Problem 69 - Prealgebra

Question

Change each fraction or mixed number to a percent. \(\frac{21}{43}\) to the nearest tenth of a percent

Step-by-Step Solution

Answer

48.8%

Step 1: Divide the Numerator by the Denominator

To convert the fraction \( \frac{21}{43} \) into a percentage, start by dividing 21 by 43. Use long division or a calculator. Doing so, you get approximately 0.488372... This is the decimal form of the fraction.

Step 2: Convert the Decimal to a Percent

To convert a decimal to a percentage, multiply it by 100. So, multiply 0.488372 by 100 to get 48.8372. This is the percentage form of the decimal.

Step 3: Round to the Nearest Tenth of a Percent

The percentage obtained is 48.8372. To round to the nearest tenth of a percent, look at the hundredths place. Since it is 3 (less than 5), the tenths place will remain 8. Thus, the rounded percentage is 48.8%.

Key Concepts

Rounding Percentages

When you're asked to round a percentage to the nearest tenth, it means you're looking at the first decimal place. For example, if you have 48.8372%, you'd focus on the first digit after the decimal to decide whether to round it up or keep it the same. The rule for rounding is simple:

• If the digit in the hundredths place is 5 or more, increase the tenths place by 1.
• If it is less than 5, leave the tenths place unchanged.

In our example, we have 48.8372%. The digit in the hundredths place is 3, which is less than 5, so we leave the tenths digit (8) as it is. Therefore, 48.8372% rounds to **48.8%**.

Decimal Conversion

The first step in converting a fraction to a percentage is turning the fraction into a decimal. This process involves simple division. Take the fraction \[\frac{21}{43}\]and divide the numerator (21) by the denominator (43).Upon division, you'll find the result to be approximately 0.488372. This number is now in decimal form, representing the fraction. What's great about a decimal is that it's just another way to represent a part of a whole, just like a fraction.Once you have the decimal, converting it into a percentage involves multiplying the decimal by 100. So, multiply 0.488372 by 100 to get **48.8372%**. This step makes it easier to visualize the fraction out of 100, aligning with the concept of percentage.

Mixed Numbers

A mixed number combines a whole number and a fraction. For example, 1 and \[\frac{3}{4}\] is a mixed number. Converting a mixed number to a percentage involves additional steps beyond what is required for a simple fraction.Here's how to convert a mixed number to a percentage:

• First, convert the fraction part to a decimal. Divide the numerator by the denominator just as you would with a simple fraction.
• For example, if you're working with \[\frac{3}{4}\], you'd divide 3 by 4 to get 0.75.
• Next, add this decimal to the whole number part. In this case, it would be 1 + 0.75 = 1.75.
• Finally, multiply by 100 to convert the entire number to a percentage. So, 1.75 becomes **175%**.

This way, you can convert mixed numbers into percentages accurately. Remember to pay attention to any whole number parts when converting, as they can significantly transform your answer.