Problem 64 - Prealgebra

Question

Write as a percent. Round to the nearest tenth of a percent. $$ \frac{37}{200} $$

Step-by-Step Solution

Answer

18.5%

Step 1: Understand the fraction

The fraction is \( \frac{37}{200} \). This fraction represents how much a part (37) is of the whole (200).

Step 2: Convert the fraction to a decimal

To convert \( \frac{37}{200} \) to a decimal, divide 37 by 200. Perform the division: \[ 37 \div 200 = 0.185 \]. So, \( \frac{37}{200} \) is equivalent to 0.185.

Step 3: Convert the decimal to a percent

To convert a decimal to a percent, multiply the decimal by 100. Multiply 0.185 by 100: \[ 0.185 \times 100 = 18.5 \]. Therefore, 0.185 as a percent is 18.5%.

Step 4: Round the percent to the nearest tenth

Observe that 18.5 is already rounded to the nearest tenth. There are no additional decimal places needing rounding. So, 18.5% is the final result.

Key Concepts

Converting Fractions to Decimals

Converting fractions into decimals is like translating one language of math into another. It can be quite simple when you break it down. Here's how you can convert any fraction to a decimal:

• Divide the numerator by the denominator. The numerator is the top number and the denominator is the bottom number. In our case, we divide 37 by 200.
• Perform the division. When you divide 37 by 200, you get 0.185. This is the decimal form of the fraction \( \frac{37}{200} \).

This process involves straightforward division, which your calculator can help with. Understanding this conversion helps when you need to use fractions for percentage calculations or in situations where decimals are more useful.

Converting Decimals to Percents

Once you have a decimal, turning it into a percent is a piece of cake! This process is important because percents are very common in everyday life, from shopping discounts to statistics. Here's how you convert a decimal to a percent:

• Multiply the decimal by 100. This moves the decimal point two places to the right and changes the scale to "per hundred" which defines percent.
• Add the percent symbol (%). After multiplying 0.185 by 100, you get 18.5. So, 18.5% is what 0.185 is in percent form.

This conversion helps interpret data easily, especially when you want to know how large or small a part is compared to a whole.

Rounding Decimals

Rounding decimals is useful to simplify numbers and make them easier to work with or understand. In our example, we needed to round to the nearest tenth of a percent. Here's a small guidance on rounding:

• Identify the place to round to. For rounding to the nearest tenth, you focus on the first decimal place.
• Look at the digit immediately to the right. If this digit is 5 or more, increase the rounding place by one; otherwise, keep it the same. Since 18.5 has nothing to round further, it remains 18.5%.

Rounding ensures precision without unnecessary complexity. It's a small change that can make big numbers more comprehensible.