Problem 54 - Prealgebra

Question

Write as a percent. $$0.175$$

Step-by-Step Solution

Answer

0.175 as a percent is 17.5%.

Step 1: Understand Percentages

A percentage represents a number as a fraction of 100. Converting a decimal to a percentage means expressing the number as parts per hundred.

Step 2: Decimal to Fraction Conversion

To convert the decimal 0.175 to a percentage, understand that this is equivalent to 0.175 per 1.

Step 3: Multiply by 100

To express the decimal as a percentage, multiply 0.175 by 100: \[ 0.175 \times 100 = 17.5 \]

Step 4: Attach the Percent Sign

After multiplying, you have 17.5. Write this result with a percent sign to express it as a percentage, which is 17.5%.

Key Concepts

Decimal to Percent

When you convert a decimal to a percent, you are essentially shifting your perspective of the number, so it's expressed in terms of hundredths. This process helps in understanding certain portions or ratios more intuitively, as percentages are widespread in daily life. Decimals are a method of writing fractions in a more standardized form where the whole is one. Altogether, converting a decimal to a percent involves manipulating this format so that it reflects the percentage format. This can be especially useful when dealing with financial figures, like discounts or interest rates, or even when explaining statistical data. Always remember, a decimal like 0.175 indicates a part of one whole unit of measure (1).

Multiplying by 100

A critical step in converting a decimal to a percent is multiplying the decimal by 100. ✓ This step re-scales your decimal value into parts per hundred, which is what a percent inherently represents. For example:

• Start with the decimal 0.175.
• Multiply it by 100: \[ 0.175 \times 100 = 17.5 \]

This multiplication shifts the decimal two places to the right, transforming our decimal into an expression suitable for written percentages. Think of it as adjusting the level of detail to make your number more universally understandable across various topics, like economics, percentages in exams, or even statistical analyses. When you multiply by 100, you are just reformulating the number to fit the "percent" format.

Attaching Percent Sign

Once you have completed the mathematical conversion by multiplying the decimal by 100, the final step is to attach the percent sign (%). A percent sign is essential because it informs others of the context of the number. In the example at hand:

• The result of the conversion was 17.5.
• Add the percent sign, turning it into 17.5%.

This simple symbol expands our understanding and presentation of numbers. It helps others instantly recognize that the number is not just any arbitrary number but specifically out of 100. Whether on a social media post about a discount or in a report on economic growth, the percent sign is an invaluable part of clear communication.