Understanding the Decimal Addition Problem

The question asks us to find the sum of four numbers: \(1254\), \(125.4\), \(12.54\), and \(1.254\). These are decimal numbers, although the first number, \(1254\), is a whole number, it can be written as \(1254.000\) to align with the others for addition.

How to Add Decimal Numbers

Adding decimal numbers is similar to adding whole numbers, but with one crucial step: aligning the decimal points. To add decimals correctly, follow these steps:

• Write the numbers vertically, one below the other.
• Make sure the decimal points are lined up in a straight vertical column.
• If the numbers have a different number of decimal places, you can add zeros to the right of the last digit of the shorter decimal numbers so they all have the same number of decimal places. This helps prevent errors.
• Add the numbers column by column, starting from the rightmost column (the smallest place value), just like with whole numbers.
• Carry over digits to the next column to the left when a sum in a column is 10 or greater.
• Place the decimal point in the sum directly below the decimal points in the numbers being added.

Solving the Addition: Step-by-Step Calculation

Let's align the given numbers vertically, adding trailing zeros where needed:

Adding column by column from right to left:

• Rightmost column (thousandths place): \(0 + 0 + 0 + 4 = 4\). Write down \(4\).
• Next column (hundredths place): \(0 + 0 + 4 + 5 = 9\). Write down \(9\).
• Next column (tenths place): \(0 + 4 + 5 + 2 = 11\). Write down \(1\) and carry over \(1\) to the units place.
• Place the decimal point in the result.
• Next column (units place): \(4 + 5 + 2 + 1\) (carried over) \( = 12\). Write down \(2\) and carry over \(1\) to the tens place.
• Next column (tens place): \(5 + 2 + 1\) (carried over) \( = 8\). Write down \(8\).
• Next column (hundreds place): \(2 + 1 = 3\). Write down \(3\).
• Next column (thousands place): \(1\). Write down \(1\).

The sum is \(1393.194\).

Result of the Addition

The sum of \(1254 + 125.4 + 12.54 + 1.254\) is \(1393.194\).

Comparing with Options

Let's compare our calculated sum with the given options:

• Option 1: \(1393.184\)
• Option 2: \(1383.184\)
• Option 3: \(1393.194\)
• Option 4: \(1383.194\)

Our result, \(1393.194\), matches Option 3.

Revision Table: Decimal Addition Key Points

Additional Information: Properties of Addition

Addition is an arithmetic operation with several important properties:

• Commutative Property: The order of the numbers being added does not affect the sum. For example, \(a + b = b + a\). In our case, adding the numbers in any order would give the same result.
• Associative Property: When adding three or more numbers, the way the numbers are grouped does not affect the sum. For example, \((a + b) + c = a + (b + c)\).
• Identity Property: The sum of any number and zero is that number. Zero is the additive identity. For example, \(a + 0 = a\).

These properties apply to both whole numbers and decimal numbers, making addition a consistent operation across different types of numbers.