Converting common fractions to decimals. Calculator online. Converting a decimal fraction to an ordinary
A large number of students, and not only, are wondering how to convert a fraction into a number. To do this, there are several fairly simple and understandable ways. The choice of a particular method depends on the preferences of the decider.
First of all, you need to know how fractions are written. And they are written as follows:
- Ordinary. It is written with the numerator and denominator through an oblique or column (1/2).
- Decimal. It is written separated by commas (1.0, 2.5, and so on).
Before proceeding with the solution, you need to know what an improper fraction is, because it occurs quite often. It has a numerator greater than the denominator, such as 15/6. An improper fraction can also be solved in these ways, without any effort and time.
A mixed number is when the result is an integer and a fractional part, for example 52/3.
Any natural number can be written as a fraction with completely different natural denominators, for example: 1= 2/2=3/3 = etc.
You can also translate using a calculator, but not all of them have such a function. There is a special engineering calculator, where there is such a function, but it is not always possible to use it, especially at school. Therefore, it is better to understand this topic.
The first step is to pay attention to what kind of fraction. If it can be easily multiplied up to 10 by the same values as the numerator, then you can use the first method. For example: an ordinary ½ is multiplied in the numerator and denominator by 5 and you get 5/10, which can be written as 0.5.
This rule is based on the fact that the decimal always has a round value in the denominator, such as 10,100,1000 and so on.
It follows from this that if you multiply the numerator and denominator, then you need to achieve exactly this value in the denominator as a result of multiplication, regardless of what comes out in the numerator.
It is worth remembering that some fractions cannot be translated; for this, it is necessary to check it before starting the solution.
For example: 1.3333, where the number 3 is repeated indefinitely, and the calculator will not get rid of it either. The solution to such a problem can only be rounding so that an integer is obtained, if possible. If this is not possible, then you should return to the beginning of the example and check the correctness of the solution to the problem, perhaps a mistake was made.
Figure 1-3. Translation of fractions by multiplication.
Consider to consolidate the described information next example translation:
- For example, you need to convert 6/20 to decimal. First of all, it should be checked, as shown in Figure 1.
- Only after making sure that it is possible to decompose, as in this case on 2 and 5, you need to proceed to the translation itself.
- Most simple option will multiply the denominator, getting the result 100, is 5, since 20x5=100.
- Following the example in figure 2, the result is 0.3.
You can fix the result and look at everything again according to Figure 3. In order to fully understand the topic and no longer resort to studying this material. This knowledge will help not only the child, but also the adult.
Translation by division
The second option for translating fractions is a little more complicated, but more popular. This method is mainly used in schools by teachers for explanation. In general, it is much easier to explain and understand faster.
It is worth remembering that for the correct conversion of a simple fraction, it is necessary to divide its numerator by the denominator. After all, if you think about it, then the decision is the process of division.
In order to understand this simple rule, consider the following example solution:
- Let's take 78/200, which needs to be converted to decimal. To do this, divide 78 by 200, that is, the numerator by the denominator.
- But before you start, it is worth checking, as shown in Figure 4.
- After you are convinced that it can be solved, you should begin the process. To do this, it is worth dividing the numerator by the denominator in a column or corner, as shown in Figure 5. In primary school Schools teach this division, and there should be no difficulty in doing so.
Figure 6 shows examples of the most common examples, they can simply be memorized so as not to waste time on a solution if necessary. Indeed, at school for each control or independent work little time is given to solve, so do not waste it on something that can be learned and simply remembered.
Interest transfer
Converting percentages to decimals is also quite easy. This is taught in the 5th grade, and in some schools even earlier. But if your child did not understand this topic in a mathematics lesson, you can clearly explain it to him again. First you need to learn the definition of what a percentage is.
A percentage is one hundredth of a number, in other words, absolutely arbitrary. For example, from 100 it will be 1 and so on.
Figure 7 shows good example interest transfer.
To convert a percentage, you just need to remove the% sign, and then divide it by 100.
Another example is shown in Figure 8.
If you need to carry out the reverse "conversion", you must do everything exactly the opposite. In other words, the number must be multiplied by one hundred and then assigned a percent sign.
And in order to convert the usual into percentages, you can also use this example. Only initially should the fraction be converted to a number, and only then to a percentage.
Based on the above, you can easily understand the principle of translation. Using these methods, you can explain the topic to the child if he did not understand it or was not present at the lesson at the time of its passage.
And there will never be a need to hire a tutor to explain to the child how to convert a fraction to a number or percentage.
