Understanding Decimal Subtraction

Subtracting decimals is a fundamental arithmetic skill. It involves finding the difference between two numbers that contain decimal points. To subtract decimals accurately, the most important step is to align the decimal points of the numbers.

Let's look at the given problem: \(1.004 - 0.4\).

Step-by-Step Decimal Subtraction

Here's how to subtract \(0.4\) from \(1.004\):

1. Align the Decimal Points: Write the numbers one below the other so that the decimal points line up vertically.
2. Add Trailing Zeros (if needed): To make the subtraction easier and avoid errors, you can add zeros to the number with fewer decimal places so that both numbers have the same number of decimal places. In this case, \(1.004\) has three decimal places, and \(0.4\) has one. We can rewrite \(0.4\) as \(0.400\).
3. Subtract as with Whole Numbers: Start subtracting from the rightmost digit, just like you would with whole numbers. If a digit in the top number is smaller than the digit below it, you'll need to borrow from the digit to its left.
4. Place the Decimal Point: Bring the decimal point straight down into the result.

Let's perform the subtraction:

Starting from the rightmost column (thousandths place):

• \(4 - 0 = 4\)
• \(0 - 0 = 0\)
• In the tenths place, we have \(0 - 4\). We need to borrow from the units place. The \(1\) in the units place becomes \(0\), and we carry over \(10\) to the tenths place. Now we have \(10 - 4 = 6\).
• In the units place, we have \(0 - 0 = 0\).

The decimal point is placed directly below the decimal points in the numbers being subtracted.

So, \(1.004 - 0.400 = 0.604\).

Comparing with Options

Now let's compare our result with the given options:

• Option 1: \(0.604\)
• Option 2: \(1\)
• Option 3: \(0.006\)
• Option 4: \(0.640\)

Our calculated result, \(0.604\), matches Option 1.

Summary of Calculation

Subtracting \(0.4\) from \(1.004\) results in \(0.604\). This is found by aligning the decimal points and subtracting column by column, remembering to borrow when necessary.

Revision Table: Key Decimal Concepts

Additional Information: Decimal Operations

Understanding decimal subtraction is part of a broader set of operations with decimals. Here are some related concepts:

• Decimal Addition: Similar to subtraction, align decimal points and add column by column, carrying over when necessary.
• Decimal Multiplication: Multiply the numbers as if they were whole numbers, then place the decimal point in the product so that the number of decimal places equals the sum of the decimal places in the numbers being multiplied.
• Decimal Division: If dividing by a decimal, move the decimal point in the divisor (and the dividend) to the right until the divisor is a whole number. Then divide as usual, placing the decimal point in the quotient directly above the decimal point in the adjusted dividend.

Mastering these operations is crucial for solving various mathematical problems.