Decimals

Addition of Decimals

To add decimals, follow these steps:

1. Align the decimal points of the numbers.

2. Add the numbers as usual, starting from the rightmost digit.

3. Carry over any extra digits to the left.

Example:

Add \(2.35\) and \(1.7\).

\[\begin{array}{r}2.35 \\+ 1.7 \\\hline4.05\end{array}\]

Subtraction of Decimals

To subtract decimals, follow these steps:

1. Align the decimal points of the numbers.

2. Subtract the numbers as usual, starting from the rightmost digit.

3. Borrow from the next column if necessary.

Example:

Subtract \(3.7\) from \(6.48\).

\[\begin{array}{r}6.48 \\- 3.7 \\\hline2.78\end{array}\]

Multiplication of Decimals

To multiply decimals, follow these steps:

1. Multiply the numbers as if they were whole numbers, ignoring the decimals.

2. Count the total number of digits to the right of the decimal points in both numbers.

3. Place the decimal point in the product so that it has the same total number of digits to the right as in the factors.

Example:

Multiply \(2.4\) by \(1.5\).

\[\begin{array}{r}2.4 \\\times 1.5 \\\hline3.6 \\\end{array}\]

The product is \(3.6\).

Division of Decimals

To divide decimals, follow these steps:

1. Move the decimal point to the right in both the dividend and the divisor until the divisor becomes a whole number.

2. Divide as usual.

3. Place the decimal point in the quotient directly above the decimal point in the dividend.

Example:

Divide \(4.8\) by \(0.6\).

\[\begin{array}{r}4.8 \\\div 0.6 \\\hline8 \end{array}\]

The quotient is \(8\).