Contents
What is the first step in dividing whole numbers by decimals?
Division of a Decimal by a Whole Number  Rules of Dividing Decimals We will learn how to find the quotient in division of a decimal by a whole number. To divide a decimal number by a whole number the division is performed in the same way as in the whole numbers.
 The rules to divide a decimal by a whole number are:
 (i) Divide as in division of numbers ignoring the decimal point.
 (ii) When you reach the tenths digit, place the decimal in the quotient.
Note: When the number of digits in the dividend is less and the division is not complete, keep adding zeroes at every step till the division is complete as in example 1 and example 2.1. Solve: 100.4 ÷ 25 100.4 ÷ 25 Therefore, 100.4 ÷ 25 = 4.016 2. Find 1.2 ÷ 25
 1.2 ÷ 25
 = (12/10) ÷ 25
 = (12/10) ×(1/25)
 = (12 × 1)/(10 × 25)
 = 12/250
Alternative Method: Therefore, 1.2 ÷ 25 = 0.048 3. Divide 115.8 by 6 Hence, 115.8 ÷ 6 = 19.3 4. Divide 335.8 by 23 Hence, 335.8 ÷ 23 = 14.6 5. Divide: 191.5 ÷ 5 191.5 ÷ 5 Therefore, 191.5 ÷ 5 = 36.3 This example shows that both dividend and quotient have decimal place i.e.1.6. Divide: 1.21 ÷ 11 First we will divide the decimal by the whole number ignoring decimal point. Now put the decimal point in the quotient in such a way, that the decimal place in the quotient becomes equal to the decimal places in the dividend. Therefore, 798.3 ÷ 36 = 22.175 8. Divide: 0.007 ÷ 14 0.007 ÷ 14 Therefore, 0.007 ÷ 14 = 0.0005 (dividend has 4 decimal places, therefore quotient also has 4 decimal places) 9. Divide: 24.66 ÷ 12 24.66 ÷ 12 Therefore, 24.66 ÷ 12 = 2.05 (dividend has 2 decimal places, therefore quotient also has 2 decimal places) 10. Divide: 316.84 ÷ 8 316.84 ÷ 8 Therefore, 316.84 ÷ 8 = 39.605 11. Divide: 6.30 ÷ 7 6.30 ÷ 7 Therefore, 6.30 ÷ 7 = 0.90 (dividend has 2 decimal places, therefore quotient also has 2 decimal places) 12.
 While comparing natural numbers we first compare total number of digits in both the numbers and if they are equal then we compare the digit at the extreme left. If they also equal then we compare the next digit and so on. We follow the same pattern while comparing the
 We will discuss how to express fraction as decimal. Let us consider some of the following examples on expressing a fraction as a decimal.1. Convert \(\frac \) into a decimal.
 We have already studied about fractions and now we will discuss here about the concept of decimal. Fractions can also be expressed as decimal Fractions.
 We will learn uses decimals in every day. In daily life we use decimals while dealing with length, weight, money etc. Use of Decimals whole Dealing with Money: 100 paise = 1 rupee We know that one paise in one hundredth of a rupee.
 We will discuss here about the addition of decimals. Decimals are added in the same way as we add ordinary numbers. We arrange the digits in columns and then add as required. Let us consider some
 We will discuss here about the subtraction of decimals. Decimals are subtracted in the same way as we subtract ordinary numbers. We arrange the digits in columns
 Equivalent decimal fractions are unlike fractions which are equal in value. Numbers obtained by inserting zeros after the extreme right digit in the decimal part of a decimal number are known as equivalent decimals.
 We will discuss how to express decimal as fraction. Let us consider some of the following examples on expressing a decimal as a fraction.1. Convert 2.12 into a fraction. Solution: 2.12
 In 5th Grade Decimals Worksheet contains various types of questions on operations on decimal numbers. The questions are based on formation of decimals, comparing decimals, Converting Fractions to Decimals, Addition of decimals, subtraction of decimals, multiplication of
 Decimal numbers can be expressed in expanded form using the placevalue chart. In expanded form of decimal fractions we will learn how to read and write the decimal numbers. Note: When a decimal is missing either in the integral part or decimal part, substitute with 0.
 Division of a decimal number by 10, 100 or 1000 can be performed by moving the decimal point to the left by as many places as the number of zeroes in the divisor. The rules of division of decimal fractions by 10, 100, 1000 etc. are discussed here.
 Addition of decimal numbers are similar to addition of whole numbers. We convert them to like decimals and place the numbers vertically one below the other in such a way that the decimal point lies exactly on the vertical line. Add as usual as we learnt in the case of whole
 Simplification in decimals can be done with the help of PEMDAS Rule. From the above chart we can observe that first we have to work on “P or Parentheses” and then on “E or Exponents”, then from
 Solve the questions given in the worksheet on decimal word problems at your own space. This worksheet provides a mixture of questions on decimals involving order of operations
 Practice the math questions given in the worksheet on dividing decimals. Divide the decimals to find the quotient, same like dividing whole numbers. This worksheet would be really good for the students to practice huge number of decimal division problems.
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Division of a Decimal by a Whole Number  Rules of Dividing Decimals
What are the 3 steps in dividing decimals?
First, convert the divisor into a whole number by shifting the decimal point to the right. Apply the same process to the dividend. Then, perform regular division with the new numbers. Finally, position the decimal point in the quotient to match the dividend.
What is the trick for dividing by 1000?
Using place value charts – You can use place value charts to help divide by 10, 100 and 1000. This helps you to see how the digits change in value. A trick to help you remember how many places the digits need to move is by looking at the zeros in 10, 100 and 1000. For example, there are 3 zeros in 1000, so you need to move the digits 3 places to the right to divide by 1000.
x10 – 1 zero move 1 place x100 – 2 zeros move 2 places x1000 – 3 zeros move 3 places
What are the rules for decimals?
TO ADD OR SUBTRACT DECIMALS: 1) Line up the decimal points vertically. Fill in any 0’s where necessary.2) Add or subtract the numbers as if they were whole numbers.3) Place the decimal point in the sum or difference so that it lines up vertically with the numbers being added or subtracted.
Can you divide by a decimal?
Multiplying and Dividing Decimals
 Multiplying and Dividing Decimals
 Learning Objective(s)
 · Multiply two or more decimals.
 · Multiply a decimal by a power of 10.
 · Divide by a decimal.
 · Divide a decimal by a power of 10.
 · Solve application problems that require decimal multiplication or division.
As with whole numbers, sometimes you run into situations where you need to multiply or divide decimals. And just as there is a correct way to multiply and divide whole numbers, so, too, there is a correct way to multiply and divide decimals. Imagine that a couple eats dinner at a Japanese steakhouse.
The bill for the meal is $58.32—which includes a tax of $4.64. To calculate the tip, they can double the tax. So if they know how to multiply $4.64 by 2, the couple can figure out how much they should leave for the tip. Here’s another problem. Andy just sold his van that averaged 20 miles per gallon of gasoline.
He bought a new pickup truck and took it on a trip of 614.25 miles. He used 31.5 gallons of gas to make it that far. Did Andy get better gas mileage with the new truck? Both of these problems can be solved by multiplying or dividing decimals. Here’s how to do it.


