Dividing Decimals: A perfect solution to a changing value
The most provocative of all basic operations is dividing decimals. Most people have had difficulties solving problems like this. And this is because the result isn’t always positive. Let’s just say for a research proposal, decimals are not the best options to base your study on. However, when dividing decimals, it’s pretty much easier to do so by rounding up numbers before solving them at all.
Dividing decimals is quite the same as dividing whole numbers, just that you have to pay much more attention to the decimal point’s position so as to determine the decimal places in the result. The decimal point in the divisor and the dividend is moved to the right, then divide as usual.
Most of the time, the divisor might not even be with the dividend, just put more zeroes to the right of the last digit of the dividend while you keep on dividing till it’s even. Also for dividing decimals, the decimal point position in the result should be placed above the dividend’s decimal point. Always check your result. This method applies if the divisor is not a whole number.
Aside from dividing decimals, multiplication of decimals is quite easy to do. First, we multiply the numbers normally while decimal points are being ignored, then a decimal point is added to the answer.
The use of rounds and estimates in dividing decimals
By rounding up numbers when dividing decimals, we make the number simpler while its value is intact and still solvable. Although the less accurate result is gotten, but this method is easier to use. Just as we apply a step by step procedure when writing an argumentative essay. When dividing decimals, we should first decide which of the last number to keep, but if this last digit is less than 5, we don’t change it. This is known as rounding down, but it is increased by 1 if the next number is more than 5. In this case, it’s rounding up.
To divide a decimal number by a whole number, such method of long division is used (note that you have to ignore the decimal point). The decimal point is placed at the same point, same goes to the dividend. Also, dividing decimals by their whole number has a trick which is changing the dividing number to a whole number while moving both their decimal point to the right side. This way, there will be more decimal places while the original two numbers are combined.
In dividing decimals, subtracting decimals is easier than any other. First, we write the numbers to be subtracted under each other making sure the decimal points are intact. The addition of zeroes such that the numbers have the same length, then we subtract normally without forgetting to add the decimal points to the answer as well.
The decimal numbers when dividing decimals have decimal points. This decimal point is between ones and tenths. For instance, 59.7 has 5 tens, 9 ones, and 7 tenths. This is very useful because of ‘place values’. When writing numbers, one crucial point to note is the place of every digit.
The significance of dividing decimals:
- solid understanding of operations
- find the product of whole numbers
- find the product of decimal numbers
- to be able to solve this problem in different ways
The history of dividing decimals
The history, in dissertation abstracts of modern methods for writing in dividing decimals started 500 years ago when fractions of decimals were used in Europe, medieval Arabia and also in ancient China. As of 1500, the decimals have been recognized worldwide. Years earlier (thousands), based on the 60 system, the place value of numbers had been used and it spreads to dealing with digits less than 1. Although in Europe, the base ten system advantages became apparent.
Simon Stevin of Bruges (Flemish Netherlands) was the founder and user of decimal fractions in dividing decimals. For example, the value of “pi” was written as 3.1416 approximately, meaning 3(0) 1 (1) 4 (2) 1 (3) 6 (4). John Napier, a Scottish mathematician used decimal fractions and also developed logarithms for calculations.
Far more centuries have adopted the use of place-value numeration in dividing decimals, ever before it could be used to solve fractions. Different range of symbols and notations which are used in differentiating numbers with fractions from whole numbers proved abortive until the acceptance of decimal fraction writing.
Here is an example of a table showing the different methods of writing fractions for dividing decimals
|Simon Stevin||1585||37 2 (1) 4(2) 5(3)|
Fraction of dividing decimals, on the other hand, is much interesting. It came to light just by observing nature, the division of days, months, years, and seasons. Also useful in trading as well. To begin with, rational numbers are a part of whole numbers representing the numbers.
The first ever to study this fraction (dividing decimals) are the Egyptians, also the use of fraction unit, as well as numerator having one with fractions. The calculation of geometric shape areas, volumes, plans, and constructions.
The use of alphabets to represent numbers in dividing decimals was brought about by the Babylon system. Take, for instance, a wedge with an arrow construction on it represents 10, a wedge represents 1, and so on. Their Pythagoreans triples of table serve the oldest theory in the history of numbers.
The use of continuous fractions in dividing decimals by Euclid’s algorithm cover letter in 300BC for solving equations of fractions was really helpful too. This was used in finding the largest denominator of two common numbers in architecture, harmonics, and also Greeks astrology.
Aryabhata from India also made use of continuous fractions in solving linear equations. He was already known for predicting the sun’s eclipse and that of the moon. The modern fraction theory by Leonard Euler explains that each rational number is expressed as a simple terminating fraction.
Dividing decimals as a Percent
The Percent of a number is one part in every 100. For the purpose of dividing decimals, this term has the symbol, “%” that comes in handy when writing a fraction of a common denominator of 100. For example, “1 in every 100 students are exceptional,” would be 1% of every student is exceptional. You can also write a percent in decimal form, and vice versa just by shifting the decimal point several times to the right side. For example; 0.17=17 %.
The symbol, “%” is also used in thesis definition for expressing percentage values. In dividing decimals, this is done Just by changing the percent of any given number to a decimal and then multiply. That way, it’s less difficult to find the percent of the given number. For example, eighteen percent means the fraction of 18/100 and also would be 0.18 in decimal.
Modern ways of dividing decimals
- Recently, when dividing decimals, we change the divisor. This is a number or digit to be divided by the dividend, which is changed to a whole number by shifting the decimal point to the right.
- shifting the dividend’s decimal point to the right, same number of places just as you’ve done to the divisor when dividing decimals.
- writing out the division problem
- placing zeroes in the empty spaces
- also in the dividend, you place numbers directly over the decimal point
- then finally, divide
Talking about multiplying and dividing integers, there are signs important to take note of. Unlike when dividing decimals, absolute values are the main target in dividing or multiplying signed integers. Two integers having the same signs gives positive results but two integers with different signs give a negative result. Also, dividing two integers of different signs give a negative result as well.
The systems of decimal numbers allow individuals to write out digits/numbers in any form of their choice. Either large or small, a system of number is converted into whole numbers for convenient problem solving. Remember, for writing of large or small numbers, we need decimal point.
System of numbers can be written to the left or the right of the decimal point just to differentiate numbers lesser than 1 from those greater than 1. This point gives information on how to place 1 and where it should be. Every digit that is placed from the right of the decimal point is divisible by 10.
To sum it up, decimal numbers can be really difficult to solve but the trick is changing the division problem to another format of whole numbers. This makes it quite easy to resolve. Write out the whole number as decimal until both have the same place of numbers at the right side of decimal point.
By moving points to the right till whole numbers appear, it makes the problem a whole number too. Also, write out the problem by using a long division. In doing so, you will be left only with long division problem using whole numbers. To solve long division problems, first you calculate how many times the divisor goes into the digit then place the number directly over the digit
Multiply digits with divisor, then subtract the leftover bringing down the next number. Finally, add the decimal point so as to extend the dividend. Remember, by rounding up numbers we make the number simpler while its value is intact and still solvable. Although the less accurate result is gotten, but this method is easier to use. Remember again that for dividing decimals, we first decide which of the last numbers to keep, but if this last digit is less than 5, we don’t change it. This is known as rounding down, but it is increased by 1 if the next number is more than 5. In this case, it’s rounding up.
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