A Guide to Decimals


When you write numbers in a base-10 numeral system, it is called decimal notation. Positional system involves a zero and symbols are used for ten values. It can represent a number irrespective of its size and the decimal separator is the indication of the start of a fractional part. The positions for each of the power of ten, hundreds, thousands are used by positional notation. Each position has a value of ten times more of the position on the right. The places to the left of the decimal point are ones, tens, hundreds and so on.

The place exactly to the right of the decimal is called the tenths place. However, the place exactly to the left of the decimal point is ones place. Therefore, in decimals, the tens place is two places to the left of the decimal. The decimal is right at the middle of the ones place and the tenths place. Moreover, you should know that the values which are positioned to the right of the decimal point, boasts a “th” ending.

Keep in Mind While Dealing with Decimals


Addition and Subtraction - If you are dealing with decimal numbers, you need to keep in mind the rules for adding or subtracting whole numbers but you need to be careful of placing the decimal point in the same column as it is placed above. Moreover, you need to use 0 to provide same number of decimal places, whenever one number has more decimal places than the other number.

Comparison - Comparing a decimal number can be little bit tricky as it does not go with the normal rule of number, which says that number with more digits is the larger one. In case of decimal numbers, first you need to consider the whole number portion first. If the number has more number of digits in the left part of the decimal then it is undoubtedly the larger number. However, in case of equal whole number, you need to assess the number towards the right of the decimal. Here, the number of digits doesn’t play any role. Assess them until you come to two different numbers and when you find that, the larger one among the two will make the larger number as a whole.

Multiplication – In case of multiplications in decimals, you should not take into account the decimals at the beginning. Just proceed with the multiplication like any other multiplication. Once you are done with the multiplication, then comes the question of placing the decimal. All you need to do is to count all the places to the right of the decimal and count that number of places in the product and place the decimal. The counting should be from right to left.

Division - If the dividend bears a decimal and the divisor doesn’t, then all you need to do is place the decimal in the quotient exactly above the decimal point in the dividend.

However, if both the divisor and the dividend bear decimal then you need to count the number of places, you need to move the decimal point in order to make the divisor a whole number. You also need to move the decimal exactly the same number of places in case of the dividend and then while dividing you need to place the decimal in the quotient exactly above the new decimal point.