Problem 29 - Algebra 1

Question

Write as a decimal rounded to the nearest hundredth. Then write as a percent. $$ \frac{25}{31} $$

Step-by-Step Solution

Answer

The fraction \(\frac{25}{31}\) as a decimal is approximately 0.81, and as a percent is 81%.

Step 1: Convert Fraction to Decimal

To convert the fraction \(\frac{25}{31}\) to a decimal, the numerator of the fraction (25) should be divided by the denominator of the fraction (31). This can be done using a calculator or if simple division is permitted. The decimal should be rounded to the nearest hundredth.

Step 2: Round Decimal

The result from the division in step 1 is a decimal. To round to the nearest hundredth, look at the third decimal point. If this number is 5 or above, round the second decimal point up. If it is below 5, keep the second decimal point as it is.

Step 3: Convert Decimal to a Percent

To convert a decimal to a percent, multiply the decimal number by 100. Then, add the % symbol to the end of the number.

Key Concepts

Fraction to Decimal Conversion

Understanding how to convert a fraction into a decimal is a foundational skill in math and crucial for various applications. Let's start with the basics: a fraction is composed of two parts, the numerator (top number) and the denominator (bottom number). The division of these two numbers gives you the decimal form.

To convert a fraction to a decimal, simply divide the numerator by the denominator. Using a calculator will get you the most accurate result, but if that's not available, long division is your go-to method. For example, converting \(\frac{25}{31}\) to a decimal involves dividing 25 by 31. This division yields a decimal number, which often has many digits after the decimal point. These are called 'non-terminating' decimals if they go on forever or 'terminating' decimals if they stop at a certain point.

Terminating decimals are straightforward as they have a clear end, but non-terminating decimals often require rounding for practical usage. Let's see how you can do rounding in the next section to make these more manageable numbers.

Rounding Decimals

Rounding decimals is important for presenting numbers in a more understandable form, especially when an exact number isn't necessary or when a non-terminating decimal is involved. To round decimals to the nearest hundredth, you focus on the third decimal place. Here is a simple process to follow:

• Identify the third decimal digit.
• If this digit is 5 or higher, increase the second decimal place by one. This is what's known as 'rounding up'.
• If this digit is less than 5, keep the second decimal place as it is. This is called 'rounding down'.

Applying this to our example, after dividing 25 by 31, you get a decimal. Assume the result is 0.8064. Since the third decimal place is '6' (which is greater than 5), you'll round up the second decimal place giving you 0.81. This rounded result is close to the precise calculation but more manageable when doing further calculations or comparisons.

Decimal to Percent Conversion

Once you have a decimal, you might be required to express this number as a percentage. This step is commonly used in fields like finance, statistics, and general arithmetic to communicate information as a portion out of a hundred, which is what 'percent' means.

To convert a decimal to a percent, the process is straightforward: multiply the decimal by 100. Then, simply attach the percent symbol (\%) to denote that the number represents a percent. Let's apply this to our rounded decimal of 0.81. Multiplying this by 100 gives us 81, and adding the percentage symbol gives us 81\%. This tells us that the original fraction \(\frac{25}{31}\) is equivalent to 81\% when it is rounded to the nearest hundredth before the conversion.

This conversion is not only helpful for homework problems but also enhances your ability to understand percentages in real-world contexts, be it discounts, growth rates, or data analysis.