Decimal Operations

Addition of Decimals

The fundamental rule for adding decimals is to position the decimal points in-line. For example, if you want to add 0.5, 2.4, and 15.52, then organize the numbers as shown below where the decimal points are in-line

Subtraction of Decimals

The Subtraction is carried out as the same manner as addition by aligning decimal points in-line. An example is stated below.

Multiplication of Decimals

Follow the simple steps to multiply decimal numbers as stated below.

• Ignore the decimal points and multiply the whole numbers.
• Count the total digits on the right side of the decimal point on both the numbers being multiplied.
• In the answer, position the decimal point from right at the digits equal to the total count.

Example

Solve 100 x 6.7365

= 100 x 67365  (Ignore the decimal point)

= 6736500

Count the decimal places right of the decimal point in the question and place it from the right; in this example it is 4

= 673.6500 (Answer)

Division of Decimals

Rule 1: When you divide decimals by a whole number, ignore the decimal point and divide as usual. Then place the decimal point at the same point as the dividend.

Example

22.6 ÷ 2

= 113 (ignore decimal)

= 11.3 (place the decimal point as the dividend; 2 digits from the left)

Rule 2: When you divide decimals by a decimal number, convert the divisor to a whole number by shifting the decimal point and place the decimal point as the dividend.

Example

225.62 ÷ 2.1

= 2256.2 ÷ 21 (Convert the divisor to a whole number by moving the decimal point to 1 decimal place)

= 107.43 (Place the decimal point as the dividend; 3 digits from the left)

Rounding off Decimals

Rounding off a decimal is applied to estimate approximate values. Mostly the rounding is used to limit the number of digits after decimal point, instead of having long string of decimal places. For example, a decimal 45.2598239831 can be rounded off to 45.26 or 45.3 or 45.

Rounding up the Decimals

Increase the decimal place value by 1 and drop the rest if the digit value next is more than or equal to 5.

• 23.567, when rounded up to 2 decimals will be 23.57
• 23.567 when rounded up to 1 decimal will be 23.6

Rounding down the Decimals

If the number next to the desired decimal place value is less than 4, leave the number as it is and disregard the rest on the right.

• 23.4425 when rounded down to 2 decimals will be 23.44 (drop 2 and 5)
• 23.4425 when rounded down to 1 decimal will be 23.4 (drop 4, 2 and 5)
• 23.4425 when rounded down to whole number will be 23 (drop 4, 4, 2, and 5)