Problem 84 - Algebra A Combined Function

Question

Write each decimal as a percent. $$ 0.005 $$

Step-by-Step Solution

Answer

0.005 as a percent is 0.5%.

Step 1: Understanding the Question

The problem asks us to convert the decimal number \(0.005\) into a percentage. This means expressing the decimal as a number out of 100.

Step 2: Conversion Formula

To convert a decimal to a percent, multiply the decimal number by 100. The formula is: \[ \text{Percent} = \text{Decimal} \times 100 \].

Step 3: Apply the Formula

Using the formula from Step 2, multiply \(0.005\) by 100: \[ 0.005 \times 100 = 0.5 \].

Step 4: Write the Percent

The result from Step 3 gives us \(0.5\). Thus, \(0.005\) as a percent is \(0.5\%\).

Key Concepts

Decimals in Mathematics

Decimals are a way to represent fractions and non-whole numbers in mathematics. They are written with a decimal point that separates the whole number part from the fractional part. Decimals can be thought of as an extension of our base 10 number system, where each position after the decimal point is a power of ten. For example, in the decimal 0.005:

• The '0' before the decimal point signifies the whole number part, which is zero in this case.
• The first '0' after the decimal point is in the tenths place, representing 1/10.
• The second '0' is in the hundredths place, representing 1/100.
• The '5' is in the thousandths place, representing 1/1000.

When working with decimals, it's important to understand these position values because they dictate the size of the fraction the decimal represents. Decimals are used in many fields such as science and engineering because they allow for precise calculations and accuracy.

Percentage Calculation

Calculation of percentages is a fundamental skill in everyday mathematics, used to express a number as a fraction of 100. This is especially useful for understanding proportions and comparisons. To convert a decimal to a percentage, we can use a straightforward method:

• Multiply the decimal number by 100.
• Add the percentage symbol '%' after the resulting number.

For instance, when converting 0.005 to a percent, we multiply it by 100:\[0.005 \times 100 = 0.5\]Therefore, 0.005 as a percent is 0.5%. This means 0.005 is equivalent to half a percent out of a whole (100%). Understanding percentage calculation helps simplify problems relating to interest rates, discounts, and statistics.

Multiplying Decimals

Multiplying decimals is an essential skill in mathematics that involves a few simple steps for accurate calculation. When you multiply two numbers that are decimals, it's quite similar to multiplying whole numbers, with an additional step of adjusting the decimal point in the result. Here's how you can multiply decimals effectively:

• Ignore the decimal points and multiply the numbers as if they were whole numbers.
• Count the number of decimal places in both of the original decimal numbers.
• Take that total number of decimal places and apply it to the product from step 1.

Let's say we're multiplying 0.005 by 100 to convert to a percentage: - First, consider 5 (from 0.005) and 100. - Multiply 5 by 100 to get 500. - Since 0.005 has three decimal places, our product (500) needs to move three decimal places to the left to become 0.5. Through this method, you can handle any decimal multiplication by accurately placing the decimal in the result, ensuring your outcome is precise.