Problem 2 - Prealgebra

Question

Find each of the following sums. (Add.) $$8.97+2.04$$

Step-by-Step Solution

Answer

The sum is 11.01.

Step 1: Align the Numbers

To properly add decimal numbers, we need to align them by their decimal points. Here, write 8.97 on top and 2.04 below it, ensuring the decimal points are in a vertical line.

Step 2: Add the Hundredths Column

Start adding the rightmost digits (the hundredths place): 7 (from 8.97) plus 4 (from 2.04) equals 11. Write down 1 and carry over 1 to the tenths place.

Step 3: Add the Tenths Column

Now, add the tenths place digits along with the carry over: 9 (from 8.97) plus 0 (from 2.04) plus the 1 carried over equals 10. Write down 0 in the tenths place and carry 1 to the units place.

Step 4: Add the Units Column

Add the units place digits, including the carry over: 8 (from 8.97) plus 2 (from 2.04) plus 1 carried over equals 11. Write the 1 under the units column and carry over 1 to the tens place.

Step 5: Account for the Tens Column

Since there is no value in the tens column of the original numbers, only the carry over remains. Thus, place 1 in the tens column.

Key Concepts

Understanding Decimal Addition

Decimal addition is very similar to adding whole numbers, but with the added importance of lining up the decimal points. This alignment ensures that digits from similar place values are directly on top of each other, making it easier to add each column.
Once the numbers are aligned, you start adding from the rightmost column, just like with whole numbers. Always remember that simple arithmetic operations like addition need to be precise to avoid errors. For example,

• Align the numbers based on their decimal points.
• Begin adding from the rightmost digit to the left.
• Keep track of any number that needs to be carried over to the next place value.

Placing decimal points correctly is crucial. After adding each column, remember to keep the decimal point in the same vertical position in your final answer. Proper alignment leads to accurate sums.

The Carry Over Effect

The concept of 'carry over' becomes more evident when adding numbers in columns, especially with decimals. When the sum of a column's digits exceeds nine, you leave the rightmost digit in its place and "carry over" the extra value to the next left column. For example, if you add 7 + 4 and get 11, you would write down 1 and carry the 1 over.
Here's how you can manage carry overs:

• Email each column start from the right, just like how you would read a book.
• Remember the extra value that exceeds 10. Write down only the digit in the ones place and carry over the digit in the tens place.
• Don’t forget to add the carried over value to the next column.

In our exercise, the carry over occurs in both the hundredths and tenths columns, showing it is normal in decimal addition. Successfully managing carry overs ensures precision in problems involving decimals.

Grasping Place Value

Place value refers to the value a digit holds based on its position within a number. Each digit's place value is ten times that of the digit to its right and one-tenth that of the digit to its left. In a decimal number:

• The first place to the right of the decimal represents tenths.
• The next place is hundredths, and so on.
• To the left of the decimal, you have units, tens, hundreds, etc.

Keeping track of these positions when adding ensures accuracy. Pay close attention to where each digit is placed. Maintaining correct alignments ensures that digits are added in the correct place value columns. For instance, when adding tenths, make sure you are only adding digits from the tenths column. By continuously being conscious of place values, you prevent common mistakes and enhance the precision of your calculations.