Examples with solutions for Multiplying and Dividing Decimal Fractions by 10, 100, etc.: Division by 10

Exercise #1

11.31:10= 11.31:10=

Video Solution

Step-by-Step Solution

To solve this problem, follow these steps:

  • Step 1: Identify the decimal number given in the problem. In this case, it is 11.31.
  • Step 2: Note that we are instructed to divide this number by 10.
  • Step 3: When dividing a number by 10, simply move the decimal point in the original number one place to the left.

Now, let's perform the calculation:

In the number 11.31, the decimal point is after the first "1". To divide by 10, move the decimal point one place to the left, resulting in the number:

1.131 1.131

This is the correct result of dividing 11.31 by 10.

Therefore, the solution to the problem is 1.131 1.131 .

Answer

1.131 1.131

Exercise #2

51.4:10= 51.4:10=

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the current position of the decimal point in the number 51.4 51.4 .
  • Step 2: Use the rule for dividing by 10 10 , which involves moving the decimal point one place to the left.
  • Step 3: Obtain the resultant number after moving the decimal point.

Now, let's work through each step:

Step 1: The number given is 51.4 51.4 , and the decimal point is after the 11.

Step 2: According to the division rule for decimals, when dividing by 10 10 , we move the decimal point one place to the left, making it 5.14 5.14 .

Step 3: The resulting number after the decimal point is moved is therefore 5.14 5.14 .

Thus, the solution to the problem is 5.14 5.14 .

Answer

5.14 5.14

Exercise #3

111.1:10= 111.1:10=

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the given information: 111.1 111.1 needs to be divided by 10 10 .
  • Step 2: Apply the rule for dividing decimals by 10: shift the decimal point in the number 111.1 111.1 one place to the left.

Now, let's work through these steps in detail:

In Step 1, we confirm that the problem provides the number 111.1 111.1 to be divided by 10 10 .

In Step 2, we apply the rule of decimal division by shifting the decimal point in 111.1 111.1 one place to the left. This means the decimal moves from between the "111" and the "1" to between the "11" and "11". Thus, the number becomes 11.11 11.11 .

Therefore, the solution to the problem is 11.11 11.11 .

Answer

11.11 11.11

Exercise #4

581.8:10= 581.8:10=

Video Solution

Step-by-Step Solution

To solve this problem, we need to divide 581.8 581.8 by 10 10 .

  • Step 1: Identify the decimal point in the number 581.8 581.8 , which is between the 1 1 and 8 8 .
  • Step 2: Move the decimal point one place to the left as per the rule of dividing by 10. This step transforms 581.8 581.8 into 58.18 58.18 .
  • Step 3: Write down the resulting number.

Therefore, when we divide 581.8 581.8 by 10 10 , the result is 58.18 58.18 .

Answer

58.18 58.18

Exercise #5

65.2:10= 65.2:10=

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the given number, which is 65.2 65.2 .
  • Step 2: Apply the rule for dividing a decimal by 10: Shift the decimal point one place to the left.
  • Step 3: Verify the result by ensuring the computation is accurate.

Now, let's work through each step:
Step 1: The problem gives us the number 65.2 65.2 .
Step 2: We'll divide by 10 by shifting the decimal point one place left. This changes 65.2 65.2 to 6.52 6.52 .
Step 3: Checking our work, 6.52 6.52 is indeed the correct result of shifting the decimal point left.

Therefore, the solution to the problem is 6.52 6.52 .

Answer

6.52 6.52

Exercise #6

12.2:10= 12.2:10=

Video Solution

Step-by-Step Solution

To solve this division problem, we will follow these steps:

  • Step 1: Identify the initial position of the decimal point in the number 12.2 12.2 .
  • Step 2: Apply the rule for division by 10 10 , which involves moving the decimal point one place to the left.
  • Step 3: Confirm the resulting value after the decimal shift.

Now, let's proceed with addressing each step:

Step 1: The number 12.2 12.2 has its decimal point positioned after the digit 2 2 .

Step 2: Dividing by 10 10 means moving this decimal point one place to the left, resulting in the decimal point being placed after the number 1 1 , turning 12.2 12.2 into 1.22 1.22 .

Step 3: Thus, the value obtained is 1.22 1.22 .

Therefore, the solution to the problem is 1.22 1.22 .

Answer

1.22 \text{1}.22

Exercise #7

13.61:10= 13.61:10=

Video Solution

Step-by-Step Solution

To solve the problem, we'll use a straightforward approach:

  • Step 1: Recognize that dividing by 10 moves the decimal point one place to the left.
  • Step 2: Start with 13.61.
  • Step 3: Move the decimal point one place left results in 1.361.

