Business Mathematics: Review of Arithmetic - Decimals

Decimals allow us to represent fractions with the convenience of whole–number representation. A decimal number consists of two strings of digits separated by a decimal point. The number 123.456 is an example of a decimal number.

Digits to the left of the decimal point represent the “whole” part of the number while digits to the right of the decimal point represent the fractional part according to the following scheme:

The value of 123.456 is 1 hundred + 2 tens + 3 ones + 4 tenths + 5 hundredths + 6 thousandths

Decimal positions further to the right would be ten thousandths, hundred thousandths, and so on.

Decimals are added and subtracted in a manner similar to whole numbers except that one must be very careful to line up the decimal points vertically. Zeros can be placed to the right of the decimal portion of the number for convenience.

Thus 1.23, 1.230, 1.2300, and 1.230000 all have the same value.

Example
Add 12.4, 13.12, and 1.765:

Example
Subtract 1.732 from 5.69:

Multiplication of decimals is similar to multiplication of whole numbers except that the number of decimal places in the product is equal to the sum of the numbers of decimal places in the numbers multiplied. Always count from the right when inserting the decimal point.

Example
Multiply 1.742 by 2.13:

To divide a decimal number by a whole number, divide as you would divide whole numbers and line up the decimal point in the quotient with the decimal point in the dividend.

Example
Divide 18.75 by 15:

To divide a decimal number by another decimal number, move both decimal points the same number of positions to the right until the divisor becomes a whole number. You may have to append zeros to the dividend.

Example
Divide 19.5 by 3.75: becomes when the decimal point is moved 2 places to the right:

Decimals may be converted to fractions by representing the digits, without the decimal point, by an appropriate power of 10 (10, 100, 1,000, etc.). Fractions may be converted to decimal form by performing a long division.

Example
Convert 0.36 to a fraction:

Example
Convert 1.25 to a fraction:


Example
Convert 15/16 to a decimal:

We perform a division, dividing 15 by 16. For convenience, extra 0s are appended to the right of the decimal in the dividend.

Solved Problems

1.  Add 11.2, 12.35, and 13.423.

2.  Subtract 6.235 from 8.7.
Solution


3.  Multiply 34.15 by 2.9.
Solution


4.  Divide 138.7 by 19.
Solution


5.  Divide 109.53 by 4.5.
Solution
First multiply both numbers by 10 to make the divisor a whole number:


6. Convert 0.125 to a fraction.
Solution


7.  Convert 7/8 to a decimal.
Solution