Problem 32 - Prealgebra

Question

Write each of the following as a decimal number. Twenty-six thousand, two hundred forty-five and sixteen hundredths

Step-by-Step Solution

Answer

The decimal number is 26,245.16.

Step 1: Identify the Integral Part

First, let's identify the integral part of the number provided in words. The phrase "twenty-six thousand, two hundred forty-five" corresponds to the number 26,245.

Step 2: Identify the Fractional Part

Next, focus on the fractional portion. The phrase "sixteen hundredths" can be translated into the fraction \( \frac{16}{100} \), which is equivalent to 0.16 as a decimal.

Step 3: Combine Integral and Fractional Parts

Combine the integral part from Step 1 and the fractional part from Step 2 to form the complete decimal number. Thus, 26,245 plus 0.16 gives us 26,245.16.

Key Concepts

Integral Part

When faced with converting a number written in words to a decimal, the first essential step is identifying the **integral part** of the given number. The integral part is simply the whole number without any fractions, which is always found on the left side of a decimal point. In our example, the phrase "twenty-six thousand, two hundred forty-five" tells us that the integral part of our number is 26,245.

It’s helpful to break it down further to see how each word contributes to the whole number:

• "Twenty-six thousand" is 26,000.
• "Two hundred forty-five" adds another 245 to it.

Therefore, putting these together, we get the integral part: 26,245.
Understanding the integral part is crucial, as it builds the foundation of your number when converting to a decimal.

Fractional Part

After identifying the integral part, the next step involves pinpointing the **fractional part**. Fractional parts represent the portion of a number between whole values, denoted by numbers right of the decimal point. In this exercise, the words "sixteen hundredths" correspond to the fraction \( \frac{16}{100} \).

To convert this fraction into a decimal:

• Remember that "hundredths" implies division by 100.
• So, \( \frac{16}{100} \) converts directly to the decimal 0.16.

It's worth noting that different fractions, such as thousandths or tenths, will change how many zeros are in the divisor, impacting the place of decimal points. Recognizing the fractional part is key to accurately completing the conversion process.

Combining Numbers

Now that we have both the integral and fractional parts, the task is all about **combining these numbers** to form the complete decimal number. The integral part, 26,245, and the fractional part, 0.16, form the number 26,245.16.

Here's a simplified step-by-step way to do this:

• Write the integral part: 26,245
• Place a decimal point after the integral part.
• Attach the fractional part to the right of the decimal point, which in this case is 0.16.
• Thus, you get 26,245.16.

Being clear on this process helps you accurately portray the number in a format widely used for calculations and everyday usage, ensuring clarity and precision in conveying numeric information.