Notice how the digits in the two solutions are exactly the same – the multiplication does not change at all. The difference lies in the placement of the decimal point in the final answers: 214 · 36 = 7,704, and 21.4 · 3.6 = 77.04.
 To find out where to put the decimal point in a decimal multiplication problem, count the total number of decimal places in each of the factors.
 21.4 the first factor has one decimal place
 3.6 the second factor has one decimal place
 77.04 the product will have 1 + 1 = 2 decimal places
 Note that the decimal points do not have to be aligned as for addition and subtraction.
Example  
Problem  3.04 · 6.1 = ?  







Answer  3.04 · 6.1 = 18.544 
Sometimes you may need to insert zeros in front of the product so that you have the right number of decimal places. See the final answer in the example below:
Example  
Problem  0.037 · 0.08 = ?  

Set up the problem. Multiply.  




Answer  0.037 · 0.08 = 0.00296  Note that you needed to add zeros before 296 to get the 5 decimal places. 
If one or more zeros occur on the right in the product, they are not dropped until after the decimal point is inserted.
Example  
Problem  2.04 · 1.95 = ?  







Answer  2.04 · 1.95 = 3.978  Answer can omit the final trailing 0. 
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 Multiplying Decimals
 To multiply decimals:
 · Set up and multiply the numbers as you do with whole numbers.
 · Count the total number of decimal places in both of the factors.
 · Place the decimal point in the product so that the number of decimal places in the product is the sum of the decimal places in the factors.
· Keep all zeros in the product when you place the decimal point. You can drop the zeros on the right once the decimal point has been placed in the product. If the number of decimal places is greater than the number of digits in the product, you can insert zeros in front of the product.
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Multiply.51.2 · 3.08 A) 15769.6
 B) 1576.96
 C) 157.696
 D) 15.7696
A) 15769.6 Incorrect. Pay attention to the placement of the decimal point. The correct answer is 157.696. B) 1576.96 Incorrect. Pay attention to the placement of the decimal point. The correct answer is 157.696. C) 157.696 Correct. To find the product, multiply 512 · 308 = 157696. Count the total number of decimal places in the factors, 3, and then place a decimal point in the product so that the product has three decimal places as well. The answer is 157.696. D) 15.7696 Incorrect. Pay attention to the placement of the decimal point. The correct answer is 157.696.
Take a moment to multiply 4.469 by 10. Now do 4.469 · 100. Finally, do 4.469 · 1,000. Notice any patterns in your products?



