Dividing Decimal Fractions - Examples, Exercises and Solutions

Understanding Dividing Decimal Fractions

Complete explanation with examples

To divide decimal numbers, we will carry out the following steps:

First step - We will make the decimal point in the dividend (the number we want to divide) disappear by moving it to the right the necessary number of places until it is completely "gone".
Second step - In the divisor (the second number in the operation, that is, the number by which it is divided) we will move the decimal point to the right the same number of places that we moved the first number (even if this number of steps is not enough to make it disappear)
Third step - We will solve the "new" exercise (with the "new" numbers).

Detailed explanation

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\( 2.6:0.1= \)

Examples with solutions for Dividing Decimal Fractions

Step-by-step solutions included
Exercise #1

0.49:0.1= 0.49:0.1=

Step-by-Step Solution

To solve the division of decimals 0.49÷0.1 0.49 \div 0.1 , follow these steps:

  • Step 1: Start by identifying the dividend (0.49 0.49 ) and the divisor (0.1 0.1 ).
  • Step 2: To simplify the division process, eliminate the decimal in the divisor. Multiply both the dividend and the divisor by 10. This gives: (0.49×10)÷(0.1×10)=4.9÷1 (0.49 \times 10) \div (0.1 \times 10) = 4.9 \div 1 .
  • Step 3: Perform the simple division with the new values: 4.9÷1=4.9 4.9 \div 1 = 4.9 .

Therefore, the result of 0.49÷0.1 0.49 \div 0.1 is 4.9 4.9 .

Answer:

4.9 4.9

Video Solution
Exercise #2

3.36:0.1= 3.36:0.1=

Step-by-Step Solution

To solve the division of two decimal numbers, we start by converting the divisor, 0.1, into a whole number to simplify the calculation.

  • Step 1: Multiply both the dividend and the divisor by 10 to eliminate the decimal in the divisor. This gives us:

3.36×10=33.6 3.36 \times 10 = 33.6 and 0.1×10=1 0.1 \times 10 = 1

  • Step 2: The division is now transformed from 3.360.1 \frac{3.36}{0.1} to 33.61 \frac{33.6}{1} .

Step 3: Dividing 33.6 by 1 results simply in 33.6.

There's no change needed to any number beyond this step, as the division by 1 does not alter the value.

Therefore, the solution to the problem is 33.6 33.6 .

Answer:

33.6 33.6

Video Solution
Exercise #3

1.3:0.1= 1.3:0.1=

Step-by-Step Solution

To solve the problem of 1.3÷0.1 1.3 \div 0.1 , we need to simplify the division process by eliminating the decimal point in the divisor using the following steps:

  • Step 1: Recognize that dividing by 0.1 is equivalent to multiplying by 10. This is because 0.1 is the same as 110 \frac{1}{10} , so dividing by 0.1 is the same as multiplying by 10.
  • Step 2: Multiply both the dividend (1.3) and the divisor (0.1) by 10 to move the decimal point one place to the right for each number. This changes 1.3 to 13 and 0.1 to 1.
  • Step 3: Perform the division 13÷1 13 \div 1 . As dividing by 1 leaves any number unchanged, we have the result 13.

Therefore, the solution to the problem 1.3÷0.1 1.3 \div 0.1 is 13 13 .

Answer:

13 13

Video Solution
Exercise #4

0.36:0.1= 0.36:0.1=

Step-by-Step Solution

To solve the problem 0.36÷0.1 0.36 \div 0.1 , we use the method of converting to whole numbers as follows:

  • Step 1: Multiply both 0.36 and 0.1 by 10 to get rid of the decimals. This gives us 3.6 3.6 and 1 1 .
  • Step 2: Perform the division of 3.6 3.6 by 1 1 , which simply results in 3.6 3.6 .

Thus, the result of 0.36÷0.1 0.36 \div 0.1 is 3.6 3.6 .

Answer:

3.6 3.6

Video Solution
Exercise #5

0.7:0.1= 0.7:0.1=

Step-by-Step Solution

To solve the problem 0.7÷0.10.7 \div 0.1, we proceed with the following steps:

  • Step 1: Convert the decimals to whole numbers. Multiply both 0.70.7 and 0.10.1 by 10 to remove the decimals. This gives us 77 and 11 respectively.
  • Step 2: Divide the resulting whole numbers. Hence, 7÷1=77 \div 1 = 7.
  • Step 3: The division is straightforward as the divisor is now a whole number.

Therefore, the solution to the problem is 77.

Answer:

7 7

Video Solution

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