1. Decimal Numbers
Decimal numbers are used to display the whole number and fraction together. This whole number and fractional part are separated by inserting a ‘.’, which is known as the decimal point. For example, you are going to buy some grocery items. The store manager says the total bill is £15 and 57 pence. So, to express this amount in one figure, you will express this amount as £15.57. There are many such real-life situations using decimal numbers. We use decimal numbers in our daily lives with money, weight, distance, length, etc.
Decimals lie between integers on the number line. They are one of the ways of representing fractions in Maths.
1.1 Reading Decimal Numbers
The method of reading a decimal number is to first read the whole number followed by ‘point’, then to read the digits in the fractional part separately. For example, we read 96.37 as ninety-six point three seven.
2. What is Decimal Manipulation?
Decimal manipulation refers to performing various mathematical operations such as addition, subtraction, multiplication, and division on decimal numbers. Decimal numbers are numbers with one or more digits to the right of the decimal point.
Here are some examples of decimal manipulation:
2.1 Addition
To add two decimal numbers, align the decimal points and add the digits in each place value column.
For example, to add 3.14 and 2.67, we align the decimal points and add 4 + 7 in the tenths place, 1 + 6 in the hundredths place, and 3 + 2 in the ones place, giving us a total of 5.81.
2.2 Subtraction
To subtract one decimal number from another, align the decimal points and subtract the digits in each place value column.
For example, to subtract 2.67 from 3.14, we align the decimal points and subtract 7 from 4 in the tenths place, 1 from 6 in the hundredths place, and 3 from 2 in the ones place, giving us a difference of 0.47.
For example:
a) 4.031 + 5.2 b) 9.563 - 4.42
2.3 Multiplication
To multiply two decimal numbers, ignore the decimal points, multiply the numbers as if they were whole numbers, and count the total number of decimal places in both numbers.
For example:
a) 75 x 1.5
b) 3.5 x 1.5
For example, to multiply 3.14 by 2.67, we multiply 314 by 267, which gives us 83738, and count a total of 4 decimal places (2 in 3.14 and 2 in 2.67). We then place the decimal point in the product 2 places from the right, giving us 8.378.
2.4 Division
To divide a decimal number by another decimal number, move the decimal point of the divisor to the right until it becomes a whole number, move the decimal point of the dividend the same number of places to the right, perform the division as if it were a whole number, and then move the decimal point in the quotient back to its original position.
For example, to divide 3.14 by 2.67, we move the decimal point of 2.67 two places to the right, giving us 267, and move the decimal point of 3.14 two places to the right as well, giving us 314. We then perform the division 314 ÷ 267, which gives us a quotient of 1.176. We then move the decimal point in the quotient back to its original position, giving us 1.176 rounded to 3 decimal places.
For example: Divide 338.56 by 16.
2.5 Rounding
To round a decimal number to a certain number of decimal places, find the digit in that place and look at the digit to the right. If it is 5 or greater, round up. If it is less than 5, round down.
For example: 3.45678 rounded to 2 decimal places is 3.46.
7.84321 rounded to 1 decimal place is 7.8.
