Which Best Describes How To Add 9.73 And 21.6

How to Add 9.73 and 21.6: A Comprehensive Guide

Adding decimal numbers might seem straightforward, but a clear understanding of the process is crucial for accuracy and confidence in various mathematical applications. This comprehensive guide will walk you through the addition of 9.73 and 21.6, explaining the underlying principles and offering practical tips to avoid common errors. We'll explore different methods, highlighting their strengths and weaknesses, and ultimately empowering you to tackle similar problems with ease.

Understanding Decimal Numbers

Before diving into the addition, let's refresh our understanding of decimal numbers. A decimal number consists of a whole number part and a fractional part, separated by a decimal point (.). The digits to the left of the decimal point represent whole units, while the digits to the right represent fractions of a unit (tenths, hundredths, thousandths, and so on).

In our example, 9.73 has a whole number part of 9 and a fractional part of 0.73 (7 tenths and 3 hundredths). Similarly, 21.6 has a whole number part of 21 and a fractional part of 0.6 (6 tenths).

Method 1: Vertical Addition with Place Value Alignment

This is the most common and reliable method for adding decimal numbers. It emphasizes place value alignment, minimizing the risk of errors.

Step 1: Vertical Arrangement and Place Value Alignment

Write the numbers vertically, ensuring that the decimal points are aligned. This crucial step ensures that you are adding corresponding place values (ones, tenths, hundredths, etc.).

   9.73
+ 21.6
-------

Step 2: Adding the Hundredths Column

Start with the hundredths column (farthest right). In this case, we have 3 hundredths in the top number and 0 hundredths in the bottom number. 3 + 0 = 3.

   9.73
+ 21.60  <-- Added a zero as a placeholder
-------
      3

Note: We added a zero as a placeholder in the hundredths column of 21.6 to ensure proper alignment and facilitate the addition. Adding zeros to the right of the last digit after the decimal point doesn't change the value of the number.

Step 3: Adding the Tenths Column

Next, add the digits in the tenths column. We have 7 tenths + 6 tenths = 13 tenths. This is equivalent to 1 whole and 3 tenths. Write down '3' and carry-over the '1' to the ones column.

   1
   9.73
+ 21.60
-------
     3

Step 4: Adding the Ones Column

Now, add the digits in the ones column, including the carry-over from the tenths column. We have 9 ones + 1 (carry-over) + 1 (from 21) = 11 ones. This is equivalent to 1 ten and 1 one. Write down '1' and carry-over the '1' to the tens column.

  11
   9.73
+ 21.60
-------
    13

Step 5: Adding the Tens Column

Finally, add the digits in the tens column, including the carry-over. We have 1 (carry-over) + 2 (from 21) = 3 tens.

  11
   9.73
+ 21.60
-------
  31.33

Therefore, 9.73 + 21.6 = 31.33

Method 2: Horizontal Addition

While vertical addition is generally preferred for accuracy, horizontal addition can be used for simpler problems. It involves adding the whole number parts and the fractional parts separately, then combining the results.

Step 1: Separate Whole and Fractional Parts

Separate the whole number parts and the fractional parts:

Whole number parts: 9 + 21 = 30 Fractional parts: 0.73 + 0.6 = 1.33

Step 2: Combine the Results

Combine the results from Step 1: 30 + 1.33 = 31.33

This method is quicker for simple problems but can be prone to errors with more complex numbers or multiple addends.

Method 3: Using a Calculator

Calculators are a convenient tool for adding decimal numbers, especially for complex calculations. Simply enter the numbers (9.73 and 21.6) and press the "+" button, followed by the "=" button. The calculator will display the result: 31.33. Calculators are efficient, but it's important to understand the underlying principles to verify the results and avoid relying solely on technology.

Common Mistakes to Avoid

• Incorrect decimal point alignment: Ensure the decimal points are perfectly aligned before adding. Misalignment leads to incorrect place value addition.

• Forgetting carry-overs: Pay close attention to carry-overs from one column to the next. Missing a carry-over results in an incorrect answer.

• Incorrect placement of the decimal point in the answer: The decimal point in the answer should be aligned vertically with the decimal points in the addends.

Practical Applications

Adding decimal numbers is essential in many real-world situations, including:

• Financial calculations: Calculating total expenses, balances, and profits.
• Measurements: Adding lengths, weights, or volumes expressed in decimal units.
• Scientific calculations: Combining data points represented as decimals.
• Everyday shopping: Calculating the total cost of items with prices expressed in decimals.

Conclusion

Adding 9.73 and 21.6 results in 31.33. Mastering this seemingly simple operation is fundamental to success in mathematics and numerous real-world applications. By understanding the principles of place value alignment, utilizing effective methods, and avoiding common mistakes, you can confidently perform decimal addition and tackle more complex mathematical problems. Remember to choose the method that best suits your needs and always double-check your work, whether you use a calculator or perform the addition manually. The consistent application of these principles will build your mathematical skills and enhance your problem-solving capabilities.