Decimal numbers such as 0.2; 1.05; 3.017 etc. as they are heard, so they are written. Zero point two, we get a fraction. One whole five hundredths, we get a fraction. Three whole seventeen thousandths, we get a fraction. The digits before the decimal point in a decimal number are whole part fractions. The number after the decimal point is the numerator of the future fraction. If after the comma single digit- the denominator will be 10, if two-digit - 100, three-digit - 1000, etc. Some of the resulting fractions can be reduced. In our examples

Converting a fraction to a decimal number

This is the reverse of the previous transformation. What is a decimal fraction? Her denominator is always 10, or 100, or 1000, or 10,000, and so on. If your usual fraction has such a denominator, there is no problem. For example, or

If a fraction, for example . In this case, you need to use the basic property of a fraction and convert the denominator to 10 or 100, or 1000 ... In our example, if we multiply the numerator and denominator by 4, we get a fraction that can be written as decimal number 0,12.

Some fractions are easier to divide than to convert the denominator. For example,

Some fractions cannot be converted to decimal numbers!
For example,

Converting a mixed fraction to an improper

A mixed fraction, such as , is easily converted to an improper fraction. To do this, you need to multiply the integer part by the denominator (bottom) and add it to the numerator (top), leaving the denominator (bottom) unchanged. That is

When converting a mixed fraction to an improper one, you can remember that you can use the addition of fractions

Converting an improper fraction to a mixed one (highlighting the whole part)

An improper fraction can be converted to a mixed fraction by highlighting the whole part. Consider an example, . Determine how many integer times "3" fit in "23". Or we divide 23 by 3 on the calculator, the whole number up to the decimal point is the desired one. This is "7". Next, we determine the numerator of the future fraction: we multiply the resulting "7" by the denominator "3" and subtract the result from the numerator "23". How would we find the excess that remains from the numerator "23", if we remove the maximum number of "3". The denominator is left unchanged. Everything is done, write down the result

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.

Useful advice

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 the 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 the 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 menu "Insert" -> "Object", 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 can be converted to an integer or decimal. An improper fraction, the numerator of which is greater than the denominator and is divisible by it without a remainder, is converted into an integer, for example: 20/5. Divide 20 by 5 and get the number 4. If the fraction is correct, that is, the numerator is less than the denominator, then convert it to a number (decimal fraction). You can learn more about fractions from our section -.

Ways to convert a fraction to a number

• The first way to convert a fraction to 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 a given fraction into a decimal fraction. To do this, pay attention to the denominator (the number that is under the line or to the right of the oblique). If the denominator can be decomposed into factors (in our example - 2 and 5), which can be repeated, then this fraction can really be converted into a final decimal fraction. For example: 11/40 =11/(2∙2∙2∙5). This common fraction will be converted into a number (decimal fraction) with a finite number of decimal places. But the fraction 17/60 =17/(5∙2∙2∙3) will be translated into a number with an infinite number of decimal places. That is, when accurately calculating a numerical value, it is quite difficult to determine the final sign after the decimal point, since there are an infinite number of such signs. Therefore, to solve problems, you usually need to round the value to hundredths or thousandths. Further, it is necessary to multiply both the numerator and the denominator by such a number that the denominator will have 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 to a number is simpler: you need to divide the numerator by the denominator. To apply this method, we simply perform the division, and the resulting number will be the desired decimal fraction. For example, you need to convert the fraction 2/15 to a number. Divide 2 by 15. We get 0, 1333 ... - infinite fraction. We write it down like this: 0.13(3). If the fraction is incorrect, that is, the numerator is greater than the denominator (for example, 345/100), then as a result of converting it to a number, an integer numerical value or a decimal fraction with an integer fractional part will be obtained. In our example, this 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 \u003d 23/7. Next, we divide 23 by 7 and get the number 3.2857143, which we reduce to 3.29.

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

In dry mathematical terms, a fraction is a number that is represented as a fraction of a unit. Fractions are widely used in human life: with the help of fractional numbers, we indicate proportions in culinary recipes, set decimal marks in competitions, or use them to calculate discounts in stores.

Representation of fractions

There are at least two forms of writing one fractional number: in decimal form or in the form common fraction. In decimal form, numbers look like 0.5; 0.25 or 1.375. We can represent any of these values ​​as an ordinary fraction:

• 0,5 = 1/2;
• 0,25 = 1/4;
• 1,375 = 11/8.