Notice that the products keep getting greater by one place value as the multiplier (10, 100, and 1,000) increases. In fact, the decimal point moves to the right by the same number of zeros in the power of ten multiplier.
4.469 · 10 = 44,69 ^  4.469 · 100 = 446,9 ^  4.469 · 1,000 = 4469, ^ 
You can use this observation to help you quickly multiply any decimal by a power of ten (10, 100, 1,000, etc).
Example  
Problem  0.03 · 100 = ?  
0.03 · 1 00 = ?  100 has two zeros.  
0.03 · 100 = 3  Move the decimal point two places to the right to find the product.  
Answer  0.03 · 100 = 3 
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Multiplying a Decimal by a Power of Ten To multiply a decimal number by a power of ten (such as 10, 100, 1,000, etc.), count the number of zeros in the power of ten. Then move the decimal point that number of places to the right. For example, 0.054 · 100 = 5.4. The multiplier 100 has two zeros, so you move the decimal point in 0.054 two places to the right—for a product of 5.4.To divide decimals, you will once again apply the methods you use for dividing whole numbers. Look at the two problems below. How are the methods similar? Notice that the division occurs in the same way—the only difference is the placement of the decimal point in the,
Example  
Problem  18.32 ÷ 8 = ?  
_ 8 ) 1 8.3 2  Set up the problem.  

Divide.  
2.2 9 8 ) 1 8.3 2  Place decimal point in the quotient. It should be placed directly above the decimal point in the dividend.  
Answer  18.32 ÷ 8 = 2.29 
But what about a case where you are dividing by a decimal, as in the problem below? In cases like this, you can use powers of 10 to help create an easier problem to solve. In this case, you can multiply the, 0.3, by 10 to move the decimal point 1 place to the right.
Example  
Problem  260.1 ÷ 0.3 = ?  
_ 0.3 ) 2 6 0.1  Set up the problem.  
_ 3,) 2 6 0 1,  Multiply divisor and dividend by 10 to create a whole number divisor.  

Divide.  
Answer  260.1 ÷ 0.3 = 867 
Often, the dividend will still be a decimal after multiplying by a power of 10. In this case, the placement of the decimal point must align with the decimal point in the dividend.
Example  
Problem  15.275 ÷ 3.25 = ?  
_ 3.2 5 ) 1 5.2 7 5  Set up the problem.  
_ 3 2 5,) 1 5 2 7,5  Multiply divisor and dividend by 100 to create a whole number divisor.  
4.7 3 2 5,) 1 5 2 7,5

