Question

Find each sum or difference without using a calculator. \(4.642-2.1\)

Short answer

2.542

Step-by-step solution

Align the Numbers by Decimal Points

Write the numbers one below the other, making sure the decimal points are aligned: \( \begin{array}{r} 4.642 \ -2.1 \end{array} \)

Append Zeros if Needed

Add zeros to the number with fewer decimal places so both numbers have the same number of decimal places: \( \begin{array}{r} 4.642 \ -2.100 \end{array} \)

Subtract from Right to Left

Subtract each column starting from the rightmost digit to the left: \[ \begin{array}{r} 4.642 \ -2.100 \ \hline 2.542 \end{array} \]

Write the Result

The result of the subtraction is \(2.542\).

Key concepts

Aligning Decimal Points

When performing decimal subtraction, it's crucial to align the decimal points. This ensures each digit is in the correct place value. Imagine stacking blocks in precise columns - this helps in subtracting digits accurately:
First, line up the decimal points of the numbers, like so:
\( \begin{array}{r} 4.642 \ -2.1 \ \ \ \ \ \end{array} \)
Notice how the decimal points are directly above one another. This alignment keeps everything organized and makes the subtraction process much more manageable.

Appending Zeros

In decimal subtraction, if one number has fewer decimal places than the other, add zeros to the shorter number. This operation is called appending zeros. For example: \( \begin{array}{r} 4.642 \ -2.1 \ \{ \text{Append } \text{2.1} \text{to } \text{2.100} } \ -2.100 \ \ \end{array} \). Appending zeros helps make sure both numbers have the same number of decimal places. It does not change the value of the number. Instead, it simplifies the subtraction process by aligning all digits into corresponding place values for proper subtraction.

Subtracting Decimals

Subtracting decimals involves working from the rightmost digit to the left, just as you would with whole numbers. Let's break it down step-by-step:

• Start with the far right column and subtract any digits there.
• If needed, borrow from the column to the left, just like in whole number subtraction.
• Continue moving left, subtracting each digit column by column.

For our example: \( \begin{array}{r} 4.642 - 2.100 \ \ Subtract the columns: \ 2.542 \ \ \end{array} \). Finally, your result after all subtraction steps is \(2.542 \). Writing out each step prevents mistakes and helps you clearly see where values change.