Trying to solve mathematical problems with fractions, the student realizes that it is not enough for him to just want to solve these problems. Knowledge of calculations with fractional numbers is also required. In some problems, all initial data are supplied in the condition in fractional form. In others, some of them may be fractions, and some may be whole numbers. To perform any calculations with these given values, we must first bring them to single species, that is, translate integer numbers into fractional ones, and then do the calculations. In general, the way to convert an integer to a fraction is very simple. To do this, write the given number itself in the numerator of the final fraction, and one in its denominator. That is, if you need to convert the number 12 into a fraction, then the resulting fraction will be 12/1.
Such modifications help to reduce fractions to common denominator. This is necessary in order to be able to subtract or add fractional numbers. When multiplying and dividing them, a common denominator is not required. You can consider an example of how to convert a number into a fraction and then add two fractional numbers. Suppose you need to add the number 12 and the fractional number 3/4. The first term (the number 12) is reduced to the form 12/1. However, its denominator is 1, while the second term is 4. For the subsequent addition of these two fractions, they must be reduced to a common denominator. Due to the fact that one of the numbers has a denominator equal to 1, this is generally easy to do. It is necessary to take the denominator of the second number and multiply by it both the numerator and the denominator of the first.
The result of multiplication will be: 12/1=48/4. If 48 is divided by 4, then 12 is obtained, which means that the fraction is reduced to the correct denominator. Thus, at the same time, you can understand how to translate a fraction into an integer. This only applies to improper fractions, because they have a larger numerator than a denominator. In this case, the numerator is divided by the denominator and, if there is no remainder, there will be an integer. With the remainder, the fraction remains a fraction, but with the selected integer part. Now regarding the reduction to a common denominator in the considered example. If the first term had a denominator equal to some other number than 1, the numerator and denominator of the first number would have to be multiplied by the denominator of the second, and the numerator and denominator of the second by the denominator of the first.
Both terms are reduced to their common denominator and are ready for addition. It turns out that in this problem you need to add two numbers: 48/4 and 3/4. When adding two fractions with the same denominator, you only need to sum their upper parts, that is, the numerators. The denominator of the sum will remain unchanged. In this example, it should be 48/4+3/4=(48+3) /4=51/4. This will be the result of the addition. But in mathematics it is customary to reduce improper fractions to proper ones. Above, it was considered how to turn a fraction into a number, but in this example, an integer will not be obtained from the fraction 51/4, since the number 51 is not divisible without a remainder by the number 4. Therefore, you need to select the integer part of this fraction and its fractional part. The integer part will be the number that is obtained by dividing by an integer the first number less than 51.
That is, one that can be divided by 4 without a remainder. The first number in front of the number 51, which is completely divisible by 4, will be the number 48. Dividing 48 by 4, the number 12 is obtained. This means that the integer part of the required fraction will be 12. It remains only to find the fractional part of the number. The denominator of the fractional part remains the same, i.e. 4 in this case. To find the numerator of the fractional part, it is necessary to subtract from the original numerator the number that was divided by the denominator without a remainder. In this example, it is required to subtract the number 48 from the number 51. That is, the numerator of the fractional part is 3. The result of the addition will be 12 integers and 3/4. The same is true when subtracting fractions. Suppose you need to subtract the fractional number 3/4 from the integer 12. To do this, the integer 12 is converted into a fractional 12/1, and then reduced to a common denominator with the second number - 48/4.
When subtracting in the same way, the denominator of both fractions remains unchanged, and subtraction is carried out with their numerators. That is, the numerator of the second is subtracted from the numerator of the first fraction. IN this example it will be 48/4-3/4=(48-3) /4=45/4. And again it turned out to be an improper fraction, which must be reduced to the correct one. To select the integer part, the first number up to 45 is determined, which is divisible by 4 without a remainder. It will be 44. If the number 44 is divided by 4, you get 11. So the integer part of the final fraction is 11. In the fractional part, the denominator is also left unchanged, and the number that was divided by the denominator without a remainder is subtracted from the numerator of the original improper fraction. That is, it is necessary to subtract 44 from 45. So the numerator in the fractional part is 1 and 12-3/4=11 and 1/4.
If one integer and one fractional number is given, but its denominator is 10, then it is easier to convert the second number into a decimal fraction, and then perform calculations. For example, you need to add the integer 12 and the fractional number 3/10. If the number 3/10 is written as decimal fraction, you get 0.3. Now it is much easier to add 0.3 to 12 and get 2.3 than to bring fractions to a common denominator, perform calculations, and then extract the integer and fractional parts from an improper fraction. Even the simplest problems with fractional numbers assume that the student (or student) knows how to convert an integer to a fraction. These rules are too simple and easy to remember. But with the help of them it is very easy to carry out calculations of fractional numbers.
