Decimal Arithmetic in Financial Mathematics

Decimals

Decimals form part of our everyday lives when dealing with financial transactions. They represent fractional parts of numbers, such as cents or pennies. In mathematics, fractions can be expressed using a decimal form which is easier to manipulate than the traditional multiplication of numerators and denominators. Here's a closer look at how decimals work in financial mathematics.

Fraction to Decimal Conversion

Converting fractions to decimals involves dividing the number by its denominator. For example, converting \frac{2}{3} as a decimal is done by dividing 2 by 3, which results in 0.6666... This process continues infinitely without repeating because it represents a division by 3. To avoid writing down all the digits, this process can also be represented by simply writing 0.6.

Addition and Subtraction of Decimals

Addition and subtraction of decimals follow the same rules as whole numbers. If adding two decimals with different place values results in zeros appearing before the decimal point, these are dropped. However, if you get a zero, keep it in place. This method ensures that both decimals have the same number of places after the decimal point.

For instance, let's consider addition and subtraction of two decimals:

2.6 + 3.8 = 6.4
2.9 - 1.3 = 1.6

In each case, the decimal points align based on their place value, making it easier to visually check and adjust the alignment.

Multiplication of Decimals

Multiplication of decimals follows a similar pattern. First, multiply the whole numbers, then multiply the decimal parts, where applicable. If the result has more decimal places than either of the original factors, round off to the desired precision.

For example, consider multiplying 2.5 by 3.4:

2.5 * 3.4 = 8.5

The result is 8.5, and no additional decimal points are required since both factors only had one digit after the decimal point.

Division of Decimals

Division of decimals involves dividing whole numbers followed by dividing the decimal parts if applicable. Just like multiplication, any additional decimal places must be rounded off to the desired precision. For example, consider dividing 2.5 by 3.4:

2.5 / 3.4 = 0.735294

Since 2.5 divided by 3.4 is approximately equal to 0.73, we round off to two decimal places, resulting in the final value of 0.73.

In summary, decimals play a crucial role in financial mathematics, enabling the manipulation of fractional values with ease. Understanding the basic concepts of decimal arithmetic, including conversion from fractions to decimals, addition, subtraction, multiplication, and division, is essential for anyone looking to work with money or perform financial calculations.