Division has been shown to exist since the dawn of human civilization. For example, the Sumerians of Southern Mesopotamia, which dates back to 4100-1750 BCE, had their own division system. However, it is likely that division has existed for thousands of years before civilisation began. Ever since early man developed the concept of sharing, it is likely that division has existed. The spoils of every hunt would be divided into equal or hierarchical portions. Evidence shows that early man was capable of basic mathematics 20,000 years ago. Notched bones used to count were found in central Africa that date back to this time.
It is unclear who the true inventor of the decimal point is. Some sources say that the Scottish mathematician John Napier invented the decimal point. However, what he invented was a new system called logarithms that reduced multiplication to addition.
Before Napier, Dutch inventor Simon Stevin introduced the groundwork for a decimal point system. Before then, the accepted method amongst mathematicians was to use fractions with written notations. This incomplete system was later developed by John Napier, who developed a complete positional decimal point system.
However, even earlier examples of the decimal point system have existed for thousands of years. As far back as 3500-2500 BC, the Iranian Elamites used an early precursor to the decimal point system. The earliest use of a decimal point dates back to the Indus Valley civilization of 2600 BC. There is also some evidence to show that the Chinese used a decimal point system in their calendar around 1400 BC.
It is because of these evolutions in the decimal system that we have simple formulas to perform decimal division. As famous mathematician Sir Isaac Newtown once wrote:
"If I have seen further, it is by standing on the shoulders of Giants."
This article will show you how to perform decimal division using several examples.
The first, simplest, and most accurate way to perform decimal division is to use a calculator. The advancement of technology means that most people have a calculator in their pocket at any one time. Mobile phones have built-in calculators, meaning the need for an external calculator is almost redundant.
Furthermore, if you have lost your phone, you can still use an online calculator using a different device. For example, you could use a laptop, desktop, or tablet to access the website. All you need is an internet connection and away you go.
The calculator will do all the leg work for you, decreasing the chance of human error in the process. However, in some cases, it may not be possible to have a mobile phone, calculator, or internet device to do it for you. This is when you need to put your brain to work and do some calculations on your own. The methods below will show you how to do this.
How do I divide decimals using a whole number?
It is much easier to divide by a decimal number if you turn it into a whole number. For example, if we have the problem 15 divided by 0.2 we should turn it into a whole number. To do this, times the divisor by 10 until it is a whole number.
So, 0.2 x 10 = 2
When you multiply the divisor by 10 you also have to multiply the dividend by the same number.
Therefore, 15 x 10 = 150
The new figures become, 150 ÷ 2 = 75
This means the correct answer for 15 ÷ 0.2 is 75.
How do I divide two decimal numbers?
To do this, you will again multiply both decimal numbers by 10. It is rather straightforward to multiply decimal numbers by 10. Just move the decimal place to the right by one place. For example, if we take the sum of 6.4 divided by 0.4.
The 6.4 dividend becomes 64, and the 0.4 divisor becomes 4. This creates a new division problem. This is:
64 ÷ 4 = 16.
This means that 6.4 ÷ 0.4 is also 16.
How do I divide decimals using long division?
It is not always possible to divide decimals by first converting them to a whole number. However, there is another method of dividing decimals that do not immediately convert to whole numbers.
We will use the division problem: 10.274 divided by 0.11 as an example.
First, you need to turn the divisor (0.11) into a whole number. So, move the decimal point by two decimal points to the right. This gives you the divisor 11.
You also need to move the decimal point of the dividend by the same number of decimal places to the right. This gives you a figure of 1027.4. So, 11/1027.4 is the new calculation. A decimal point should then be placed above and in line with the below decimal.
The number 11 is too big to go into the first two numbers of 1027.4, (1 and 10). So, instead, you need to divide 102 by 11 which gives a figure of 9. You then place that 9 above the 2 in the sum 11/1027.4.
Next, you bring down the 7. You can then divide 37 by 11 three times. The next number in your answer should be placed just above the 7 in the division problem 11/1027.4. So the 9 should be above the 2, and the 3 should be above the 7.
If you bring the next number down (4) you now get 44. Then, 44 divided by 11 is 4. Put the next number in the quotient (4) directly above the 4 in 11/1027.4. So above the 1027.4 part of the division is figure 93.4. This means that the final answer for 10.274 divided by 0.11 is 93.4.
The main point to remember when you divide numbers this way is to make sure the decimal points and the numbers are placed in the correct place.