Problem 67 - Algebra 1: Concepts and Skills

Question

Find the sum. $$0.987+1.4$$

Step-by-Step Solution

Answer

2.387

Step 1: Line up the decimals

First, we need to line up the decimal points of the numbers. This can be done by simply looking at the decimal points. For example: \n 0.987 \n+1.4 \n ----

Step 2: Add the numbers

Starting from the right, begin to sum each pair of digits. If the first pair from the right doesn't have a pair, add a zero. So the sum will look like the following: \n 0.987 \n+1.400 \n ---- \n 2.387

Step 3: Final Answer

After adding both numbers, we get the final answer as 2.387

Key Concepts

Decimal Alignment

When adding decimals, one of the first important steps is to ensure the decimals are lined up correctly. This is known as decimal alignment. By aligning the decimal points vertically, we make sure each digit is in the correct place, which is essential for accurate addition. Imagine stacking transparent blocks perfectly so that each layer matches. Similarly, in decimal addition, ensuring the decimal points fall into a straight line vertically helps maintain the correct place value during calculations.

This is crucial because each column in a number represents a different place value, such as tenths, hundredths, and so on. If the decimals are not aligned, the place values may shift, resulting in incorrect sums. In our example, when we align the decimals of 0.987 and 1.4, we see they line up as:

• 0.987
• +1.4

Next, we can fill in missing spaces with zeros to make the numbers easier to work with.

Place Value

Understanding place value is vital when you deal with decimal arithmetic. Place value refers to the value of each digit in a number, depending on its position. After aligning the decimals, it's essential to consider each digit's place value. This refers to whether the digit is in the units, tenths, hundredths, or another spot.

For decimal numbers like 0.987, the place values can be broken down as follows:

• 0 in the unit's place
• 9 in the tenths place
• 8 in the hundredths place
• 7 in the thousandths place

Meanwhile, in 1.400, the 1 is in the units place, followed by 4 in the tenths. After aligning the decimals, you should make sure any empty spaces below other numbers are filled with zeros to keep your columns consistent. This helps maintain the integrity of the place value relationships.

Arithmetic Operations

When performing arithmetic operations like addition with decimals, follow steps methodically to ensure accuracy. After aligning and understanding the place values, the next step is to move on to the actual addition. Begin from the rightmost digit, which is the smallest place value, and proceed towards the left or larger place values.

For our example of 0.987 + 1.400, here's how it’s done:

• Start from the right: 7 (thousandths) + 0 equals 7.
• Next, 8 (hundredths) + 0 = 8.
• Then, 9 (tenths) + 4 = 13; write 3 and carry over 1.
• Finally, add the units: 0 + 1 + 1 (carry) equals 2.

So, the result of the addition is 2.387. Always check your work by reviewing your addition steps to ensure the sum is accurate. This methodical approach helps you tackle any decimal arithmetic with confidence.