Question

Write each decimal number as a percent. $$0.065$$

Short answer

Answer: 6.5%

Step-by-step solution

Multiply the decimal number by 100

Multiply 0.065 by 100: $$0.065 \times 100 = 6.5$$ Step 2: Add the percent symbol

Add the percent symbol

Now add the percent symbol to the result obtained in step 1: $$6.5\%$$ The decimal number 0.065 written as a percent is 6.5%.

Key concepts

Percent Conversion

Converting a decimal to a percent is a key skill in understanding how to interpret and represent numbers in different ways. This process involves two main steps. Initially, you multiply the decimal by 100, which essentially shifts the decimal point two places to the right. For example, when we take our decimal number, .065, and multiply it by 100, we get 6.5. The reason behind this multiplication is that a percent is actually a fraction with a denominator of 100. So, when you multiply by 100, you are converting your decimal into a fraction of 100.

In the final step, after multiplying by 100, you add the percent symbol (%) to the number, signifying that it is now a percentage. Therefore, 0.065 as a decimal translates to 6.5% as a percent. Remembering that 'percent' means 'per hundred' can make this transition intuitive and easier to comprehend.

Decimal Multiplication

The multiplication of decimals is largely analogous to the multiplication of whole numbers. However, it is essential to keep track of the placement of the decimal point in the product. When multiplying a decimal by 100, you are essentially moving the decimal point two places to the right, which makes sense as we are scaling the number by a factor of 100. For instance, multiplying 0.065 by 100 positions the decimal point between the 6 and the 5, giving us 6.5.

Understanding this process eliminates the need for writing multiple zeroes and counting places after the decimal point, simplifying calculations and minimizing potential errors. Decimal multiplication is not just used in percent conversion but is a fundamental operation that is used across various fields of study and real-life scenarios.

Math Problem Solving

Math problem solving involves a systematic approach to tackle mathematical challenges using various methods and strategies. In the context of converting decimals to percents, problem-solving can be broken down into recognizable steps, building upon prior knowledge, and applying systematic operations.

To solve these kinds of problems, begin by understanding what is being asked—here, translating a decimal to a percentage. Next, apply the appropriate mathematical operations—in this case, multiplying by 100 and adding the percent symbol. Finally, ensure that the answer makes sense in the context of the problem, such as checking that a percentage falls within the range of 0% to 100%. With practice, these steps become second nature, empowering students to approach similar mathematical problems with confidence.