Problem 21 - Prealgebra

Question

Change each decimal to a percent. $$0.23$$

Step-by-Step Solution

Answer

0.23 as a percent is 23%.

Step 1: Understand the Relationship Between Decimals and Percents

To convert a decimal to a percent, realize that "percent" means "per hundred." Thus, you can convert a decimal to a percent by multiplying the decimal by 100.

Step 2: Multiply the Decimal by 100

To convert the decimal 0.23 to a percent, calculate \(0.23 \times 100\). This step effectively shifts the decimal point two places to the right.

Step 3: Calculate and Add the Percent Symbol

Calculate \(0.23 \times 100 = 23\). The result represents the percent value, so add the percent symbol. Hence, the percent equivalent is 23%.

Key Concepts

Percent Conversion

Converting decimals to percents is a common mathematical process. The term 'percent' itself gives us a clue: it means 'per hundred.' This means that when converting a decimal to a percent, you are essentially finding out how many parts out of one hundred the decimal represents. For instance, the conversion of the decimal 0.23 to a percent involves realizing that you're looking for how much out of 100 this number represents.
To achieve this conversion, a simple multiplication by 100 is required. This multiplication transforms the decimal into its percent form, effectively scaling the number to determine its value on a scale of one hundred. This results in 0.23 becoming 23% after it is multiplied by 100.
Understanding percent conversion is pivotal for tasks like understanding discounts, interpreting data, or grasping various statistical information.

Decimal Place Value

Decimal place value is an essential concept in mathematics, especially when working with conversions. It places numbers to the right of the decimal point, denoting fractional amounts of a whole number. Each place to the right indicates a tenth, a hundredth, or a thousandth, and so forth, of a unit.
In the decimal 0.23, the digit '2' is in the tenths place, implying it represents two-tenths (\( \frac{2}{10} \)). Similarly, the '3' is in the hundredths place, signifying three hundredths (\( \frac{3}{100} \)).
When converting to a percent, understanding this place value helps to realize why multiplying by 100 shifts the decimal point. It transforms the partitions of the decimal into whole numbers, thus making the conversion straightforward. Having a firm grasp of place value helps reinforce the logic behind moving the decimal two spots to the right when multiplying by 100.

Multiplying Decimals

Multiplying decimals is a critical arithmetic operation that underpins various mathematical processes, including decimal to percent conversion. When you multiply a decimal by 100, you're effectively multiplying it by 10 twice. This 'double shift,' ensures that the decimal point moves two places to the right, making the number larger and thereby suitable for conversion into a percent.
To visualize, consider multiplying 0.23 by 100. The calculation:\[ 0.23 \times 100 = 23 \] indicates that you have taken 0.23 and multiplied by ten twice, thus converting it into 23, a freely floating number ready to be expressed as a percentage.
This multiplication not only aids in converting decimals to percents but also helps in magnifying smaller figures for clearer interpretation in practical scenarios such as finance and daily transactions.