Then press the buttons, and the task is completed. As a result, you will get either an integer or a decimal fraction. A decimal fraction can have a long remainder after . In this case, the fraction must be rounded to a certain digit you need using rounding (numbers up to 5 are rounded down, from 5 inclusive and more - up).
If the calculator is not at hand, but you will have to. Write the numerator of a fraction with a denominator, between them a little corner, meaning. For example, convert the fraction 10/6 to a number. To begin with, divide 10 by 6. It turns out 1. Write down the result in a corner. Multiply 1 by 6, you get 6. Subtract 6 from 10. You get a remainder of 4. The remainder must be divided by 6 again. Add 0 to 4, and divide 40 by 6. You get 6. Write 6 in the result, after the decimal point. Multiply 6 by 6. You get 36. Subtract 36 from 40. You get the remainder again 4. Then you can not continue, because it becomes obvious that the result will be the number 1.66 (6). Round the given fraction to the digit you need. For example, 1.67. This is the final result.
Related article
Sources:
- converting fractions to whole numbers
Fractions are needed to denote numbers that consist of one or more parts of the unit. The term "fraction" comes from the Latin fractura, which means "to crush, break". There are ordinary and decimal fractions. At the same time, in ordinary fractions, a unit can be divided into any number of parts, and in decimal fractions, this number must be a multiple of 10. Any fraction can be both ordinary and decimal.
You will need
- To calculate the result, you will need a calculator or a piece of paper and a pen.
Instruction
So, for starters, take an ordinary fraction and divide it into parts. For example, 2 1/8, in which 2 is an integer part, and 1/8 is a fraction. From it you can see that the number was divided by 8, but only one was taken. The part that was taken is the numerator, and the number of parts into which it is divided is the denominator.
note
Often there are fractions that cannot be fully converted to decimals. This is where rounding comes in handy. If you want to round to thousandths, then look at the fourth number after the decimal point. If it is less than 5, then write down in response, the first three digits after the decimal point without change, otherwise, one must be added to the last digit of the three. For example, 0.89643123 can be written as 0.896, but 0.89663123 can be written as 0.897.
If you calculate the result manually, then before dividing the fraction, it is better to reduce it as much as possible, and also to select whole parts from it.
Sources:
- how to convert fractions
Fraction is one of the elements of formulas for the input of which in the word processor Word there is a Microsoft Equation tool. With it, you can enter any complex mathematical or physical formulas, equations and other elements that include special characters.
Instruction
To launch the Microsoft Equation tool, you need to go to the address: "Insert" -> "Object", in the dialog box that opens, on the first tab from the list, select Microsoft Equation and click "OK" or double-click on the selected item. After launching the editor, a toolbar will open in front of you and an input field will be displayed: a rectangle in a dotted one. The toolbar is divided into sections, each of which contains a set of action signs or expressions. When you click on one of the sections, a list of the tools in it will expand. From the list that opens, select desired symbol and click on it. Once selected, the specified character will appear in a selected rectangle in the document.
The section that contains elements for writing fractions is located in the second line of the toolbar. When you hover your mouse cursor over it, you will see the tooltip "Fraction and Radical Patterns". Click a section once and expand the list. The drop-down menu has templates for horizontal and oblique fractions. Among the options that appear, you can choose the one that suits your task. Click on desired option. After clicking, in the input field that opened in the document, a fraction symbol and places for entering the numerator and denominator, framed by a dotted line, will appear. The default cursor is automatically placed in the field for entering the numerator. Enter the numerator. In addition to numbers, you can also enter symbols, letters, or action signs. They can be entered both from the keyboard and from the corresponding sections of the Microsoft Equation toolbar. After the numerator water, press the TAB key to move to the denominator. You can also go by clicking the mouse in the field for entering the denominator. Once written, click with the mouse pointer anywhere in the document, the toolbar will close, the fraction input will be completed. To edit , double-click on it with the left mouse button.
If, when you open the "Insert" -> "Object" menu, you did not find the Microsoft Equation tool in the list, you need to install it. Run the installation disc, disc image, or Word distribution file. In the installer window that appears, select "Add or remove components. Adding or removing individual components" and click "Next". In the next window, check the item "Advanced application settings". Click next. In the next window, find the list item "Office Tools" and click on the plus sign on the left. In the expanded list, we are interested in the item "Formula Editor". Click on the icon next to "Formula Editor" and, in the menu that opens, click "Run from computer". After that, click "Update" and wait until the required component is installed.
A fraction is a number that consists of one or more fractions of a unit. There are three types of fractions in mathematics: common, mixed, and decimal.