Now, let's apply these steps to calculate:

Starting with 13.61 13.61 , when dividing by 10, the decimal moves one position to the left:

13.611.361 13.61 \rightarrow 1.361 .

Thus, the solution to the division is 1.361 1.361 .

Answer

1.361 1.361

Exercise #8

20.1:10= 20.1:10=

Video Solution

Step-by-Step Solution

To solve 20.1÷10 20.1 \div 10 , we follow these steps:

  • Step 1: Identify that we are dividing by 10, so we will move the decimal point one place to the left.
  • Step 2: Start with the number 20.1 and move the decimal point one place left to get 2.01.
  • Step 3: Write the new number after shifting the decimal, which gives us 2.01.

After carrying out these steps, we find that the solution to the problem is 2.01 2.01 .

Answer

2.01 2.01

Exercise #9

2.6:10= 2.6:10=

Video Solution

Step-by-Step Solution

To solve this problem of dividing 2.6 by 10, we will observe the following steps:

  • Step 1: Recognize that dividing by 10 shifts the decimal point one place to the left.
  • Step 2: Identify the position of the decimal point in the number 2.6, which is immediately after the 2.
  • Step 3: Move the decimal point one place to the left, changing 2.6 to 0.26.

Thus, when you divide 2.6 by 10, the result is 0.26 0.26 .

The correct answer is confirmed to be :

0.26 0.26

.

Answer

0.26 0.26

Exercise #10

0.123:10= 0.123:10=

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the given decimal number, 0.1230.123.
  • Step 2: Apply the rule for dividing a decimal by 1010, which involves moving the decimal point one place to the left.
  • Step 3: Perform the movement of the decimal point.

Now, let's work through each step:

Step 1: We have the decimal number 0.1230.123.

Step 2: The rule for dividing by 1010 tells us to move the decimal point one place to the left.

Step 3: Moving the decimal point one place to the left, 0.1230.123 becomes 0.01230.0123.

Therefore, the solution to the problem is 0.0123 0.0123 .

Checking the answer against the choices, the correct choice is: : 0.0123 0.0123 .

Answer

0.0123 0.0123

Exercise #11

4.61:10= 4.61:10=

Video Solution

Step-by-Step Solution

To solve this problem, we need to divide the number 4.61 by 10.

When dividing a decimal by 10, we move the decimal point one place to the left. This is a standard rule of arithmetic for dealing with powers of ten:

  • Starting decimal: 4.61 4.61
  • Move the decimal point one place left: 0.461 0.461

Therefore, the result of dividing 4.61 by 10 is 0.461\boxed{0.461}.

Answer

0.461 0.461

Exercise #12

23.1:10= 23.1:10=

Video Solution

Step-by-Step Solution

To solve this problem, let's follow a simple approach using the decimal shifting rule:

  • Step 1: Identify the initial decimal point position in 23.1, which is between '3' and '1'.
  • Step 2: To divide by 10, move the decimal point one position to the left.

Now, moving the decimal point one place to the left converts 23.1 to 2.31.

Therefore, the solution to the problem is 2.31 2.31 , which corresponds to choice .

Answer

2.31 2.31

Exercise #13

113.4:10= 113.4:10=

Video Solution

Step-by-Step Solution

To solve this problem, we need to perform division of the decimal number 113.4 113.4 by 10 10 .

  • Step 1: Understand the operation: Division by 10 10 involves moving the decimal point one position to the left.
  • Step 2: Locate the decimal point in the number 113.4 113.4 . It is between the digits 3 3 and 4 4 .
  • Step 3: Move the decimal point one position to the left to divide by 10 10 .

By moving the decimal one position to the left, the number 113.4 113.4 becomes 11.34 11.34 .

Therefore, the result of dividing 113.4 113.4 by 10 10 is 11.34\mathbf{11.34}.

Answer

11.34 11.34

Exercise #14

0.061:10= 0.061:10=

Video Solution

Step-by-Step Solution

To solve the problem, we will use the rule for dividing a decimal by 1010, which requires moving the decimal point one position to the left:

  • Identify the current decimal position in the number 0.0610.061, which is between the zero and six in 0.0610.061.

  • Move the decimal point one position to the left to divide by 1010.

  • After moving, the decimal point between 00 and 66 is positioned before the first 00, resulting in 0.00610.0061.

Thus, the result of dividing 0.0610.061 by 1010 is 0.0061\mathbf{0.0061}.

