Convert decimals to fractions worksheet: Grade 5 Math Worksheets: Convert decimals to fractions

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Converting Decimals to Fractions (10ths & 100ths)

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4 ways to replace a dot with a comma in Excel

A dot instead of a comma for fractional numbers can lead to significant consequences when calculating in Excel. Most often, such errors occur when data is imported into a table from other sources.

If fractional numbers have a dot instead of a comma, the program automatically treats them as a text data type. Therefore, before performing mathematical calculations and calculations, you should format and prepare the imported data.

Select and copy the data from the table below:

9002 3

No.	Currency pair	Translation	Sell	Buy 9001 2	Spread
1	EUR/USD	1	1.1347	1.1350	0.0003
2	GBP/USD	1	1.5438	1.5442	0.0004
3	USD/CHF	1	0.9543	0.9547	0.0004
4	USD/JP Y	100	1.1948	1.1945	-0.0003

Now go to your worksheet and right click on cell A1. From the context menu that appears, select the Paste Special option. In the dialog box, select Unicode Text and click OK.

As you can see, Excel only recognizes numbers in column C. The values ​​in this column are right-aligned. Left in other columns. In all cells, the default format is «General», and in cells D3, D5, E3, E5, the format «Date» is generally displayed. We copied the data through special paste and all formats of the original table are eliminated. There is only one reason — instead of a comma there is a dot. This data type is not prepared and cannot be used for calculations.

Note. If you copy data from other sources without a special paste, then the format is copied along with the data. In such cases, the «General» (default) cell format can be changed. Then it is impossible to visually distinguish where the number is recognized, and where the text is.

All subsequent steps must be performed from scratch. Delete everything on the sheet or open a new one for further work.

There are 4 ways to replace a dot with a comma in imported data:



Method 1 replacing a dot with a comma in Excel using Notepad

Windows Notepad does not require the use of complex settings and functions, but only acts as an intermediary in copying and pre-preparing data.

1. Copy the data from the original label on this page. Open the Windows Notepad program (Start — All Programs — Accessories — Notepad) and paste the copied data into it for preparation.
2. Select the «Replace» option from the «Edit» menu (or the hot key combination CTRL+H). In the dialog box that appears, enter a period (.) in the What field and a comma (,) in the What field. And click the «Replace All» button.

Notepad has replaced all dots with commas. The data is now ready to be copied and pasted onto the worksheet.

This is a very simple but very effective method.

Method 2 temporarily change Excel settings

Before you change the dot to comma in Excel, evaluate the task correctly. It might be better to make the program temporarily treat the dot as a decimal separator in fractional numbers. We just specify in the settings that in fractional numbers the separator is a dot instead of a comma.

To do this, open «File» — «Options» — «Advanced». In the «Edit Options» section, temporarily uncheck the «Use system separators» checkbox. And in the «Integer and fractional separator» field, remove the comma and enter a period.

It is highly recommended to return the default settings after performing the calculations.

Attention! This method will work if you make all the changes before importing the data, and not after.

Method 3 Temporarily change system settings in Windows

The principle of this method is similar to the previous one. Only here we change similar settings in Windows. In the settings of the regional standards of the operating system, you need to replace the comma with a period. Now more about how to do it.

Open «Start» — «Control Panel» — «Regional and Language Options». Click on the «Advanced» button. In the window that appears, change in the first field «Separator of the integer and fractional parts» — enter the value we need. Then OK and OK.

Attention! If you open this file on another computer that has different system locale settings, you may experience problems with calculations.

Method 4 Use the find and replace function in Excel.

This method is similar to the first one. Only here we use the same function from Notepad, but in Excel itself.

In this method, unlike the above, we first paste the copied plate onto a blank sheet, and then we prepare it for performing calculations and calculations.

An important disadvantage of this method is the complexity of its implementation, if some fractional numbers with a dot after insertion were recognized as a date, and not as text. Therefore, we will first get rid of the dates, and then we will deal with the text and points.

1. Pre-select the columns where fractional numbers with a dot as a separator will be located. In this case it is 3 columns D:F.
2. Set the selected range to the text format of the cells to avoid automatic date conversion of some numbers in advance. To do this, select a text format from the drop-down list on the Home tab in the Number section. Or press CTRL + 1 , in the «Format Cells» window that appears, select the «Number» tab, and in the «Number Formats» section, select «Text».
3. Copy the table and right-click on cell A1. From the context menu, select the Paste Special option. Select Unicode Text and click OK. Pay attention to how the values ​​in cells are now displayed: D3, D5, E3, E5, in contrast to the very first copy of the table.
4. Click on the tool «Home» — «Find and Select» — «Replace» (or press the combination CTRL + H).
5. In the window that appears, enter a dot in the «Find» field, and a comma in the second field. And click «Replace All».
6. Select the 3 columns D:F again and change the cell format to Numeric CTRL+SHIFT+1. Do not forget to increase the bit depth to 4, as described in paragraph #2.

All periods changed to commas. And the text is automatically converted to a number.

