Problem 19 - Prealgebra

Question

Change each percent to a decimal. $$0.9 \%$$

Step-by-Step Solution

Answer

0.009

Step 1: Understand the Problem

The goal is to convert the percentage given as \(0.9\%\) into a decimal form. Remember, percentages represent parts per hundred.

Step 2: Apply Percentage to Decimal Conversion

To convert a percentage to a decimal, divide the percentage by 100. This is because \(1\%\) is equivalent to \(\frac{1}{100}\).

Step 3: Perform the Calculation

Divide \(0.9\) by \(100\). This is done by moving the decimal point two places to the left: \(0.9\% = 0.009\).

Key Concepts

Understanding Percent

When you see a percentage, it means you're looking at a way to express a number as a portion of 100. Think of this as dividing something into 100 equal parts. For instance, if you have 50%, it implies 50 out of 100, or half of a whole. In the case of 0.9%, it's a very small portion, less than 1%.
Common uses of percentages include:

• Calculating discounts during sales, e.g., 20% off.
• Understanding test scores, e.g., scoring 75% means you got 75 out of every 100 questions correct.
• Financial terms, like interest rates, which tell you how much extra money will be added per 100 units of currency.

Percentages can make understanding proportions easier, especially when comparing different amounts, due to their standardized form.
When converting percentages to other forms like decimals, we can often gain a clearer understanding of their relative sizes.

Converting Percent to Decimal

Turning a percentage into a decimal makes it easier to use in calculations. The conversion involves moving the decimal point two spots to the left. This is equivalent to dividing by 100. For example:

• To convert 50%, move the decimal point from the end (50) two places left, becoming 0.50.
• For our specific example, 0.9%, we move the decimal point from after the 9 two places left, resulting in 0.009.
• Numbers less than 1%, such as 0.9%, underscore how small the percentage is in decimal form.

Why do we divide by 100? Since each percentage point is a part of a whole that’s divided into 100 parts. By dividing by 100, we're finding out how much of the whole we have. This method lets you seamlessly switch between percentage and decimal notations.

Basic Arithmetic and Decimals

Once you have converted a percentage into a decimal, you can use it in basic arithmetic operations like addition, subtraction, multiplication, and division, which makes calculations smoother.
Consider these uses:

• Adding percentages as decimals: 0.3 + 0.009 becomes 0.309, representing a combined percentage of 30.9%.
• Subtracting: You can subtract smaller percentages from larger ones. Subtract 0.009 from 0.2 to get 0.191, reflecting a new smaller percentage.
• Multiplying: If you want to find a portion of a number, you multiply the decimal. For example, 0.009 of 150 is calculated by multiplying 0.009 by 150, yielding 1.35.
• Dividing: When dividing by a decimal, remember you can convert it to a whole number by moving the decimal place right as you adjust the other value inversely.

Converting percentages to decimals often makes operations like these less cumbersome and more intuitive. Using decimals in arithmetic helps ensure precision, especially in financial calculations and scientific contexts.