Problem 290 - Intermediate Algebra

Question

In the following exercises, convert each decimal to a percent. $$ 2.254 $$

Step-by-Step Solution

Answer

225.4%

Step 1: Convert Decimal to Fraction

To convert the decimal 2.254 to a percentage, we first need to understand that a percentage is a fraction with a denominator of 100. Start by converting the decimal to a fraction. The decimal 2.254 can be written as \( \frac{2254}{1000} \).

Step 2: Fraction to Percentage

Next, convert the fraction to a percentage by multiplying the fraction by 100. This is done to adjust the fraction to have a denominator of 100. Hence, \( \frac{2254}{1000} \times 100 = 225.4 \).

Step 3: Final Conversion

Hence, when multiplying the decimal number 2.254 by 100, we obtain 225.4%. So, 2.254 as a percentage is 225.4%.

Key Concepts

decimal to fraction

To convert a decimal to a fraction, start with the decimal number itself. Let's use the decimal 2.254 as an example. The decimal can be represented as a fraction by considering its place value. Since 2.254 has three digits after the decimal point, it can be written as \( \frac{2254}{1000} \). Here’s how it works:

• The decimal portion (0.254) represents the number over a power of 10 equal to the number of decimal places (3 in this case, so 1000).
• Combine the whole number part with the fractional part to get the final fraction.

Therefore, the decimal 2.254 as a fraction is \( \frac{2254}{1000} \). This first step is fundamental for converting into percentages.

fraction to percentage

To convert a fraction to a percentage, you need to adjust the fraction so that its denominator becomes 100. Our fraction from the previous step is \( \frac{2254}{1000} \). To get from a fraction to a percentage, you can multiply the fraction by 100.

• When you multiply \( \frac{2254}{1000} \) by 100, you effectively change the denominator from 1000 to 10, making it easier to understand.

Thus, \( \frac{2254}{1000} \) multiplied by 100 is \( 225.4 \). Therefore, 2.254 as a percentage is 225.4%.

multiplying by 100

Multiplying by 100 is a straightforward but crucial step in converting a fraction to a percentage. When you multiply the fraction \( \frac{2254}{1000} \) by 100, it simplifies the fraction and converts it into a percentage directly.

• This multiplication adjusts the numerator according to the percentage scale, keeping the same ratio.
• Remember, multiplying any fraction by 100 effectively shifts the decimal point two places to the right.

For our running example, multiplying \( \frac{2254}{1000} \) by 100 gives us 225.4%. This is the final conversion, and it shows that 2.254 as a percentage is 225.4%.