Problem 15 - Prealgebra

Question

Express each decimal or fraction as a percent. Round to the nearest tenth, if necessary. $$0.008$$

Step-by-Step Solution

Answer

The decimal 0.008 expressed as a percent is 0.8%.

Step 1: Understanding Percent Conversion

To convert a decimal to a percent, you need to multiply the decimal number by 100. This step essentially shifts the decimal point two places to the right.

Step 2: Multiply by 100

Take the decimal 0.008 and multiply it by 100: \[ 0.008 \times 100 = 0.8 \] This converts the decimal to a percentage.

Step 3: Round the Result

Since the problem asks to round to the nearest tenth, verify if rounding is needed. The number 0.8 is already at one decimal place which is the tenths place, so no further rounding is necessary.

Key Concepts

Decimal to Percent

Understanding how to convert decimals to percents is crucial in math, as it is a common way to compare values in percentages. A percent represents a fraction of 100, which is why converting from a decimal involves multiplying by 100. This operation is straightforward:

• Take any decimal number, like 0.008.
• Multiply it by 100 to get the percentage. This action is akin to moving the decimal point two spaces to the right.

For instance, multiplying 0.008 by 100 gives us 0.8. This tells us that 0.008 is equivalent to 0.8% when expressed as a percentage. Understanding this concept allows you to quickly transform decimals into a format that is often easier to interpret and compare in everyday contexts.

Rounding

Rounding numbers is a fundamental skill in math. It helps simplify numbers to make them easier to understand or use. Rounding to the nearest tenth specifically involves looking at the digit in the hundredths place.

• If this digit is 5 or greater, you round up the tenth's place by one.
• If it is less than 5, you simply discard the hundredths place and keep the tenth's place the same.

In the case of the number 0.8, it already stands in the tenths place, and there's nothing in the hundredths place to consider, so no rounding is required. Understanding rounding rules can help make decisions quickly about how to represent numbers.

Basic Arithmetic

Basic arithmetic includes simple operations such as addition, subtraction, multiplication, and division. These operations form the backbone of math and are essential for more complex calculations. In our example, transforming the decimal 0.008 to a percentage involves multiplication, one of the four fundamental operations. Multiplication by 100 not only shifts the decimal point but also scales the number to a percent. To ensure accuracy in arithmetic:

• Pay attention to the placement of the decimal point.
• Use each operation carefully to avoid errors.

Mastering these basic operations is key to successfully handling a variety of math tasks and solving problems efficiently.