Ultimate Guide to Decimal and Its OperationsUltimate Guide to Decimal and Its Operations

Introduction to Decimals
A decimal is basically numbers separated by a decimal point. Some basic examples of decimals are 0.3, 0.45, and 1.2345. The number of decimal places a decimal has depends on the size of the decimal. We always start counting the decimal place after the decimal point. For example, 0.7 has one decimal place, 0.12 has two decimal places, while 1.234 has 3 decimal places.

Types of Decimals
A terminating decimal is a decimal with an exact value, for example 0.25. On the other hand, 0.3333 is an example of a repeating decimal because there are one or more digits that are repeated. A dot is normally written above the repeated digit(s). And notwithstanding, 3.1428571 is an example of a non-repeating or non-terminating decimal because the decimals continue without a repeating pattern.

Converting Fractions to Decimals
All fractions can be changed into decimals simply by dividing the numerator by the denominator. Let’s say you are given the fraction one over two (½) or half. To convert this fraction into a decimal, simply take the number one (numerator) and divide it by the number two (denominator). Upon doing so, you will get the decimal 0.5. This is a pretty straightforward example, but sometimes when you convert a fraction into a decimal, you may get a repeating or non-repeating decimal as the answer. So how do you know what to write as the final answer? Well, there’s where rounding off decimal places come in. We’ll cover this in the next section.

Rounding off Decimal Places
A number can be rounded off to a specified number of decimal places. The basic steps to follow when rounding off a number to a given decimal place is illustrated below.

  • Check how many decimal places the question needs you to round off to. Let’s say you are asked to round off 9.673 to 1 decimal place.
  • Look at the digit next to the decimal place to round off to.
  • If the number is 5 or more, add 1 to the original decimal place and remove the rest to the right.
  • If the number is less than 5, then remove all the numbers to the right of the original decimal place.

The Four Operations of Decimals
The addition, subtraction, multiplication and division (commonly known as four operations) of decimals are pretty much similar to that of integers. You can observe the following steps below to see a summary on the order of operations when dealing with decimals and all the four operations.

  • Always look for brackets and simplify expressions within the brackets first.
  • Starting from left to right, perform multiplication or division next (whichever comes earlier).
  • Again from left to right, perform addition or subtraction next (whichever comes earlier).
  • Finally, simplify the expression.

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