Problem 46 - Prealgebra

Question

Fractions and decimals as percents. To write 0.46 as a percent, multiply by_________:\(0.46=0.46\)__________=__________.

Step-by-Step Solution

Answer

To convert 0.46 to a percent, multiply by 100: 0.46 becomes 46%.

Step 1: Understand the Conversion

To convert a decimal to a percent, you need to multiply the decimal by 100.

Step 2: Set Up the Equation

Write down the decimal 0.46 and multiply it by 100 to set up the equation: \(0.46 \times 100\).

Step 3: Perform the Multiplication

Calculate \(0.46 \times 100\) which equals 46. Therefore, \(0.46 = 46\%\).

Step 4: Fill in the Blanks

Insert the calculated values into the original statement: To write 0.46 as a percent, multiply by 100: \(0.46 = 0.46 \times 100 = 46\%\).

Key Concepts

Fractions and Decimals

Fractions and decimals are two different ways to express quantities that are not whole numbers. Understanding their relationship can help simplify many math problems.

A fraction, like \( \frac{1}{2} \), represents a part of a whole. In contrast, a decimal like 0.5 shows the same concept using the base-ten system. Converting between these two forms is a fundamental skill in math.

Here are some key differences to remember:

• Fractions use a numerator and a denominator to show parts of a whole.
• Decimals rely on the placement of digits to the right of the decimal point to indicate value.

Converting between fractions and decimals involves division. For example, the fraction \( \frac{1}{4} \) is 0.25 as a decimal because 1 divided by 4 equals 0.25.

Percentage Conversion

Converting a decimal to a percentage involves a simple multiplication. Percentages are just another way of expressing fractions and decimals, but out of 100.

To convert a decimal to a percent:

• Multiply the decimal by 100.
• Then, add the percent symbol (%) to the result.

For instance, to transform the decimal 0.46 into a percentage, you multiply 0.46 by 100. This converts it to 46. Therefore, 0.46 is equivalent to 46%.
Remember, moving from decimals to percentages is just a matter of shifting the decimal point two places to the right and adding the percentage sign.

Math Problem-Solving

Math problem-solving often requires a step-by-step approach to ensure accuracy. Learning to systematically work through a problem can make difficult math problems more manageable.

Here's a simple strategy to tackle math problems:

• Identify the problem and what is being asked.
• Break the problem down into smaller, manageable steps.
• Apply the necessary mathematical operations, such as multiplication or division.
• Check your answer to confirm the solution is correct.

For example, if you're asked to convert a decimal to a percent, apply these steps by recognizing you need to multiply by 100, performing the calculation, and finally labeling your answer with a percent symbol.

Prealgebra Concepts

Prealgebra serves as the foundation on which higher-level math is built. Mastering its concepts makes all future math studies easier.

Key prealgebra concepts include:

• Understanding numbers and their relationships (including fractions, decimals, and percentages).
• Basic operations like addition, subtraction, multiplication, and division.
• Recognizing patterns and solving simple equations.

Working with fractions, decimals, and percentages is a crucial part of prealgebra. These skills are essential for tackling more complex problems in algebra. Practice, patience, and persistence are the best ways to become proficient in these areas.