Problem 75 - Prealgebra

Question

Write as a percent. Write the remainder in fractional form. $$\frac{17}{25}$$

Step-by-Step Solution

Answer

68% (no remainder as a fraction needed)

Step 1: Convert to Decimal

To express \(\frac{17}{25}\) as a percent, we first need to convert it into a decimal. We do this by dividing 17 by 25.\[\frac{17}{25} = 0.68\]

Step 2: Convert Decimal to Percent

Next, we'll convert the decimal into a percent. We do this by multiplying the decimal by 100.\[0.68 \times 100 = 68\%\] So, \(\frac{17}{25}\) is equivalent to 68\%.

Step 3: Write the Remainder as a Fraction

Now we need to consider if there is a remainder when converting to percent. Since \(\frac{17}{25} = 0.68\) exactly, there is no remainder. Generally, when converting a decimal to a fraction, we look for non-zero decimals past the hundredths place, but in this case, the conversion is exact without a remainder.

Key Concepts

Fractions to Decimals

Converting fractions to decimals is an essential arithmetic skill. This process involves division. To convert a fraction like \( \frac{17}{25} \) into a decimal, we divide the numerator (the top number) by the denominator (the bottom number). In this case, dividing 17 by 25 gives us 0.68.

Here are steps you can follow for any fraction:

• Divide the Numerator: Take the top number of your fraction and divide it by the bottom number. This will give you a decimal.
• Perform Long Division if Necessary: If the division doesn't come out evenly, you might need to use long division. Keep dividing until you find a repeating pattern or reach an ending point.

Understanding these steps makes converting fractions straightforward and prepares you for further calculations.

Converting Fractions

Once you have the decimal result from a fraction, you might want to convert it into different formats for various applications, like percentages or another fraction form. Converting decimals back to fractions involves figuring out the fraction equivalent of the decimal number.

In our case with 0.68, we note that it can be written as \( \frac{68}{100} \). By dividing both the numerator and denominator by their greatest common divisor, we can simplify this fraction. Here, the simplified fraction is indeed \( \frac{17}{25} \), proving the original fraction.

• Identify the Decimal: Recognize the decimal place: tenths, hundredths, etc.
• Simplify: If you can simplify the fraction, make sure to do so for the most accurate representation.

This understanding helps in ensuring that decimals correctly convert back into their simplest fractional forms.

Decimal to Percent Conversion

The transition from a decimal to a percent is a common and useful skill, especially in fields like finance or statistics. To convert a decimal like 0.68 into a percent, you simply multiply it by 100. This moves the decimal point two places to the right, changing it into a percentage. So, 0.68 becomes 68%.

Here are the steps summarized:

• Multiply by 100: Take your decimal and multiply by 100 to convert to percent.
• Adjust Decimal Point: Think of this as moving the decimal point two places to the right.

It is a straightforward conversion that makes interpreting values in different contexts much easier. Because percentages are widely used, mastering this conversion can be very helpful for everyday calculations.