Problem 4 - Prealgebra

Question

Find each of the following sums. (Add.) $$0.06+0.92+0.65$$

Step-by-Step Solution

Answer

The sum of 0.06, 0.92, and 0.65 is 1.63.

Step 1: Align Decimal Points

When adding decimals, it's important to align the decimals to ensure the correct addition of each column. Start by writing:\[\begin{array}{r} 0.06 \ 0.92 \+0.65 \\hline\end{array}\]

Step 2: Add the Hundredths Place

Look at the rightmost column, which is the hundredths place. Add the numbers in this column: \(6 + 2 + 5 = 13\). Write down the 3 in the hundredths place of the sum and carry over the 1 to the tenths column.

Step 3: Add the Tenths Place

Next, add the digits in the tenths place along with any carryover. This gives us \(0 + 9 + 6 + 1 = 16\). Write down 6 in the tenths place and carry over the 1 to the ones column.

Step 4: Add the Units Place

Finally, add the digits in the units place and include any carryover. The calculation is \(0 + 1 = 1\). Write the result in the units place.

Step 5: Write the Final Answer

Combine all the values you calculated from each column to form the final answer. This looks like: \[\begin{array}{r} 0.06 \ 0.92 \+0.65 \\hline1.63\end{array}\] Hence, the sum is 1.63.

Key Concepts

Understanding Decimal Alignment

When adding decimals, aligning the decimal points is the very first step. This ensures that you're adding each digit to the correct place value—just like how you'd add whole numbers by stacking them neatly. For example, in the exercise provided, we set up the numbers like this:

• 0.06
• 0.92
• +0.65

This alignment shows the decimal points directly above each other, helping you identify the tenths and hundredths easily. This way, each column only contains digits of the same place value, which prevents mistakes.

Carrying Over in Addition

Carrying over is an essential part of adding numbers, especially when the sum of digits in a column exceeds 9. In our decimal exercise, you witness this when the sum of the hundredths column is 13. Here's how it works:

• Add 6, 2, and 5 to get 13.
• Write down the 3 in the hundredths place.
• Carry over the 1 to the next left place, which is the tenths column.

This ensures that every extra 10 is efficiently moved to the higher place value, allowing accurate addition across all columns.

Place Value in Decimals

Let's pause to understand place values in decimal numbers. The place value indicates the position of a number, which in turn shows its worth. A key concept is that each place to the right of the decimal represents a fraction of a whole. For instance, in decimal numbers:

• The first digit to the right of the decimal is the tenths place.
• The second digit is the hundredths place.
• The third digit, if any, would be the thousandths place

This means in 0.65, for instance, 6 is in the tenths place and 5 is in the hundredths place. Correct understanding of place value ensures precise calculations during operations, helping organize digits correctly during addition.

Mastering Basic Arithmetic

Basic arithmetic, especially addition, is foundational. When working with decimals, the rules don’t change; we just need to carefully align and sum up digits. This involves knowing how to take care of carries and understanding the simplest mathematic operations:

• Addition: Combine the values in each column starting from the rightmost side.
• Carrying over: When any column sums to 10 or more, move the extra to the next left column.
• Writing the final result: Combine all columns from right to left to get the final sum.

With these steps, adding decimals becomes straightforward and intuitive, building crucial skills for more complex math in the future.