Problem 36 - Algebra 1

Question

Find the percent of a number. $$2 \% \text { of } 105$$

Step-by-Step Solution

Answer

2% of 105 is 2.1

Step 1: Understand percentage

In mathematics, percentage is a way of expressing a number as a fraction of 100. When we say 2%, it means 2 out of 100 or \(\frac{2}{100}\).

Step 2: Applying the percentage to the number

To find 2% of 105, multiply 105 by 2% or 0.02 (since \(\frac{2}{100} = 0.02\)). This is achieved using the formula: Percentage of a number = (percentage / 100) * number

Step 3: Perform the calculation

Replace the variables in the formula with the actual values. Therefore, \((0.02) * 105 = 2.1\)

Key Concepts

Percentage Calculation

Percentage calculation is a fundamental concept in mathematics, often utilized for comparing proportions and determining shares. To compute the percentage of a number, we essentially scale the number according to a per hundred rate. For example, finding 2% of 105 involves converting the percentage into a decimal (since 2% equals \(0.02\) when it is divided by 100) and then multiplying it by the number in question.

Steps involved in percentage calculation include:

• Converting the percentage into a decimal.
• Multiplying this decimal by the number to get the percentage of the number.

Following these steps ensures accurate results and simplifies what may initially seem to be a complex calculation. Hence, to find 2% of 105, you would perform \(0.02 \times 105 = 2.1\), which signifies that 2% of 105 is 2.1.

Mathematical Percentage

In mathematics, a percentage is a way of expressing a number as a fraction of 100. The term 'percent' translates to 'per hundred', and it is symbolized using the percent sign (%). This representation is extremely useful for various calculations such as discounts, interest rates, and statistics among others.

Understanding how to handle percentages mathematically involves a few key points:

• Recognizing that the '%' symbol means 'per hundred'.
• Knowing how to convert percentages to decimals by dividing by 100.
• Using the decimal equivalent in multiplication to find a portion of a quantity.

By mastering these concepts, students are better equipped to tackle problems that involve finding a specific percentage of a number, as well as converting a decimal or fraction into a percentage value.

Expressing Numbers as Percentages

Expressing numbers as percentages is a powerful tool for communicating proportions, ratios, and comparisons. To convert a decimal or a fraction to a percentage, we multiply it by 100 and add the percent sign. Conversely, when expressing a percentage as a number, we remove the percent sign and divide by 100 to get the decimal equivalent.

For example, the fraction \(\frac{1}{5}\) is equivalent to 20% because when we multiply \(\frac{1}{5}\) by 100, we get 20. Similarly, to express 0.85 as a percentage, we multiply by 100 and get 85%.

This approach is not only useful in basic arithmetic but is also crucial in subjects like finance, where expressing numbers as percentages can help in understanding interest rates, stock price changes, and more. Remember, accuracy in expressing numbers as percentages is key, hence always double-check calculations for correctness.