And if we easily convert 0.5 and 0.25 from an ordinary fraction to a decimal and vice versa, then in the case of the number 1.375, everything is not obvious. How to quickly convert any decimal number to a fraction? There are three easy ways.

Getting rid of the comma

The simplest algorithm involves multiplying a number by 10 until the comma disappears from the numerator. This transformation is carried out in three steps:

Step 1: To begin with, we will write the decimal number as a fraction “number / 1”, that is, we will get 0.5 / 1; 0.25/1 and 1.375/1.

Step 2: After that, multiply the numerator and denominator of new fractions until the comma disappears from the numerators:

• 0,5/1 = 5/10;
• 0,25/1 = 2,5/10 = 25/100;
• 1,375/1 = 13,75/10 = 137,5/100 = 1375/1000.

Step 3: We reduce the resulting fractions to a digestible form:

• 5/10 = 1 x 5 / 2 x 5 = 1/2;
• 25/100 = 1 x 25 / 4 x 25 = 1/4;
• 1375/1000 = 11 x 125 / 8 x 125 = 11/8.

The number 1.375 had to be multiplied by 10 three times, which is no longer very convenient, but what will we have to do if we need to convert the number 0.000625? In this situation, we use the following method for converting fractions.

Getting rid of the comma is even easier

The first method describes in detail the algorithm for "removing" a comma from a decimal fraction, however, we can simplify this process. Again, we follow three steps.

Step 1: We consider how many digits are after the decimal point. For example, the number 1.375 has three such digits, and 0.000625 has six. We will denote this number by the letter n.

Step 2: Now it is enough for us to represent the fraction in the form C/10 n , where C are the significant digits of the fraction (without zeros, if any), and n is the number of digits after the decimal point. For example:

• for the number 1.375 C \u003d 1375, n \u003d 3, the final fraction according to the formula 1375/10 3 \u003d 1375/1000;
• for the number 0.000625 C \u003d 625, n \u003d 6, the final fraction according to the formula 625/10 6 \u003d 625/1000000.

Essentially, 10n is 1 with n zeros, so you don't have to worry about raising the tens to a power - just specify 1 with n zeros. After that, it is desirable to reduce the fraction so rich in zeros.

Step 3: Reduce the zeros and get the final result:

• 1375/1000 = 11 x 125 / 8 x 125 = 11/8;
• 625/1000000 = 1 x 625/ 1600 x 625 = 1/1600.

The fraction 11/8 is improper fraction, since its numerator is greater than its denominator, which means that we can select the whole part. In this situation, we subtract the whole part of 8/8 from 11/8 and get the remainder 3/8, therefore, the fraction looks like 1 and 3/8.

Transformation by ear

For those who know how to read decimals correctly, it is easiest to convert them by ear. If you read 0.025 not as "zero, zero, twenty-five", but as "25 thousandths", then you will have no problem converting decimal numbers to common fractions.

0,025 = 25/1000 = 1/40

Thus, the correct reading of the decimal number allows you to immediately write it as an ordinary fraction and reduce it if necessary.

Examples of using fractions in everyday life

At first glance, common fractions are practically not used in everyday life or at work, and it is difficult to imagine a situation where you need to convert a decimal fraction to a common one outside school tasks. Let's look at a couple of examples.

Work

So, you work in a candy store and sell halva by weight. For ease of sale of the product, you divide halva into kilogram briquettes, but few buyers are ready to purchase a whole kilogram. Therefore, you have to divide the treat into pieces every time. And if another buyer asks you for 0.4 kg of halva, you will sell him the right portion without any problems.

0,4 = 4/10 = 2/5

Life

For example, you need to make a 12% solution for painting the model in the shade you need. To do this, you need to mix paint and thinner, but how to do it right? 12% is a decimal fraction of 0.12. We convert the number to an ordinary fraction and get:

0,12 = 12/100 = 3/25

Knowing the fractions, you can mix the components correctly and get the right color.

Conclusion

Fractions are widely used in everyday life, so if you often need to convert decimals to fractions, you will need an online calculator that can instantly get the result in the form of an already reduced fraction.