The correct choice among the given options is Choice 2 with the value 0.0061 0.0061

Answer

0.0061 0.0061

Exercise #15

1.65:10= 1.65:10=

Video Solution

Step-by-Step Solution

To solve the problem of dividing 1.65 by 10, we apply the rule for decimal division by powers of ten:

  • Step 1: Identify the given number, which is 1.65.
  • Step 2: Apply the rule for division by 10. This involves moving the decimal point one place to the left.
  • Step 3: Starting with 1.65, move the decimal point one place to the left to get 0.165.

Therefore, after dividing 1.65 by 10, we obtain 0.165 0.165 .

Answer

0.165 0.165

Exercise #16

0.8:10= 0.8:10=

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Understand that dividing by 10 shifts the decimal point one place to the left.
  • Step 2: Apply this knowledge to the number 0.8.

Now, let's work through each step:

Step 1: The number given is 0.8 0.8 . We need to divide this number by 10. When dividing by 10, we shift the decimal point one place to the left.

Step 2: Shifting the decimal point of 0.8 0.8 one place to the left results in 0.08 0.08 .

Therefore, the solution to the problem is 0.08 0.08 .

Answer

0.08 0.08

Exercise #17

0.1:10= 0.1:10=

Video Solution

Step-by-Step Solution

To solve this problem, follow these steps:

  • Step 1: Recognize that we are dividing 0.10.1 by 1010.
  • Step 2: Apply the rule for dividing by 1010, which involves shifting the decimal point in 0.10.1 one place to the left.

Let's solve the problem:

Step 1: We have the number 0.10.1, and we need to divide it by 1010.
Step 2: Since dividing by 1010 shifts the decimal point one place to the left, move the decimal in 0.10.1 one place left.
Therefore, 0.10.1 becomes 0.010.01 after shifting the decimal point.

Thus, the solution to the problem is 0.01 \boxed{0.01} .

Answer

0.01 0.01

Exercise #18

2.2:10= 2.2:10=

Video Solution

Step-by-Step Solution

To solve this problem, let's follow these steps:

  • Step 1: Identify the given number and divisor.
  • Step 2: Understand how dividing by 10 affects decimal placement.
  • Step 3: Perform the division and verify the result with the choices provided.

Now, let's work through each step:

Step 1: The problem gives us the number 2.22.2 and requires dividing it by 1010.

Step 2: When dividing a number by 1010, you move the decimal point one place to the left. This is a result of how the base-10 system works; dividing by a power of 10 shifts the decimal point left.

Step 3: In the number 2.22.2, the decimal is currently after the numeral "2." Moving the decimal one place left, we have:

2.20.222.2 \rightarrow 0.22

Therefore, the result of 2.2÷102.2 \div 10 is 0.22\textbf{0.22}.

To ensure accuracy, we compare this result with the provided choices. Choice number 3, 0.220.22, matches our solution.

Thus, the solution to the problem is 0.220.22.

Answer

0.22 0.22

Exercise #19

1.71:10= 1.71:10=

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Understand decimal division by powers of ten.
  • Step 2: Perform the decimal point shift.
  • Step 3: Compare the result with the provided options.

Now, let's work through each step:

Step 1: The operation involves division by 1010, which is equivalent to shifting the decimal point of the number one place to the left. We begin with the number 1.711.71.

Step 2: In 1.711.71, the decimal point is moved one place to the left, changing it to 0.1710.171.

Step 3: Check this answer against the options given:

  • Option 1: 0.170.17
  • Option 2: 0.710.71
  • Option 3: 0.1710.171
  • Option 4: 0.7110.711

The correct answer is Option 3: 0.1710.171.

Therefore, the solution to the problem is 0.1710.171.

Answer

0.171 0.171

Exercise #20

0.3:10= 0.3:10=

Video Solution

Step-by-Step Solution

To solve this problem, we need to divide 0.3 0.3 by 10 10 . We can achieve this by using the following steps:

  • Step 1: Understand that dividing by 10 10 means moving the decimal point one place to the left.
  • Step 2: Currently, the number is 0.3 0.3 . To divide by 10 10 , shift the decimal one place left to obtain the new value.
  • Step 3: After moving the decimal point, the new value becomes 0.03 0.03 .

This simple operation demonstrates that when dividing by powers of ten, the decimal point moves to the left by as many places as there are zeros in the power (one zero here, for dividing by ten).

Therefore, the solution to the problem is 0.03 \text{0}.03 .

Answer

0.03 \text{0}.03