Problem 37 - Algebra 1

Question

Find the percent of a number. $$0.8 \% \text { of } 120$$

Step-by-Step Solution

Answer

So, 0.8% of 120 is 0.96.

Step 1: Convert percent to decimal

To start off, convert the percentage to a decimal. This involves dividing the percentage, 0.8 in this case, by 100. The formula is: 0.8/100 = 0.008.

Step 2: Multiply the decimal with the given number

Now multiply this decimal value (0.008) with the given number (120). So, 0.008 * 120 = 0.96

Key Concepts

Percent to Decimal Conversion

Understanding how to convert a percentage to a decimal is fundamental, and it can be done in a breeze. The word 'percent' means 'per hundred', which is a clue to the conversion process. To convert a percent to a decimal, divide it by 100. This is essentially shifting the decimal point two places to the left.

For example, to convert 0.8% into a decimal, you simply divide 0.8 by 100, which gives you 0.008. It's like taking off the '%' sign and replacing it with '0.01 times'. This step sets you up for any further calculations involving percentages, and it's crucial for correctly applying them in various mathematical contexts.

Multiplying Decimals

Once you have your percent converted to a decimal, the next step usually involves multiplying this decimal by a number. To multiply decimals, line up the numbers without considering the decimal points and multiply as you would with whole numbers. Afterward, count the total number of digits to the right of the decimal points in the numbers you are multiplying. Then, place the decimal point in your answer so that it has the same number of digits to its right.

For instance, to multiply 0.008 by 120, ignore the decimals and compute 8 * 120, which equals 960. Since 0.008 has three digits to the right of the decimal, the answer must have three digits to the right of the decimal as well, giving us 0.960. Simplifying this we get 0.96. This is crucial to ensure precision in your answer and residing in harmony with the decimal system.

Percentages in Algebra

Percentages often appear in algebraic expressions and equations, serving as a way to express ratios or proportions. In algebra, working with percentages requires you to incorporate the concepts of decimal conversion and multiplication of decimals within the algebraic structures. This fundamental understanding allows you to solve for unknowns and to create equations that model real-world scenarios.

For example, finding 'x percent of y' translates to multiplying the decimal equivalent of 'x' by 'y'. As such, the algebraic representation of finding 0.8% of 120 becomes solving for '0.008 times 120' to yield 0.96. Mastering the use of percentages in algebra is essential for complex problem-solving and developing deeper mathematical comprehension.