dividing decimals

We know how to divide whole numbers, for example, 10 ÷ 5. In this lesson, we will learn division cases where either the dividend is a decimal number or a divisor is a decimal number or both the dividend and divisor are decimal numbers.
The following 4 cases may arise:

Case I - Dividend is a whole number and divisor is a decimal number. For example, 22 ÷ 0.5

Case II - Both divisor and dividend are decimal numbers. For example, 34.50 ÷ 1.5

Case III - Dividend is a decimal number and divisor is a whole number. For example, 4.26 ÷ 6

Case IV - Dividend and Divisor both are whole numbers. For example 7 ÷ 5

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In this lesson, we will understand the steps followed to solve each of these four cases. Let's begin with Case I. 

Case I: Divisor is a decimal number

Let us take an example, 22 ÷ 0.5

Convert the divisor to a whole number. Multiply the divisor by 10 or powers of 10 till you can get rid of the decimal point. Remember to multiply the dividend also with the same number.

\(\frac{22}{0.5} =\frac{22 \times 10}{0.5 \times 10} = \frac{220}{5} \)

22 ÷ 0.5 can be represented as 220 ÷ 5, now follow case IV to solve the problem(both the dividend and the divisor are whole numbers now.)

Note: After changing the divisor to a whole number, follow case III or IV depending on the dividend value.

Case II: Dividend and Divisor are decimal numbers

Let us take an example, 34.5 ÷ 1.5

First, convert the divisor to a whole number. 

\(\frac{34.5}{1.5} =\frac{34.5 \times 10}{1.5\times 10} = \frac{345}{15} \)

34.50 ÷ 1.5 can be represented as 345 ÷ 15

Now as both the dividend and the divisor are whole numbers follow case IV.

Note: After changing the divisor to a whole number, follow case III or IV depending on the dividend value.

Case III: Dividend is a decimal number and divisor a whole number

Let us take an example and learn how to perform such division:

1.  4.26 ÷ 6
   
2. Write the decimal point in the quotient just above the dividend decimal point.
   
3. Check the digit coming before the decimal point in the dividend, 4, as it is less than 6 so it goes into 4, zero times. 
   
4. Solve a long division problem:
   

 

Case IV -  Dividend and Divisor both are whole numbers and the result of the division is a decimal

Let us learn how to divide a whole number that is not completely divisible by the divisor. 

1. 7 ÷ 5
   
2. As 7>5, 5 can go one time into 7.
   
   
    
3. 7 is not completely divisible by 5 and leaves the remainder 2. Add a decimal point in the dividend and add as many zeroes you like (zero after the decimal point doesn't change the value)
   
    
4. Position the decimal point in the quotient directly above the dividend's decimal point:
    

So, when you divide 7 by 5 the answer is 1.4

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Division by 10, 100, and 1000 (powers of ten)

When a decimal number is divided by powers of ten like 10, 100, or 1000, we move the decimal point to the left for as many places (steps) as there are 0's in the divisor. For example, 2.5 ÷ 100