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Chapter 6: Problem 68

Write as a percent. If necessary, round to the nearest tenth of a percent. $$\frac{37}{200}$$

Short Answer

Expert verified
The percent equivalent of the fraction \( \frac{37}{200} \) is 18.5%

Step by step solution

01

Convert Fraction into Decimal

To do this, take the numerator (the top number, 37) and divide it by the denominator (the bottom number, 200). In this case, \( \frac{37}{200} = 0.185 \)
02

Convert Decimal to Percent

Now, to turn this decimal into a percent, you need to multiply it by 100. This gives: \(0.185 \times 100 = 18.5\)
03

Rounding

The problem instructs to round to the nearest tenth of a percent if necessary. In this case, no rounding is needed.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Fractions to Decimals
Changing fractions into decimals is a common math task. It's useful in many practical scenarios, from calculating discounts to understanding ratios. To convert a fraction into a decimal, you simply need to divide the numerator, which is the top number, by the denominator, the bottom number. For example, if you have the fraction \(\frac{37}{200}\), you perform the division: 37 divided by 200. When you do the division, you'll get the decimal 0.185.

Here are some tips to make this easier:
  • Write down the division clearly, aligning numbers to avoid mistakes.
  • Remember, the result represents the same value as the fraction, just in a different form.
  • Check if the division gives a repeating decimal, and if so, be aware of how to represent it.
Mastering this simple conversion prepares you for further conversions, such as turning decimals into percents.
Decimals to Percents
Once you have a decimal, converting it to a percent is straightforward. This operation is about scaling the decimal to express it out of 100, since percents are simply parts per hundred. To transform a decimal into a percent, multiply the decimal by 100. Using our example, take 0.185 and multiply it by 100. This gives you 18.5.

Here鈥檚 why you multiply by 100:
  • "Percent" means "per 100," so multiplying by 100 adjusts the decimal into this context.
  • Imagine shifting the decimal point two places to the right, effectively using the multiplication concept.
  • This step is crucial in everyday calculations like determining tax rates or interpreting statistical data accurately.
Understanding this will help ensure you handle any percent-related problems with confidence.
Rounding Percents
Rounding percents is a useful skill when exactness isn't needed, or to make numbers easier to interpret. Rounding means adjusting a number to a specific decimal place, which simplifies data presentation. In the case of 18.5%, the instruction is to round to the nearest tenth of a percent, but since it is already in this form, no rounding is needed.

Here鈥檚 how you decide when and how to round:
  • Check the digit right after the decimal place you鈥檙e rounding to. If it's 5 or higher, round up.
  • If it's less than 5, keep the number as is.
  • Apply this understanding to various contexts, including financial reporting and academic data.
Rounding is not just about precision but also about how information is presented and understood effectively.

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