Problem 20 - Prealgebra

Question

Write each fraction as a decimal correct to the hundredths column. $$\frac{15}{51}$$

Step-by-Step Solution

Answer

The decimal form of \( \frac{15}{51} \) rounded to the nearest hundredth is 0.29.

Step 1: Divide the Numerator by the Denominator

To convert a fraction to a decimal, we divide the numerator by the denominator. In this case, divide 15 by 51.

Step 2: Perform the Division

Perform the division 15 ÷ 51 using a calculator or long division. This will give the decimal representation of the fraction.

Step 3: Identify the Result

The result of 15 ÷ 51 is approximately 0.29411764705882. We need to consider rounding.

Step 4: Round to the Hundredths Place

Round 0.29411764705882 to the nearest hundredths. The digit in the hundredths place is 9 and the digit following it is 4, which means we round down.

Step 5: Write the Final Answer

The fraction \( \frac{15}{51} \) as a decimal rounded to the nearest hundredths is 0.29.

Key Concepts

Rounding Decimals

When converting fractions to decimals, it is often important to round the decimal to a specific place value. In our example, the decimal needs to be rounded to the hundredths column. Rounding helps simplify the number, making it easier to work with or understand in real life. To round correctly, pay attention to the digit immediately after the place value you are focusing on.

• If this digit is 5 or more, you round up, increasing the target digit by one.
• If it is less than 5, you round down, leaving the target digit as it is.

For instance, from the division of 15 by 51, we get 0.29411764705882. Here, you focus on the hundredths place, which is 9, and look at the next digit, 4. Since 4 is less than 5, you round down, leaving the decimal as 0.29. This is how rounding to the nearest hundredths place is done.

Numerator and Denominator

Understanding the terms 'numerator' and 'denominator' is essential when dealing with fractions. A fraction is composed of two parts:

• The numerator, which is the top number and represents how many parts we have.
• The denominator, which is the bottom number and tells us how many parts make up a whole.

For the fraction \( \frac{15}{51} \), 15 is the numerator and 51 is the denominator. This fraction tells us that 15 parts out of a total of 51 parts are being considered.

When converting this fraction to a decimal, you perform a division of the numerator by the denominator: 15 divided by 51. This division gives the decimal form of the fraction.

Long Division

Long division is a method for dividing numbers to find the quotient and remainder. This method can also convert fractions into decimal form without a calculator. For the fraction \( \frac{15}{51} \), long division involves dividing 15 by 51.

Here's a quick guide on performing long division for this fraction:

• Set up the division: Place the numerator (15) inside the division box and the denominator (51) outside.
• Determine the quotient: Since 51 doesn't go into 15, you'll consider 150 (15.0) by adding a decimal point to allow further division.
• Perform the division: Determine how many times 51 fits into 150, which is 2 times. Multiply and subtract the result from 150, then continue the process by bringing down additional zeros.
• Repeat: Continue this process to expand the decimal as needed.

This manual division process helps you understand how the decimal form is reached and is useful when calculators are unavailable. It provides familiarity with the behavior of numbers and decimals.