Problem 60 - Algebra 1: Concepts and Skills

Question

ADDING DECIMALS Add. $$ 0.09+0.05 $$

Step-by-Step Solution

Answer

The sum of 0.09 and 0.05 is 0.14.

Step 1: Align the decimal points

When adding decimals, align the decimal points and add as if adding normal numbers. Write down both numbers one below another with decimal points aligned: \n 0.09\n+0.05

Step 2: Perform the addition

Once the numbers are properly aligned, add the numbers normally from right to left: \n 0.09 \n +0.05 \n------ \n 0.14

Key Concepts

Step by Step Solution

When approaching a problem of adding decimals, breaking it down into clear steps will assist you. Here's a straightforward way to do it:

• Align the Numbers: Start by placing the numbers one on top of the other so that the decimal points are aligned. This ensures accuracy in the addition process.
• Fill in Missing Places: If one number has fewer digits after the decimal point than the other, fill in the empty places with zeros. This won't change the value of the number, but it helps in keeping your columns straight.
• Add from Right to Left: Like you do in whole number addition, start adding the digits from the rightmost side (the smallest decimal place) and move towards the left. Remember that any carry-over should be passed to the next left column.

This straightforward approach helps make the addition process organized and less error-prone, ensuring you get the correct answer every time.

Aligning Decimal Points

An essential part of decimal addition is ensuring that the decimal points are perfectly lined up. This keeps digits of the same place value column (e.g., tenths, hundredths) in a vertical line, making it easier to add them.

• Importance: Aligning decimal points allows each digit to be placed in its proper position, and prevents place value errors. Misalignment can lead to incorrect results.
• Consistency: Always follow the same method for alignment, whether you're adding a large or small number of decimals, as consistency keeps mistakes at bay.
• Check Alignment: Take a moment before proceeding with addition to double-check that all decimal points line up correctly. This small step can save you from larger mistakes later on.

By taking care of the alignment first, the actual process of addition becomes much simpler and straightforward.

Decimal Addition

Adding decimals involves adding numbers that are part of a whole, similar to whole number addition but with a few extra rules to follow.

• Understand Decimals: Each digit in a decimal number has a specific value based on its position relative to the decimal point. Knowing this helps you add them correctly.
• Use of Zero: Use zeros to fill up any vacant spaces to the right of the digits to ensure each decimal has the same number of places. This does not affect the numbers' values but helps avoid confusion.
• Example: In the problem \(0.09 + 0.05\), aligning the decimals properly and identifying digits by their place value makes the process straightforward.
• Adding Up: Once places are filled and decimal points aligned, add as you would integers, carrying over when necessary.

These simple steps ensure you accurately add decimal numbers every time, bolstering your confidence with each successful calculation.