Divide.325 goes into 1527 four times, so the number 4 is placed above the digit 7. The decimal point in the quotient is placed directly above the decimal point in the dividend.  
Answer  15.275 ÷ 3.25 = 4.7 
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Dividing Decimals Divide as you would with whole numbers. Then place the decimal point in the quotient directly above the decimal point in the dividend. To divide by a decimal, multiply the divisor by a power of ten to make the divisor a whole number. Then multiply the dividend by the same power of ten. You can think of this as moving the decimal point in the dividend the same number of places to the right as you move the decimal point in the divisor. Then place the decimal point in the quotient directly over the decimal point in the dividend. Finally, divide as you would with whole numbers.table>
Divide: 25.095 ÷ 0.5. A) 5,019
 B) 501.9
 C) 50.19
 D) 0.5019
A) 5,019 Incorrect. Multiply both the divisor and the dividend by 10 (this will change 0.5 into a whole number), and then divide. Then place the decimal point in the quotient directly over the decimal point in the dividend. The correct answer is 50.19. B) 501.9 Incorrect. Multiply both the divisor and the dividend by 10 (this will change 0.5 into a whole number), and then divide. Then place the decimal point in the quotient directly over the decimal point in the dividend. The correct answer is 50.19. C) 50.19 Correct. This problem can be set up as 250.95 ÷ 5; the quotient is 50.19. D) 0.5019 Incorrect. Remember that when you divide, you do not count the total number of decimal places in the divisor and dividend. You change the divisor to a whole number, then move the decimal point in the dividend the same number of places and divide. Finally, place the decimal point in the quotient directly over the decimal point in the dividend. The correct answer is 50.19.
Recall that when you multiply a decimal by a power of ten (10, 100, 1,000, etc), the placement of the decimal point in the product will move to the right according to the number of zeros in the power of ten. For instance, 4.12 · 10 = 41.2. Multiplication and division are inverse operations, so you can expect that if you divide a decimal by a power of ten, the decimal point in the quotient will also correspond to the number of zeros in the power of ten. In the examples above, notice that each quotient still contains the digits 4469—but as another 0 is added to the end of each power of ten in the divisor, the decimal point moves an additional place to the left in the quotient.
Dividing by Powers of Ten To divide a decimal by a power of ten (10, 100, 1,000, etc.), count the number of zeros in the divisor. Then move the decimal point in the dividend that number of decimal places to the left; this will be your quotient. 
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Example Problem 31.05 ÷ 10 = ? 31.05 ÷ 1 0 = ? 10 has one zero. 31.05 ÷ 10 = 3.105 Move the decimal point one place to the left in the dividend; this is the quotient. Answer 31.05 ÷ 10 = 3.105table>
Divide.0.045 ÷ 100 A) 0.00045
 B) 0.045
 C) 4.5
 D) 4,500
A) 0.00045 Correct. There are two zeros in the divisor (100), so to find the quotient, take the dividend (0.045) and move the decimal point two places to the left. The quotient is 0.00045. B) 0.045 Incorrect.0.045 is the dividend in the problem; it cannot be the quotient unless the divisor is 1. The correct answer is 0.00045. C) 4.5 Incorrect.4.5 would be the correct answer if you multiplied 0.045 by 100, not divided it by 100. The correct answer is 0.00045. D) 4,500 Incorrect.4,500 would be the correct answer if you multiplied 0.045 by 100,000, not divided it by 100. The correct answer is 0.00045.
Solving Problems by Multiplying or Dividing Decimals Now let’s return to the two problems from the beginning of this section. You know how to multiply and divide with decimals now. Let’s put that knowledge to the test.
Example  
Problem  A couple eats dinner at a Japanese steakhouse. The bill for the meal totals $58.32—which includes a tax of $4.64. To calculate the tip, they can double the tax. How much tip should the couple leave?  
4.64 x 2  Set up a multiplication problem.  

Multiply.  

Count the number of decimal places in the two factors, and place the decimal point accordingly.  
Answer  The couple should leave a tip of $9.28. 
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Example Problem Andy just sold his van that averaged 20 miles per gallon of gasoline. He bought a new pickup truck and took it on a trip of 614.25 miles. He used 31.5 gallons of gas for the trip. Did Andy get better gas mileage with the new truck? _ 3 1.5 ) 6 1 4.2 5 Set up a division problem. _ 3 1 5,) 6 1 4 2,5 Make the divisor a whole number by multiplying by 10; do the same to the dividend. 1 9.5 3 1 5,) 6 1 4 2,5 3 1 5
 2 9 9 2
 2 8 3 5
 1 5 7 5
 1 5 7 5
 0
Learning to multiply and divide with decimals is an important skill. In both cases, you work with the decimals as you have worked with whole numbers, but you have to figure out where the decimal point goes. When multiplying decimals, the number of decimal places in the product is the sum of the decimal places in the factors.
What is an example of dividing decimals?
Frequently Asked Questions – Can remainder be a decimal number while performing division? No, the remainder can never be a decimal number while performing division. How many places will the decimal point shift if a decimal number is divided by 10,000? There are 4 zeroes in 10,000.
 So, the decimal point will shift 4 places to the left.
 How to divide a whole number by a decimal? We first convert the divisor into a whole number by shifting the decimal point.
 We make a similar shift in the dividend and then perform the division.
 For example: Divide 12 by 0.4.
 Change the divisor 0.4 to 4 by shifting the decimal point one place to the right.
Similarly, after shifting the decimal point 12, we get 120. Thus, $12 \div 0.4 = 120 \div 4 = 30$. Can the quotient be a decimal number when two whole numbers are divided? Yes, the quotient can be a decimal number when one whole number does not divide the other whole number completely.
How to divide 10000 hours by 24?
10000 to day’s formula: Divide number of hours 10000 by 24 hours day = 416.667 days in 10,000 hours equates to 1.1408 years long.
What is 1000 split into 5?
1000 divided by 5 is 200.
What is the first step when dividing a fraction to a whole number?
Step 1: Convert the whole number to an improper fraction. Step 2: Find the reciprocal of the second fraction (divisor). Step 3: Change the division sign to a multiplication sign and multiply.
What is the first step in the procedure of dividing a whole number by a fraction?
Step 1: Begin by converting the whole number into a fraction. We can do this by placing the whole number as the numerator of the fraction. In the place of the denominator, we will place 1. Step 2: Next, we will find the reciprocal of the fraction given as a divisor.