Decimal Numbers:

Decimal numbers are not integers, meaning they are not whole numbers. They express a value which is or includes a part of a whole number in tenths, hundreds, thousands, etc., with the help of a decimal point.

We can have a decimal number that expresses only a part of a number and is less than 1, such as

or we can have a decimal number, where the part that is less than 1 (the part expressed in tenths and/or hundreds and/or thousandths, etc.) is a part of a much bigger number, such as:

There is no limit to how many numbers may follow the decimal point. In the decimal number:

the number 24 is followed by the decimal point and then the next digit (4) is the value of the tenths, the following digit (3) is the value of the hundredths and the next (5) is the value of the thousandths.

We can add, subtract, multiply and divide decimal numbers in exactly the same way we do with integers, with one very important warning: Always make certain that the decimal points of the various numbers in your calculations are aligned.

For example, if we are asked to add the numbers 5.25 and 14.6 we must show our addition as:

Notice how the decimal points of both numbers are underneath each other. Also, notice how we have included a zero in the hundredths digit of number 14.6, writing it down as 14.60. This is done to force us to have the decimal points aligned, one underneath the other, to make certain that we are adding the hundredths digits of the two number together, the tenths digits together, etc.

Similarly, in subtracting of decimal numbers, we have to ensure once again that the decimal points are aligned, as in the following example: Subtract 24.65 from 50!

Notice that we have included a zero in both the tenths and the hundredths digit of the number 50 since we have to have a number from which to subtract the hundredths and tenths digits of 24.65 and since 50 is an integer, we have added two zeros in those two digits.

When a decimal number is included in multiplication, you may perform the operation as though you were multiplying integers, the multiplication is done in exactly the same way. Once you have determined your product, you add the number of decimal places (the digits following the decimal points) in the two numbers being multiplied and the total of the decimal places will determine the position of the decimal point in the product.

For example, if we are multiplying 25.3 by 5.06:

We are not quite finished yet, as we now have to determine the position of the decimal point in our product. The first number we are multiplying, 25.3, has one decimal place, as the only digit following the decimal point is 3. The second number, 5.06, has two decimal places, since 0 and 6 follow the decimal point. Together, we therefore have three decimal places in the two numbers and we therefore take our result of 128018 and position the decimal point three digits to the left:

Whatever the total of decimal places in the two numbers multiplied will be, you will always start at the end of the number that is your solution and position the decimal point by that number of digits TO THE LEFT!

When you have a decimal number in a division and it happens to be the number that is being divided, as in:

we will perform the division exactly as we would a division of two integers, except that we will keep going even after we have reached the decimal point and beyond that:

If the decimal number happens to be the number that we are dividing by, as in the following example:

to treat ourselves to the convenience of not having to work with a decimal number, we will multiply both numbers by 10 and instead, we will divide

This will now become a simple division of two integers and we hope that you will get the correct answer of 36.

Examples:

Answers: