Problem 28 - Algebra 1

Question

Write as a decimal rounded to the nearest hundredth. Then write as a percent. $$ \frac{11}{12} $$

Step-by-Step Solution

Answer

The decimal form of \(\frac{11}{12}\) is 0.92 and the percent form is 92%.

Step 1: Convert Fraction to Decimal

To perform this action, divide the numerator (11) by the denominator (12). This can be done either on paper or using a calculator. In this case, the answer comes out to 0.916666666667. This decimal goes on forever, but is required to be rounded to the nearest hundredth, which is 0.92.

Step 2: Convert Decimal to Percent

Once the decimal is obtained, the next step is to convert it into a percent. To perform this action, multiply the decimal by 100. Therefore, 0.92 x 100 = 92. It is necessary though not to forget to attach the percent sign (%) at the end. Therefore, the percent form of the decimal 0.92 is 92%.

Key Concepts

Fraction to Decimal Conversion

Converting fractions into decimals is a basic mathematical skill that is often used in various applications. To convert a fraction to a decimal, you simply divide the numerator (the top number of the fraction) by the denominator (the bottom number). For instance, to convert \(\frac{11}{12}\) to a decimal, divide 11 by 12 using a calculator or long division. The result is a decimal number that can sometimes be infinite or repeating. When this occurs, it's essential to round the decimal to make it manageable and understandable.

Rounding Decimals

Rounding decimals is crucial when we need a number to be more manageable or when we're required to give an answer to a certain degree of precision. To round a decimal to the nearest hundredth, you look at the third decimal place. If this digit is 5 or higher, you round the second decimal place up. If it's 4 or lower, you keep the second decimal place as it is.

For example, with our fraction \(\frac{11}{12}\) converted to a decimal, we obtained 0.916666666667. Rounding to the nearest hundredth means looking at the third decimal place (which is 6 in this case) and rounding up the second decimal place to 2, giving us 0.92. Rounding is a fundamental concept that ensures the precision and usability of our calculations in everyday scenarios.

Decimal to Percent Conversion

Once you have a decimal, converting it to a percent is straightforward: you multiply the decimal by 100. Moving the decimal point two places to the right accomplishes the same result. This conversion reflects the idea that a percent is simply a different way of expressing a number as a part out of a hundred.

So, for the decimal 0.92, we multiply by 100 which gives us 92. Remember, the 'percent' signifies 'out of 100', so you must add the percent symbol (%) to indicate that 92 is not just a pure number but a percentage. Therefore, 0.92 in decimal form is 92% when converted to a percent.