Problem 11 - Prealgebra

Question

Find each of the following sums. (Add.) $$5.0003+6.78+0.004$$

Step-by-Step Solution

Answer

The sum is 11.7843.

Step 1: Identify the Numbers

The numbers to be added are 5.0003, 6.78, and 0.004. We need to add these to find their sum.

Step 2: Align Decimal Points

Write the numbers in a column, aligning them by the decimal point:\[\begin{array}{c} 5.0003 \ +6.7800 \ +0.0040 \\hline\end{array}\]

Step 3: Add Column by Column

Start by adding from the rightmost column (thousands of a thousandth) to the leftmost column. Ensure each column is correct before moving to the next:\[\begin{array}{c} 5.0003 \ +6.7800 \ +0.0040 \\hline 11.7843 \\end{array}\]

Step 4: Combine the Total

After summing each column, the total sum of 5.0003, 6.78, and 0.004 is 11.7843.

Key Concepts

Aligning Decimals

Aligning decimals is essential when adding numbers that have different decimal places. To begin, ensure every decimal point is lined up directly beneath one another vertically. This allows you to correctly match the digits according to their place value, making it easier to add them correctly.
For example, the numbers 5.0003, 6.78, and 0.004 need to be stacked with their decimal points aligned:

• 5.0003
• 6.7800
• +0.0040

Notice we add zeros to make sure every number has the same amount of decimal places. This step is crucial because it ensures you are adding the tenths to the tenths, the hundredths to the hundredths, etc. Keeping everything aligned properly prevents mistakes in calculation.

Place Value

Understanding place value is essential for correctly adding decimals. Each digit in a number has a place, and each place has a value, depending on its position relative to the decimal point.
For instance, in the number 5.0003:

• The '5' is in the ones place.
• The '0' immediately after the decimal point is in the tenths place.
• '3' is in the thousandths place.

In our addition example, it's crucial to consider that only digits in the same place value are to be added together. This understanding prevents errors, such as adding a tenth to a thousandth. Each place value acts like a marker that helps you efficiently navigate through numbers, ensuring correct and systematic addition.

Step by Step Addition

Step by step addition involves taking a structured approach that simplifies the process of adding decimals. It ensures that each part of the number is added in sequence, minimizing the risk of oversight.
First, start from the rightmost column, which is typically the smallest place value. Add the numbers in this column together, carrying over any extra value to the next column if necessary. For example, if you have the column:

• 0.0003
• 0.0000
• 0.0040

Add these together before moving to the next column to the left, which is the ten-thousandths place, and so on.
Once all columns are summed, you combine the values to get your total. This methodical approach ensures each digit contributes correctly to the final sum, resulting in a precise calculation like: 11.7843.