Instead of the 4th and 5th paragraphs, you can use a formula with functions in a separate column:

For example, select the range of cells G2:I5, enter this formula and press CTRL+Enter. And then move the values ​​of the cells in the range G2:I5 to the range D2:F5.

This formula finds a point in text using the FIND function. Then the second function changes it to a comma. And the VALUE function converts the result to a number.

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Decimal fractions — how to solve examples 5, 6 class

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6 for school, but also to write a music track or make up a website. In this article, we deal with the theory and learn how to perform basic actions with fractions.

The concept of a decimal fraction

Before answering the question of how to find a decimal fraction, let’s look at the basic definitions, types of fractions and the difference between them.

The fraction is a number in mathematics, in which a and b are numbers or expressions. In fact, this is just one of the forms in which a number can be represented. There are two notation formats:

• common view — ½ or a/b,
• decimal — 0.5.

In an ordinary fraction, it is customary to write the dividend above the line, which becomes the numerator, and below the line there is always a divisor, which is called the denominator. The line between the numerator and denominator means division.

In decimal, the denominator is always 10, 100, 1000, 10000, etc. Basically, decimal is what you get when you divide the numerator by the denominator. The decimal fraction is written on a line separated by commas to separate the integer part from the fractional part. Like this:

• 0.8
• 7.42
• 9.932

End decimal is a fraction in which the number of digits after the decimal point is exactly defined.

Infinite decimal is when the number of digits after the decimal point is infinite. For convenience, mathematicians agreed to round these numbers to 1-3 after the decimal point.

Solve your math homework for 5.

Detailed solutions will help you understand the most difficult topic.

Properties of decimal fractions

The main property of decimal fraction sounds like this: if one or more zeros are added to the decimal fraction on the right, its value will not change. This means that if your fraction has a lot of zeros, you can simply discard them. For example:

• 0.600 = 0.6
• 21.10200000 = 21.102

Basic features
The fraction has no value, provided that the divisor is zero. A fraction is zero if the numerator is zero and the denominator is not. Two fractions a/b and c/d are said to be equal if a * d = b * c. If the numerator and denominator are multiplied or divided by the same natural number, then the fraction equal to it will be obtained

Common and decimal fractions are old friends. Here is how they are related:

• The integer part of the decimal is equal to the integer part of the mixed fraction. If the numerator is less than the denominator, then the integer part is equal to zero.
• The fractional part of a decimal fraction contains the same digits as the numerator of the same fraction in ordinary form.
• The number of digits after the decimal point depends on the number of zeros in the denominator of the common fraction. That is, 1 digit is a divisor of 10, 4 digits is a divisor of 10000.

Studying in mathematics courses is a great way to consolidate the acquired knowledge in practice and pull up complex topics.

How to write a decimal fraction

Let’s look at examples of how to write a decimal fraction. A small reminder: first we write the integer part, put a comma and then write down the numerator of the fractional part.

Example 1. Convert the common fraction 16/10 to decimal.

How we solve:

1. The denominator is 10 — this is one zero.
2. We count from right to left in the numerator of the fractional part one sign and put a comma.
3. In the resulting decimal fraction, the number 1 is the integer part, the number 6 is the fractional part.

Answer: 16/10 = 1.6.

Example 2. Convert 37/1000 to decimal.

How do we decide:

1. The denominator is 1000, which is three zeros.
2. We count from right to left in the numerator of the fractional part three characters and put a comma.
3. Since there are only two digits in the numerator, we write zeros in the empty spaces.
4. In the resulting decimal fraction, the number 0 is the integer part, 037 is the fractional part.

Answer: 37/1000 = 0.037.

How to read decimals

For the teacher to understand you correctly, it is important to read decimals correctly. First, we pronounce the integer part with the addition of the word «whole», and then the fractional part with the designation of the category — it depends on the number of digits after the decimal point:

How many decimal places?	Reads like
one digit — tenths;	1.3 — one whole, three tenths;
two digits — hundredths	2.22 — two whole, twenty-two hundredths;
three digits — thousandths;	23.885 twenty-three point eight hundred and eighty-five thousandths;
four digits — ten thousandths;	0.5712 — zero point five thousand seven hundred twelve ten thousandths;
etc.

Save a visual picture to remember faster.

Converting decimals

So that no task confuses you with its wording, it is important to know how to convert decimals to other types. Now let’s learn!

How to convert a decimal to a percentage

Already in the fifth grade, math problems hint that fractions are somehow related to percentages. And it’s true: percent is one hundredth of any number, denoted by the% sign.

1% \u003d 1/100 \u003d 0.01

To find out how to convert percentages to fractions, you need to remove the % sign and divide our number by 100, as in the example above.

And to convert decimal fraction to percent — multiply the fraction by 100 and add the% sign. Let’s take an example:

0.15 = 0.15 100% = 15%.

Expressing a fraction as a percentage is simple: first, turn it into a decimal fraction, and then apply the previous rule.

2/5 = 0.4
0.4 100% = 40%

8/25 = 0.32
0.32 100% = 32%

ratio of parts and whole. Visual plate is our friend-helper:

Converting decimals

Quick reminder:

Decimal is a number with a remainder, where the remainder comes after the whole part and is separated by a comma.

