In the form of an ordinary fraction, a decimal fraction. Converting a decimal fraction to a common fraction and vice versa: rule, examples

A fair number of people ask questions about how to convert a fraction to a decimal fraction. There are several ways. The choice of a specific method depends on the type of fraction that needs to be converted to another form, or more precisely, on the number in its denominator. However, for reliability, it is necessary to indicate that an ordinary fraction is a fraction that is written with a numerator and a denominator, for example, 1/2. More often, the line between the numerator and denominator is drawn horizontally rather than obliquely. A decimal fraction is written as an ordinary number with a comma: for example, 1.25; 0.35, etc.

So, in order to convert a fraction to a decimal without a calculator you need to:

Pay attention to the denominator common fraction. If the denominator can be easily multiplied up to 10 by the same number as the numerator, then you should use this method as the simplest. For example, the common fraction 1/2 is easily multiplied in the numerator and denominator by 5, resulting in the number 5/10, which can already be written as a decimal fraction: 0.5. This rule is based on the fact that a decimal fraction always has a round number in its denominator: 10, 100, 1000 and the like. Therefore, if you multiply the numerator and denominator of a fraction, then it is necessary to achieve exactly the same number in the denominator as a result of the multiplication, regardless of what is obtained in the numerator.

There are ordinary fractions, the calculation of which after multiplication presents certain difficulties. For example, it is quite difficult to determine how much the fraction 5/16 should be multiplied to get one of the above numbers in the denominator. In this case, you should use the usual division, which is done in a column. The answer should be a decimal fraction, which will mark the end of the transfer operation. In the example above, the resulting number is 0.3125. If columnar calculations are difficult, then you can’t do without the help of a calculator.

Finally, there are ordinary fractions that cannot be converted to decimals. For example, when converting the common fraction 4/3, the result is 1.33333, where the three is repeated ad infinitum. The calculator will also not get rid of the repeating three. There are several such fractions, you just need to know them. A way out of the above situation can be rounding, if the conditions of the example or problem being solved allow rounding. If the conditions do not allow this, and the answer must be written exactly in the form of a decimal fraction, it means that the example or problem was solved incorrectly, and you should go back several steps to find the error.

Thus, converting a fraction to a decimal is quite simple, and this task is not difficult to cope with without the help of a calculator. It is even easier to convert decimal fractions into ordinary fractions by performing the reverse steps described in method 1.

Video: 6th grade. Converting a fraction to a decimal.

A fraction is a number that is made up of one or more units. 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 are taken from the number, 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 = 5. Therefore, any whole number can be written as an ordinary improper fraction or a series of such fractions. Let's consider the entries of the same number in the form of a number of different ones.

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 notation is understood as the sum of the whole and its fractional part.

Decimals

A decimal is a special type 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, first indicate whole part, then the fractional part is fixed through a separator (period or comma).

The notation of a fractional part is always determined by its dimension. The decimal notation looks like this:

Rules for converting between different types of fractions

Converting a mixed fraction to a common fraction

A mixed fraction can only be converted to an improper fraction. To translate, it is necessary to bring the whole part to the same denominator as the fractional part. In general it will look like this:
Let's look at the use of this rule using specific examples:

Converting a common fraction to a mixed fraction

An improper fraction can be converted into a mixed fraction by simple division, resulting in the whole part and the remainder (fractional part).

For example, let's convert the fraction 439/31 to mixed:

Converting fractions

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 a power of 10.

For example:

In some cases, you may need to find the quotient by dividing by corners or using a calculator. And some fractions cannot be reduced to a final decimal. For example, the fraction 1/3 when divided will never give the final result.

A fraction can be converted to a whole number or decimal. An improper fraction, the numerator of which is greater than the denominator and is divisible by it without a remainder, is converted to a whole number, for example: 20/5. Divide 20 by 5 and get the number 4. If the fraction is proper, that is, the numerator is less than the denominator, then convert it to a number (decimal fraction). More information You can learn about fractions from our section -.

Ways to convert a fraction to a number

The first way to convert a fraction into a number is suitable for a fraction that can be converted to a number that is a decimal fraction. First, let's find out whether it is possible to convert the given fraction to a decimal fraction. To do this, let's pay attention to the denominator (the number that is below the line or to the right of the sloping line). If the denominator can be factorized (in our example - 2 and 5), which can be repeated, then this fraction can actually be converted into a final decimal fraction. For example: 11/40 =11/(2∙2∙2∙5). This common fraction will be converted to a number (decimal) with a finite number of decimal places. But the fraction 17/60 =17/(5∙2∙2∙3) will be converted into a number with an infinite number of decimal places. That is, when accurate calculation For a numerical value, it is quite difficult to determine the final decimal place, since there are an infinite number of such signs. Therefore, solving problems usually requires rounding the value to hundredths or thousandths. Next, you need to multiply both the numerator and the denominator by such a number so that the denominator produces the numbers 10, 100, 1000, etc. For example: 11/40 =(11∙25)/(40∙25) =275/1000 = 0.275
The second way to convert a fraction into a number is simpler: you need to divide the numerator by the denominator. To apply this method, we simply perform division, and the resulting number will be the desired decimal fraction. For example, you need to convert the fraction 2/15 into a number. Divide 2 by 15. We get 0.1333... - an infinite fraction. We write it like this: 0.13(3). If the fraction is improper, that is, the numerator is greater than the denominator (for example, 345/100), then converting it to a number will result in an integer numeric value or a decimal with a whole fractional part. In our example it will be 3.45. To convert mixed fraction such as 3 2 / 7 into a number, then you must first turn it into an improper fraction: (3∙7+2)/7 =23/7. Next, divide 23 by 7 and get the number 3.2857143, which we reduce to 3.29.

