Problem 78 - Algebra 1: Concepts and Skills

Question

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

Step-by-Step Solution

Answer

The decimal \(0.005\) as a percentage is \(0.5\%\).

Step 1 - Identify the Decimal

First, identify the decimal given. The decimal provided for this exercise is \(0.005\).

Step 2 - Move the Decimal Point

Convert the decimal to a percentage by moving the decimal point two places to the right. Therefore, \(0.005\) becomes \(0.5\)

Step 3 - Add the Percentage Sign

After moving the decimal two places, simply add the percentage (%) sign. So, the result is \(0.5\%\).

Key Concepts

Understanding Decimals

Decimals are a way to represent numbers that are not whole. Think of them as fractions or parts of a whole. For example, the decimal 0.005 is a very small number, specifically five one-thousandths of one. Decimals use base 10, meaning each place to the right of the decimal point represents a fraction with a denominator that is a power of ten.

• The first place to the right is tenths, like 0.1.
• The second place is hundredths, akin to 0.01.
• The third place is thousandths, just like 0.001.

To clearly understand how small or large a decimal number is, it's crucial to familiarize yourself with these place values. This helps in estimating the magnitude of the numbers you are working with.

Grasping Percents

Percent, denoted by the symbol '%', means 'per hundred'. It allows us to express numbers as a part of 100. This makes it easy to understand proportions at a glance. So when you see 0.5%, it actually means 0.5 out of 100.

Percents are widely used in daily life—from sale discounts in stores to interest rates at banks. That familiarity makes conversions between decimals and percents valuable. Understanding that 100% equals one whole unit can help conceptualize other percentages as fractions or decimals. Always remember that when dealing with percents, you are handling hundredths of the whole.

Mathematical Conversion Between Decimals and Percents

Converting decimals to percents is easy once you get the hang of it.

• Start by identifying the decimal. For example, 0.005 as given in the exercise.
• Next, move the decimal point two spaces to the right. This action changes 0.005 to 0.5.
• Finally, add the percent sign (%) to signify that it is now a percentage.

These steps are simple yet effective for mathematical conversion, allowing you to switch back and forth between these two expressions. Remember, the key action here is moving the decimal point two places, which is effectively multiplying by 100, adjusting the number to a percentage form.