Question

Write each percent as a decimal number. $$53 \frac{2}{5} \%$$

Short answer

Question: Convert the percentage $$53 \frac{2}{5}\%$$ into a decimal number. Answer: The decimal equivalent of $$53 \frac{2}{5}\%$$ is $$0.534$$.

Step-by-step solution

Convert the fraction into decimal

In this step, we need to convert $$\frac{2}{5}$$ into decimal. To do so, we simply divide the numerator (2) by the denominator (5). $$\frac{2}{5} = 0.4$$

Combine the decimal with the whole number

To combine the fraction part (0.4) with the whole number (53), we need to add them together, $$53 + 0.4 = 53.4$$

Divide by 100 to express as a decimal

Lastly, we need to express our combined number (53.4) as a decimal by dividing it by 100. $$\frac{53.4}{100} = 0.534$$ So, $$53 \frac{2}{5}\%$$ is equal to the decimal number $$0.534$$.

Key concepts

Percent to Decimal Conversion

Understanding how to transform percentages into decimals is essential in mathematics and in real life, as it allows you to work with numbers in various forms. The key to percent to decimal conversion is recognizing that 'percent' means 'per hundred'. Therefore, converting a percent to a decimal involves dividing the percentage value by 100.

For instance, if you have a whole number percentage like 75%, you simply move the decimal point two places to the left, making it 0.75. But when the percentage includes a fraction, as in the exercise with 53 2/5%, you first need to convert the fractional part into a decimal, which is done by dividing the numerator by the denominator. After that, you add this decimal to the whole number part, and since percentages represent values 'per hundred,' the final step is to divide by 100 to get the decimal representation.

This three-step conversion process is: convert the fraction (if any) to a decimal, add this to the whole number, and finally, divide by 100. Applying these steps ensures a smooth transition from percent to decimal.

Decimal Representation

Decimals are a way of expressing fractions and real numbers without using fractions. In decimal representation, each digit to the right of the decimal point represents a power of one-tenth. For example, the decimal 0.5 denotes 5 tenths, and 0.25 represents 25 hundredths or 2 tenths and 5 hundredths.

To write a number as a decimal, you need to understand place value. The first place after the decimal point is the tenths place, followed by hundredths, thousandths, and so on. When converting from a percent to a decimal or a fraction to a decimal, the goal is to express the number in terms of these place values. This simplifies calculations and makes the comparison of numbers more straightforward. The value 0.534, in the textbook exercise, is a decimal representation where the 5 is in the tenths place, the 3 is in the hundredths place, and the 4 is in the thousandths place.

Fraction to Decimal Conversion

Fractions represent parts of a whole, and converting them into decimals is another conversion skill necessary for working with numbers in various applications. To convert a fraction to a decimal, divide the numerator (the top number) by the denominator (the bottom number). This division will give you a decimal that is equivalent to the fraction.

For example, in the fraction 2/5, you would divide 2 by 5, resulting in the decimal 0.4. It's often helpful to recognize common fractions and their decimal equivalents, such as 1/2 being equal to 0.5, or 3/4 equal to 0.75. These quick recognitions can speed up calculations and are useful in checking your work for errors.

In summary, you convert a fraction to a decimal by division, leading to an equivalent form of the number that may be easier to work with, especially for addition, subtraction, and comparison.