Common fractions
An ordinary fraction is written as a ratio in which the numerator reflects how many parts of the number are taken, and the denominator shows how many parts the unit is divided into. If the numerator is less than the denominator, then we have a proper fraction. For example: ½, 3/5, 8/9.
If the numerator is equal to or greater than the denominator, then we are dealing with an improper fraction. For example: 5/5, 9/4, 5/2 Dividing the numerator can result in a finite number. For example, 40/8 \u003d 5. Therefore, any integer can be written as an ordinary improper fraction or a series of such fractions. Consider writing the same number as a series of different .
- mixed fractions
IN general view A mixed fraction can be represented by the formula: 
Thus, a mixed fraction is written as an integer and an ordinary proper fraction, and such a record is understood as the sum of a whole and its fractional part.
- Decimals
A decimal is a special kind of fraction in which the denominator can be represented as a power of 10. There are infinite and finite decimals. When writing this type of fraction, the integer part is first indicated, then the fractional part is fixed through the separator (dot or comma).
The record of the fractional part is always determined by its dimension. Decimal notation as follows: 
Translation rules between different types of fractions
- Converting a mixed fraction to a common fraction
A mixed fraction can only be converted to an improper fraction. For translation, it is necessary to bring the whole part to the same denominator as the fractional part. In general, it will look like this: 
Consider the use of this rule on specific examples:
- Converting an ordinary fraction to a mixed one
An improper common fraction can be converted into a mixed one by simple division, which results in the integer part and the remainder (fractional part).
For example, let's translate the fraction 439/31 into a mixed one: 
- Translation of an ordinary fraction
In some cases, converting a fraction to a decimal is quite simple. In this case, the basic property of a fraction is applied, the numerator and denominator are multiplied by the same number, in order to bring the divisor to the power of 10.
For example:
In some cases, you may need to find the quotient by dividing by a corner or using a calculator. And some fractions cannot be reduced to a final decimal fraction. For example, the fraction 1/3 will never give the final result when divided.
Materials on fractions and study sequentially. below for you detailed information with examples and explanations.
1. Mixed number into a common fraction.Let's write the number in general form:
We remember a simple rule - we multiply the whole part by the denominator and add the numerator, that is:
Examples:
2. On the contrary, an ordinary fraction into a mixed number. *Of course, this can only be done with an improper fraction (when the numerator is greater than the denominator).
With “small” numbers, no action, in general, needs to be done, the result is “seen” immediately, for example, fractions:
*Details:
15:13 = 1 remainder 2
4:3 = 1 remainder 1
9:5 = 1 remainder 4
But if the numbers are more, then you can’t do without calculations. Everything is simple here - we divide the numerator by the denominator by a corner until the remainder is less than the divisor. Division scheme:
For example:
* The numerator is the dividend, the denominator is the divisor.
We get the integer part (incomplete quotient) and the remainder. We write down - an integer, then a fraction (there is a remainder in the numerator, and we leave the denominator the same):
3. We translate the decimal into an ordinary one.
Partially in the first paragraph, where we talked about decimal fractions, we have already touched on this. As we hear, so we write. For example - 0.3; 0.45; 0.008; 4.38; 10.00015
We have the first three fractions without an integer part. And the fourth and fifth have it, we will translate them into ordinary ones, we already know how to do this:
*We see that fractions can also be reduced, for example, 45/100 = 9/20, 38/100 = 19/50 and others, but we will not do this here. For reduction, a separate paragraph awaits you below, where we will analyze everything in detail.
4. Ordinary translate into decimal.
It's not all that simple. For some fractions, you can immediately see and clearly what to do with it so that it becomes decimal, for example:
We use our wonderful basic property of a fraction - we multiply the numerator and denominator, respectively, by 5, 25, 2, 5, 4, 2, we get:
If there is an integer part, then nothing complicated either:
We multiply the fractional part, respectively, by 2, 25, 2 and 5, we get:
And there are those for which, without experience, it is impossible to determine that they can be converted into decimals, for example:
What numbers should you multiply the numerator and denominator by?
Here again, a proven method comes to the rescue - division by a corner, a universal method, you can always use it to convert an ordinary fraction to a decimal:
So you can always determine whether a fraction is converted to a decimal. The fact is that not every ordinary fraction can be converted to decimal, for example, such as 1/9, 3/7, 7/26 are not translated. And what then turns out for a fraction when dividing 1 by 9, 3 by 7, 5 by 11? I answer - infinite decimal (we talked about them in paragraph 1). Let's divide:
That's all! Good luck to you!
Sincerely, Alexander Krutitskikh.
