Problem 72 - Prealgebra

Question

Write as a percent. Round to the nearest tenth of a percent. $$\frac{2}{5}$$

Step-by-Step Solution

Answer

\(40\%\)

Step 1: Convert the fraction to a decimal

To convert the fraction \(\frac{2}{5}\) into a decimal, divide the numerator by the denominator. So, \(2 \div 5 = 0.4\).

Step 2: Convert the decimal to a percent

To convert a decimal to a percent, multiply the decimal by 100, then add the percent sign. So, \(0.4 \times 100 = 40\). This means \(0.4\) as a percent is \(40\%\).

Step 3: Round to the nearest tenth of a percent

Since \(40\%\) does not have any further decimals to consider, it is already rounded to the nearest tenth of a percent.

Key Concepts

Fraction to Decimal Conversion

Converting a fraction to a decimal is an essential step when you want to express fractional values in a different form. To do this, you simply divide the numerator (the top number in the fraction) by the denominator (the bottom number). This division gives you a decimal, which is another way to represent the same value. For example, in the fraction \( \frac{2}{5} \), you would divide 2 by 5. The calculation would look like this: \( 2 \div 5 = 0.4 \).
This tells you that \( \frac{2}{5} \) is the same as 0.4 in decimal form.

• The numerator tells you how many parts you have.
• The denominator tells you the total number of equal parts.

By performing this simple division, fractions become much easier to compare, visualize, and use in further mathematical operations.

Rounding Decimals

Rounding decimals is a useful skill when you need to make a number easier to understand or work with. In certain cases, precise numbers are less important than having a simple, approximate value. Rounding can help with this.
To round a decimal, you need to look at the digit immediately to the right of the place value you are rounding to.
Let's consider the decimal 40.

• If you are rounding to the nearest whole number, you look at the digit after the decimal point. Since 0 is less than 5, you keep the decimal as 40.
• In cases where the decimal has further digits like 0.45, you look at the digit in the tenths place (4), and then at the number in the hundredths place (5). Since 5 is 5 or more, you round the tenths place up, making it 0.5.

When the exercise asks you to round to the "nearest tenth of a percent," it means you check if the number in the tenths place needs to rise based on the value of the next place over.

Mathematical Operations for Conversion

Understanding and performing mathematical operations for converting different numerical forms smoothly is crucial in various types of math problems. The key operations you use for conversion include division and multiplication.
When converting a decimal to a percent, you typically multiply the decimal by 100. This shifts the decimal point two places to the right, converting it into a percentage.
For example, once you have 0.4 from the fraction \( \frac{2}{5} \), you multiply this decimal by 100: \( 0.4 \times 100 \). This equals 40, meaning 0.4 as a percent is 40%.

• Division is used when going from fraction to decimal.
• Multiplication is engaged while transforming decimals to percentages.

These operations streamline the transition from one numerical form to another, making it easier to express values in contexts that require percentage formats.