The easiest way to convert a fraction into a number is to use a calculator or other computing device. First we indicate the numerator of the fraction, then press the button with the “divide” icon and enter the denominator. After pressing the "=" key, we get the desired number.

Very often in school curriculum Mathematicians children are faced with the problem of how to convert a fraction to a decimal. In order to convert a common fraction to a decimal, let us first remember what a common fraction and a decimal are. An ordinary fraction is a fraction of the form m/n, where m is the numerator and n is the denominator. Example: 8/13; 6/7, etc. Fractions are divided into regular, improper and mixed numbers. A proper fraction is when the numerator is less than the denominator: m/n, where m 3. An improper fraction can always be represented as a mixed number, namely: 4/3 = 1 and 1/3;

Converting a fraction to a decimal

Now let's look at how to convert a mixed fraction to a decimal. Any common fraction, whether proper or improper, can be converted to a decimal. To do this, you need to divide the numerator by the denominator. Example: simple fraction (proper) 1/2. Divide numerator 1 by denominator 2 to get 0.5. Let's take the example of 45/12; it is immediately clear that this is an irregular fraction. Here the denominator is less than the numerator. Converting an improper fraction to a decimal: 45: 12 = 3.75.

Converting mixed numbers to decimals

Example: 25/8. First we transform mixed number into an improper fraction: 25/8 = 3x8+1/8 = 3 and 1/8; then divide the numerator equal to 1 by the denominator equal to 8, using a column or on a calculator and get a decimal fraction equal to 0.125. The article provides the easiest examples of conversion to decimal fractions. Having understood the translation technique into simple examples, you can easily solve the most difficult of them.

Then press the buttons and the task is completed. The result will be either a whole number or a decimal fraction. A decimal fraction may have a long remainder after . In this case, the fraction must be rounded to the specific digit you need, using rounding (numbers up to 5 are rounded down, from 5 inclusive and more - up).

If you don't have a calculator at hand, you will have to. Write the numerator of the fraction with the denominator, with a corner between them indicating . For example, convert the fraction 10/6 to a number. First, divide 10 by 6. You get 1. Write 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 the number 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. The remainder is again 4. You don’t have to continue further, since it becomes obvious that the result will be the number 1.66(6). Round this fraction to the digit you need. For example, 1.67. This is the final result.

Sources:

converting fractions with whole numbers

Fractions are used to represent numbers that consist of one or more parts of a unit. The term "fraction" comes from the Latin fractura, which means "to crush, break." There are differences between ordinary and decimal fractions. Moreover, in ordinary fractions, a unit can be divided into any number of parts, and in a decimal, this quantity must be a multiple of 10. Any fraction can be either ordinary or decimal.

You will need

To calculate the result you will need a calculator or a piece of paper and a pen.

Instructions

So, first, take a common 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 taken is the numerator, and the number of parts divided by is the denominator.

note

There are often fractions that cannot be completely converted to decimals. In this case, rounding comes to the rescue. If you want to round to the nearest thousand, look at the fourth decimal place. If it is less than 5, then write down the answer, the first three digits after the decimal point without changing, otherwise you must add one 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.

Helpful advice

If you are calculating the result manually, then before dividing the fraction it is better to reduce it as much as possible, and also separate whole parts from it.

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how to convert fractions

Fraction is one of the elements of formulas for entering in the Word word processor there is a Microsoft Equation tool. Using it, you can enter any complex mathematical or physical formulas, equations and other elements that include special characters.

Instructions

To launch the Microsoft Equation tool, you need to go to: “Insert” -> “Object”, in the dialog box that opens, on the first tab from the list you need to 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 dotted rectangle. The toolbar is divided into sections, each of which contains a set of action symbols or expressions. When you click on one of the sections, a list of tools located in it will expand. From the list that opens, select the desired symbol and click on it. Once selected, the specified symbol will appear in the selected rectangle in the document.

The section containing elements for writing fractions is located in the second line of the toolbar. When you hover your mouse over it, you will see the tooltip “Patterns of Fractions and Radicals”. Click the section once and expand the list. The drop-down menu contains templates for horizontal and oblique fractions. From the options that appear, you can choose the one that suits your task. Click on the desired option. After clicking, in the input field that opens 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 numerator input field. Enter the numerator. In addition to numbers, you can also enter symbols, letters or action signs. They can be entered either from the keyboard or from the corresponding sections of the Microsoft Equation toolbar. After the numerator, press the TAB key to move to the denominator. You can also go by clicking in the field to enter the denominator. Once written, click the mouse pointer anywhere in the document, the toolbar will close, and entering the fraction will be completed. To edit, double-click on it with the left mouse button.

If, when you open the “Insert” -> “Object” menu, you do not find the Microsoft Equation tool in the list, you need to install it. Run installation disk, disk image or Word distribution file. In the installer window that appears, select “Add or remove components. Add or remove individual components" and click "Next". In the next window, check the “Advanced application settings” option. Click Next. In the next window, find the “Office Tools” list item and click on the plus sign on the left. In the expanded list, we are interested in the “Formula Editor” item. 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.