

Decimal to Percent

Once a decimal is found, like in our previous result of 0.225, converting it to a percentage is straightforward. Percent means "per hundred" so to convert from a decimal to a percent:- Multiply your decimal by 100.- In this case, \( 0.225 \times 100 = 22.5 \% \).This method shows that 22.5% of something is equivalent to the decimal 0.225. It visually aligns a numerical value with a typical percentage format, often used in statistics and daily life calculations, such as understanding discounts in shopping or grades in exams.

Transforming decimals to percentages reinforces the idea that percentages are just another way of representing parts of a whole.

Math Rounding

Rounding is an essential part of mathematics, particularly when dealing with percentages. It simplifies numbers, making them easier to work with. When converting fractions or decimals to percentages, you may need to round results to the nearest tenth or other specified places.

- The rule is simple: if the number in the next smallest place (i.e., the hundredths when rounding to the nearest tenth) is 5 or more, round up. - So, in our example of 22.5%, there's no need to adjust since it's already set at the nearest tenth accurately.
Rounding helps to make figures more digestible, particularly in situations where exact numbers are less important than overall trends or estimates, such as in financial forecasts or statistical data.

Prealgebra

Prealgebra lays down the foundation for all future mathematics studies. Understanding fractions, decimals, and percentages is a key part of this level of math.

- It encompasses number operations, recognizing patterns, and preparing for algebraic reasoning. - Concepts like converting fractions to decimals and percentages help form the base upon which more advanced topics like algebra and calculus are built. Grasping these basics ensures that students have the necessary skills to progress confidently into more complex math studies. Prealgebra is more than just computations; it is about understanding the relationship between numbers and the real world, applying simple mathematical concepts to everyday situations.