Problem 15 - Elementary Algebra

Question

For the following problems, convert each decimal to a percent. $$ 0.446 $$

Step-by-Step Solution

Answer

Question: Convert the decimal 0.446 to a percent. Answer: 44.6%

Step 1: Multiply by 100

To convert the decimal to a percent, we need to multiply it by 100. So, we have: $$ 0.446 \times 100 = 44.6 $$

Step 2: Add the percentage symbol

Now that we have multiplied the decimal by 100, we need to add the percentage symbol to the result. Therefore, the solution is: $$ 44.6\% $$ So, the decimal 0.446 converted to a percent is 44.6%.

Key Concepts

Decimals

Decimal numbers are fundamental in mathematics and everyday life. They are numbers that use a decimal point to separate the whole number part from the fractional part. For example, in the number 0.446, the decimal point is between the 0 and the 446.

Decimals are another way to express fractions. In fact, the decimal 0.446 is equivalent to the fraction \( \frac{446}{1000} \). The digits after the decimal point represent portions of ten, hundred, thousand, etc. This system allows for precise representation of numbers that are not whole.

When working with decimals, it's important to remember that they represent part of a whole. For example:

• 0.1 represents 1 tenth
• 0.01 represents 1 hundredth
• 0.001 represents 1 thousandth

Understanding decimals is crucial for converting them to percents, as demonstrated in many mathematical and real-world scenarios.

Percentage Conversion

Percentage conversion is a way to express a given number as a part of 100. This is particularly useful in comparing proportions. A percentage is essentially a fraction with a denominator of 100.

The process of converting a decimal into a percent involves understanding the relationship between decimals and percentages. Since percentages are a representation of a fraction of 100, converting from decimal to percent is straightforward. For instance, converting 0.446 to a percent results in 44.6%.

To convert a decimal into a percentage, follow these steps:

• Multiply the decimal by 100 to shift its decimal point two places to the right.
• Add a percentage sign (%) to indicate that the number is now expressed as a part of 100.

Converting decimals to percents simplifies the comparison of different quantities, making it an essential skill in many fields.

Multiplication by 100

Multiplying by 100 is a key step in the process of converting decimals to percentage. This operation changes the decimal into a whole number that can easily be expressed as a percentage.

When you multiply a decimal by 100, you move its decimal point two places to the right. For example, multiplying 0.446 by 100 results in 44.6. This operation mirrors the fact that a percent is a fraction out of 100.

The steps for multiplying by 100 are:

• Identify the decimal point in the number.
• Shift the decimal point two places to the right.
• The new number is now ready to be expressed as a percentage by adding the percent sign.

Multiplying by 100 is a simple yet powerful technique for transforming decimals into an easy-to-understand percentage form.