Problem 69 - Algebra A Combined Function

Question

Write each percent as \(a\) decimal. $$ 0.1 \% $$

Step-by-Step Solution

Answer

0.001

Step 1: Understand Percent to Decimal Conversion

Percent means "per hundred," so the percentage is a fraction out of 100. Hence, to convert a percentage to a decimal, divide by 100.

Step 2: Apply the Conversion to the Given Percentage

Given the percentage is 0.1%, apply the conversion by dividing 0.1 by 100. This can be expressed as \( \frac{0.1}{100} \).

Step 3: Perform the Division

Calculate the division: \( 0.1 \div 100 = 0.001 \). This is done by moving the decimal point two places to the left.

Step 4: Verify Your Answer

Check if the decimal makes sense. Yes, 0.001 is a correct and logical conversion of 0.1% to a decimal, as moving a decimal point two places to the left is consistent with dividing by 100.

Key Concepts

Decimal Conversion

Decimal conversion is a process of transforming other number formats into decimals. Decimals are an expression of a whole number plus a fraction of a whole number, separated by a decimal point. Why are decimal conversions useful? They help in simplifying operations like addition, subtraction, multiplication, and division, ensuring easier and quicker calculations. There are some basic conversion techniques:

• Fractions to decimals: Convert by dividing the numerator by the denominator.
• Percentages to decimals: Convert by dividing by 100.
• Mixed numbers to decimals: Convert the fractional part and add it to the whole number part.

Once numbers are in decimal form, they become easy to manage in various mathematical operations. Remember, each digit in a decimal holds a place value expressed in powers of ten.

Percent to Decimal

Converting a percent to a decimal involves a simple mathematical adjustment. Understanding what "percent" signifies is crucial here - it literally means "per hundred." When you have a percentage, say 0.1%, you're essentially being told that it is 0.1 out of 100. To switch from a percent to a decimal, you divide the percentage value by 100. This can be visualized as moving the decimal point two places to the left. Here's how it works step-by-step using 0.1% as an example:

• Write the percentage as a fraction over 100: \( \frac{0.1}{100} \).
• Perform the division: \( 0.1 \div 100 \).
• Move the decimal point: The outcome is 0.001.

This conversion is intuitive after practice and integral for handling various mathematical operations involving percentages.

Mathematical Operations

Mathematical operations with decimals often involve the basic operations - addition, subtraction, multiplication, and division. Understanding the impacts of operations on the placement of the decimal point is important for accuracy.

• Addition and Subtraction: Align the decimal points of the numbers involved. This ensures each place value is accurately added or subtracted.
• Multiplication: Multiply as if there are no decimal points, then count the total decimal places in the factors and place the decimal in the product appropriately.
• Division: Move the decimal point in the divisor to the rightmost position and do the same transformation in the dividend. Perform the division as usual, placing the decimal point in the quotient correspondingly.

While it might appear trivial, precision in handling decimals in these operations ensures that your results are not only correct but also reflect the appropriate magnitude.