Problem 41 - Prealgebra

Question

Express each decimal or fraction as a percent. Round to the nearest tenth,if necessary. $$0.0006$$

Step-by-Step Solution

Answer

0.06%

Step 1: Understand the Problem

We need to convert the given decimal number 0.0006 into a percent. To do this, it is important to understand that converting a decimal to a percent involves multiplying the decimal by 100.

Step 2: Convert Decimal to Percent

To convert 0.0006 to a percent, multiply it by 100. This is because 1 percent equals one-hundredth, so 100 times a decimal equals its percent value. Therefore, we calculate: \[0.0006 \times 100 = 0.06\]

Step 3: Understand Rounding

Since we need to round to the nearest tenth and the calculated percent value is already a single digit (0.06), we only need to ensure it is properly represented. In this case, 0.06 does not need rounding and stands as it is.

Key Concepts

Rounding Decimals

Rounding decimals is an essential skill when working with numbers. When you round a decimal, you're simplifying it to make it easier to understand or use.
This is particularly important in situations where exact values aren't necessary.
When rounding to the nearest tenth, follow these guidelines:

• Identify the digit in the tenth place. This is the first digit that comes after the decimal point.
• Look at the digit directly to the right (the hundredth place).
• If the hundredth place is 5 or greater, round the tenth place up by one.
• If it's less than 5, keep the tenth place digit unchanged.

Applying these rules allows you to ensure that your numbers are as accurate as you need them to be, without unnecessary complexity.

Understanding Percentages

Percentages are a way to express numbers as parts of a hundred. This concept aligns with many real-life situations such as discounts, interest rates, and statistics, making it a versatile mathematical concept. It's crucial to grasp how percentages are derived from decimals.
A percentage represents a number out of 100, so converting a decimal into a percentage involves multiplying the decimal by 100.
For instance,

• If you have a decimal like 0.75, multiplying it by 100 gives you 75%. This represents that the decimal 0.75 is equal to 75 out of 100.
• Similarly, multiplying 0.25 by 100 results in 25%.

By understanding and practicing this conversion, you can seamlessly switch between decimals and percentages in various contexts.

Expressing Fractions as Percents

Just like decimals, fractions can also be converted to percentages. This process involves a simple transformation that makes fractions easier to compare and understand in the context of 100. To convert a fraction to a percent:

• Start by dividing the numerator (top number) by the denominator (bottom number).
• This operation turns the fraction into a decimal.
• Then, multiply the resulting decimal by 100 to get the percentage.

For example, with a fraction like 1/4, first divide 1 by 4 to get 0.25. Multiplying 0.25 by 100 results in 25%, indicating that 1/4 is equivalent to 25% of a whole.
Practicing these conversions will improve your ability to understand and communicate mathematical ideas accurately.