Problem 77 - Prealgebra

Question

Write as a percent. Write the remainder in fractional form. $$\frac{9}{16}$$

Step-by-Step Solution

Answer

\( \frac{9}{16} = 56\% + \frac{1}{4}\% \)

Step 1: Understanding Fractions as Decimals

First, we need to convert the fraction \( \frac{9}{16} \) into a decimal form so that we can then easily convert it to a percentage. This is done by dividing the numerator (9) by the denominator (16) using long division or a calculator.

Step 2: Performing the Division

Divide 9 by 16. When you do this, you'll find that \( \frac{9}{16} = 0.5625 \). This decimal form will help us in converting the fraction to a percentage.

Step 3: Converting Decimal to Percent

Now, take the decimal \( 0.5625 \) and convert it to a percentage. To convert a decimal to a percent, simply multiply by 100. Therefore, \( 0.5625 \times 100 = 56.25\% \).

Step 4: Writing the Percent with Fraction

The percent conversion is 56.25\%. To write the decimal part as a fraction, note that 0.25 is equivalent to \( \frac{1}{4} \). Thus, 56.25\% can be expressed as 56\% and \( \frac{1}{4} \) of a percent.

Key Concepts

Fractions to Decimals

When working with fractions, converting them to decimal form is often a helpful step. To do this conversion, you simply divide the numerator (top number) by the denominator (bottom number). In our example, we have the fraction \( \frac{9}{16} \). This means we should divide 9 by 16 to find the equivalent decimal.To tackle this, you can use:

• A calculator for quick division.
• Long division for a more in-depth understanding.

Through division, you discover that \( \frac{9}{16} = 0.5625 \). This decimal result is the foundation for further conversions and calculations.

Decimal to Percent

Once you have a decimal, converting it to a percentage is a snap! You simply need to multiply the decimal number by 100. This is because 'percent' means 'per hundred.' Let's walk through this using our example, where our decimal is 0.5625.The calculation:

• Multiply 0.5625 by 100.

This calculates to \( 0.5625 \times 100 = 56.25\% \).In summary, shifting from a decimal to a percent involves multiplying by 100. Always remember to include the percent sign (\%) with your final number.

Long Division

Long division might seem like a long process, but it reveals a deeper understanding of numbers. By using long division to convert the fraction \( \frac{9}{16} \) into a decimal, you divide 9 by 16.Here's how you can do it step-by-step:

• Determine how many times 16 fits into 90 (the first part), which is 5 times, giving 80. Write 5 in the quotient area.
• Subtract 80 from 90 to get a remainder of 10.
• Drop down the next 0, making it 100. How many times does 16 fit into 100? That's 6 times, because 16 times 6 is 96. Subtract to get a remainder of 4.
• Repeat, bringing down more zeros and dividing until you get a remainder of zero or decide on the desired precision, which here is up to four decimal places, giving us 0.5625.

Long division helps you understand the process behind decimal conversion, reinforcing the concept that division is really about "how many times one number contains another."