Problem 44 - Elementary Algebra

Question

Convert each percent to its decimal equivalent. $$ 0.0001 \% $$

Step-by-Step Solution

Answer

0.000001

Step 1: Understanding Percents

Percent (%) means per hundred. So when we talk about 0.0001%, it means 0.0001 per 100.

Step 2: Converting Percent to Decimal

To convert a percentage to a decimal, we divide by 100. Thus, for 0.0001%, we divide 0.0001 by 100.

Step 3: Performing the Division

Perform the division: \( \frac{0.0001}{100} = 0.000001 \). This division shifts the decimal point two places to the left.

Step 4: Decimal Form

The decimal equivalent of 0.0001% is 0.000001.

Key Concepts

Percentages

Percentages are a way of expressing a number as a part per hundred. The symbol '%' represents this relation. For example, when we say 0.0001%, it literally means 0.0001 parts out of 100.

To understand percentages better, think about how we often use them in daily life.

• If you say you scored 80% on a test, you mean you got 80 out of every 100 possible points right.
• Sales discounts usually come as percentages, helping you calculate the reduced price.
• Statistics, like unemployment rates or financial growth, often use percentages to easily convey changes.

This unit makes it easy to compare different types of data in a fair, standardized way. It's always good to start any percentage problem by asking yourself what the percentage represents. This will help you understand what kind of calculation you need to perform next.

Decimals

Decimals are another form of representing numbers, especially fractions, in a more readable way. They are based on the number 10, which makes them compatible with our usual number system.

When you convert a percentage to a decimal, you provide the same number in a base-10 format. Converting a percentage to a decimal involves division by 100, which moves the decimal point two places to the left. This is based on understanding that 100 is represented as 10², shifting the point helps get the same numeric value.

For instance, converting 0.0001% to decimal involves taking 0.0001 and moving the decimal two spots leftwards, resulting in 0.000001.

Decimals often provide a more direct way to perform mathematical operations like multiplication or addition because they eliminate the extra step of the 'one hundred' that percentages inherently involve.

Division

Division is one of the four basic arithmetic operations and is crucial for converting percentages to decimals. When we talk about division, we are discussing how to distribute a number into equal parts or groups.

In the context of percentage conversion, division helps us transform a percentage into its decimal form. To convert a percentage, we divide the given number by 100. This is a straightforward division which can sometimes be done mentally by moving the decimal point.

Consider 0.0001%:

• First, understand the problem as dividing 0.0001 by 100.
• Perform the actual division, which means shifting the decimal two places left.
• The result here is 0.000001, a simpler number to use in further calculations.

Division, in this sense, is not just about breaking down numbers; it's about understanding and manipulating number forms efficiently for different mathematical processes.