Problem 12 - Elementary and Intermediate Algebra

Question

a. Write \(9 \%\) as a decimal. b. Write 0.035 as a percent.

Step-by-Step Solution

Answer

a. 9% is 0.09 as a decimal; b. 0.035 is 3.5% as a percent.

Step 1: Understanding Percentages

Percentages represent a fraction of 100. For example, 9% means 9 out of 100, or 9 per 100.

Step 2: Converting Percent to Decimal

To convert a percentage to a decimal, you divide by 100. For 9%, this means calculating \( \frac{9}{100} = 0.09 \).

Step 3: Verify the Decimal Conversion

Check the division: 9 divided by 100 is indeed 0.09. Thus, 9% is equal to 0.09 as a decimal.

Step 4: Understanding Decimals

Decimals represent parts of a whole, where the place value of digits after the decimal point corresponds to tenths, hundredths, etc. In 0.035, 3 is in the hundredths place and 5 is in the thousandths place.

Step 5: Converting Decimal to Percent

To convert a decimal to a percentage, multiply by 100. For the decimal 0.035, you calculate \( 0.035 \times 100 = 3.5 \% \).

Step 6: Verify the Percentage Conversion

Check the multiplication: 0.035 times 100 is 3.5. Therefore, 0.035 is equivalent to 3.5% as a percentage.

Key Concepts

Decimal Conversion

Converting a percentage to a decimal is a simple process once you understand the relationship between percentages and decimals. A percentage is essentially a number out of 100. To convert it into a decimal, you'll want to divide by 100. This is because moving from a percentage to a decimal requires shifting the decimal point two places to the left. For example, to convert 9% into a decimal, you divide 9 by 100 or simply move the decimal two spaces to the left, giving you 0.09.
Decoding decimals involves understanding the position values after the decimal point. The first place is the tenths, the second is hundredths, and so on. This is vital when converting back from a decimal to a percentage, ensuring each digit's place value is respected.

Percentage Calculation

Percentages offer an easy way to express proportions and compare values. In its most basic form, a percentage indicates parts per hundred. If you start with a decimal and want to turn it into a percentage, you multiply it by 100. This moves the decimal point two places to the right. For instance, if given the decimal 0.035, simply calculate:\[ 0.035 \times 100 = 3.5 \% \]
This conversion underscores the close interplay between decimals and percentages. It’s less about memorizing formulas and more about understanding:

• Multiplying by 100 to convert to a percentage
• Dividing by 100 to convert to a decimal

Understanding these basics empowers you to switch between these forms effortlessly.

Mathematics Fundamentals

Knowing how to navigate between percentages and decimals builds a solid foundation in mathematics. These conversions not only enhance numerical literacy but also improve understanding of broader math concepts such as fractions and ratios.

• Percentages, decimals, and fractions are interconnected. Transforming one form into another involves interpreting small shifts in numbers.
• Grasp the idea of place values, as they play a role in handling decimals.
• Acknowledge that many real-world applications involve converting between these different forms.

Furthermore, practicing these conversions strengthens problem-solving skills and numerical fluency. Before tackling more complex problems, ensure you're comfortable with these fundamental conversions. Mastery here opens the door to tackling more intricate mathematical tasks.