Question

Write each percent as a decimal number. $$58 \%$$

Short answer

Answer: The decimal representation of 58% is 0.58.

Step-by-step solution

Understand the concept of percentage and decimal representation

In order to convert a percentage into a decimal number, we need to remember that a percentage is a representation of a fraction out of 100. While a decimal number is the representation of that same fraction in base-10 format.

Write the percentage as a fraction

To do this, write the percentage (58%) as a fraction with 100 in the denominator. $$\frac{58}{100}$$

Convert the fraction into a decimal number

Now, divide the numerator 58 by the denominator 100: $$\frac{58}{100} = 0.58$$ The decimal representation of 58% is 0.58.

Key concepts

Percentages

Percentages are a way to express numbers as parts of a whole, specifically out of 100. This is where the term "percent" comes from, meaning "per hundred." For example, when we say 58%, we're referring to 58 parts out of 100.

Percentages are useful in many areas including finance, statistics, and general computations, as they allow for easy comparisons between different quantities. When working with percentages, it's helpful to envision them as being on a scale of 0 to 100.

• 0% means none or nothing.
• 50% represents half.
• 100% represents the whole or total.

In practice, percentages make it easier to add, subtract, and compare fractions that have different denominators by setting them in a uniform scale that relates them all to 100.

Decimals

Decimals are numbers expressed in base-10 system, which is the number system we use most commonly in daily life. Decimals allow us to represent fractions in a linear and easy-to-understand format, using powers of ten. For instance, the decimal 0.58 can be broken down as 0.5 (five tenths) and 0.08 (eight hundredths).

When converting a percentage to a decimal, you're simply finding what that percentage looks like in this base-10 system. To do this, you move the decimal point two places to the left (equivalent to dividing by 100). That's why 58% becomes 0.58. This reflects the percentage's part-out-of-100 identity in a simpler, decimal form that's often better for calculations and comparisons.

• Decimals make calculations simpler, especially for multiplication and division.
• Easier to input into digital systems which primarily understand decimal representations.
• Provides a uniform method to represent fractions consistently.

Fractions

Fractions are mathematical expressions representing a division of a whole into parts. They consist of a numerator and a denominator, usually displayed as one number over another.

The numerator signifies how many parts are being considered, while the denominator represents the total number of equal parts. For example, the fraction \( \frac{58}{100} \) signifies 58 parts of a whole that has 100 parts in total.

Fractions are sometimes clearer and more intuitive than decimals in showing relationships between numbers, especially in problems involving proportions.

• Convert a percentage to a fraction by placing the percentage number over 100.
• Fractions are useful in various operations such as addition and subtraction directly.
• They provide an exact representation of numbers which can sometimes suffer precision loss in decimal form.

Whether working as part of preparing ingredients for a recipe or calculating discounts during shopping, understanding fractions can enhance numerical literacy and practical applications.