Problem 19 - Prealgebra

Question

Express each percent as a fraction or mixed number in simplest form and as a decimal. $$88 \%$$

Step-by-Step Solution

Answer

88% is \(\frac{22}{25}\) as a fraction and 0.88 as a decimal.

Step 1: Convert Percent to Fraction

To convert a percentage to a fraction, we recognize that percent means per 100. Therefore, 88% can be written as the fraction \(\frac{88}{100}\).

Step 2: Simplify the Fraction

To simplify the fraction \(\frac{88}{100}\), find the greatest common factor (GCF) of 88 and 100. The GCF is 4. Divide both the numerator and the denominator by 4: \(\frac{88 \div 4}{100 \div 4} = \frac{22}{25}\). So, the fraction in simplest form is \(\frac{22}{25}\).

Step 3: Convert Percent to Decimal

To convert a percentage to a decimal, divide the percentage by 100. Thus, 88% as a decimal is \(\frac{88}{100} = 0.88\).

Key Concepts

Simplifying Fractions

Simplifying fractions is all about reducing a fraction to its simplest or smallest form without changing its value. To simplify a fraction, we must find the greatest common factor (GCF) of both the numerator (the top number) and the denominator (the bottom number). Then, divide both numbers by this GCF.Take \(\frac{88}{100}\) as an example. Here, we need to determine the GCF of 88 and 100. The GCF is the largest number that divides both evenly.

• With 88 and 100, we find that 4 is their GCF.

So, \(\frac{88}{100}\) becomes \(\frac{22}{25}\) after dividing both the numerator and denominator by 4. It's like having the same fraction in a cleaner, neater form. Simplifying fractions helps us talk about those numbers more easily and can make arithmetic operations faster.

Converting Percentages

Converting percentages involves transforming a given percentage into either a fraction or a decimal. This is essential because it allows us to use the convenience of percentages to handle various numerical problems.When you see 88\%, think of it as 88 per 100. The term per cent literally means per one hundred. So, to express 88\% as a fraction, you write it as \(\frac{88}{100}\).

• This method helps because converting a percentage to a fraction simplifies calculations in problems requiring proportions or ratios.

And if you need to go further, you can always simplify this fraction to its simplest form, \(\frac{22}{25}\). Being able to convert percentages makes math problems more approachable and less confusing.

Decimal Conversion

Deciding to convert a percentage into a decimal is another straightforward mathematical maneuver. This is practical in financial math, statistics, or just any calculation where decimals are preferred over fractions.Let's take 88\% again. To switch from percent to decimal, you divide by 100. Why? Because percent means "per 100," so dividing by 100 shifts the decimal point two places to the left by design.

• Therefore, \(\frac{88}{100}\), when calculated, equals 0.88.

This compact form, 0.88, is helpful for straightforward addition or multiplication and makes comparisons between numbers quick and intuitive. Whether you're balancing your checkbook or analyzing data, seeing the numbers in a decimal form can simplify your task.