Mixed shot is also a number with a remainder, but the remainder is written as a simple fraction (with a dash).

To convert decimals to mixed fractions, you do not need to memorize special algorithms. It is enough to understand the definitions and read the given fraction correctly — this is what schoolchildren do in the 5th grade. And now let’s practice!

Example 1. Convert 5.4 to a mixed number.

How we decide:

1. Read aloud: five point four. “Four tenths” suggests that there will be 4 in the numerator and 10 in the denominator. In mixed form, this fraction looks like this: 5 4/10.
2. And now let’s reduce the numerator and denominator by two (because we can) and get: 5 2/5.

Answer: 5.4 = 5 2/5.

Example 2. Convert 4.005 to a mixed number.

How we decide:

1. Read aloud: four point five thousandths. So 5 goes to the numerator, and 1000 goes to the denominator. In mixed form, it turns out like this: 4 5/1000. After reduction: 4 1/200.

Answer: 4.005 = 4 1/200.

Example 3. Convert 5.60 to a mixed number.

How we decide:

1. Read aloud: five point sixty hundredths. We send 60 to the numerator and 100 to the denominator. In mixed form, the fraction is as follows: 5 60/100.
2. Let’s reduce the fractional part by 10 and get 5 6/10. Or you can remember about the property of a decimal fraction and simply discard the zeros in the numerator and denominator.

Answer: 5.60 = 5 6/10.

How to convert a decimal to a common fraction

Let’s not invent a wheel and consider the easiest way to convert a decimal to a common fraction. Here’s how to do it:

1. Let’s rewrite the original fraction in a new form: put the original decimal fraction in the numerator, and one in the denominator. For example:
   • 0.35 = 0.35/1
   • 2.34 = 2.34/1
2. Multiply the numerator and denominator by 10 so many times that the comma disappears from the numerator. In this case, after each multiplication, the comma in the numerator is shifted to the right by one sign, and zeros are added to the denominator, respectively. An example is easier:
   • 0.35 = 0.35/1 = 3.5/10 = 35/100
   • 2.34 = 2.34/1 = 23.4/10 = 234/100
3. And now we reduce — that is, we divide the numerator and denominator into multiples of them:
   • 0.35 \u003d 35/100, divide the numerator and denominator by five, we get 6/20, divide by 2 again, we get the final answer 3/10.
   • 2.34 = 234/100 = 117/50 = 2 17/50.

Do not forget about minus in the answer if the example was about a negative number. Very annoying mistake!

Operations with decimals

You can do the same things with decimals as with any other numbers. Let’s consider the most common ones with simple examples.

How to divide a decimal by a natural number

1. Divide the integer part of a decimal by this number.
2. Put a comma in the quotient and continue the calculation as in normal division.

Example 1. Divide 4.8 by 2.

How to solve:

1. Record division by a corner.
2. Divide the whole part by two. Write the result in a quotient and put a comma.
3. Multiply the quotient by the divisor, write down, look at the remainder of the division. But we haven’t finished yet, so we don’t write down the remainder «zero». We demolish 8 and divide it by 2.
4. Dividing again. We write the resulting 4 in the quotient and multiply it by the divisor:

Answer: 4.8 : 2 = 2.4.

Example 2. Divide 183.06 by 45.

How do we solve:

1. Record the angle division.
2. Divide the integer part of 183 by 45. Write down the result, put a comma in the quotient.
3. Write result of difference 183 and 180. Demolish 0. Write 0 to quotient to demolish 6.
4. Record the result of the difference between 306 and 270. 36 is not divisible by 45, so add zero and produce the difference.

Answer: 183.06 : 45 = 4.068.

How to divide a decimal by a common fraction

To divide a decimal by a common or mixed fraction, you need to represent the decimal fraction as a common fraction, and write the mixed number as an improper fraction.

Example 1. Divide 0.25 by 3/4.

How to solve:

1. Write 0.25 as a fraction: 0.25 = 25/100.
2. Divide a fraction according to the rules:

Answer: 0.25: 3/4 = 1/3.

Example 2 Divide 2. 55 by 1 1/3.

How to solve:

1. Write 2.55 as a fraction: 2.55 = 255/1000.
2. Write 1 1/3 as a fraction: 1 1/3 = 4/3.
3. Divide a fraction according to the rules:

Answer: 2.55: 1 1/3 = 1 73/80.

How to multiply a decimal by a common fraction

To multiply a decimal by a common or mixed fraction, two rules for 6th grade are used. At the first, we reduce the decimal fraction to the form of an ordinary fraction and then multiply by the desired number. In the second case, we convert an ordinary or mixed fraction to a decimal and then multiply.

Example 1. Multiply 2/5 by 0.8.

How to solve:

1. Write 0.8 as an ordinary fraction: 0.8 = 8/10.
2. Multiply according to the rules: 2/5 ∗ 8/10 = 2/5 ∗ 4/5 = 8/25 = 0.