Decimal Multiplication Division by 10 100 1000 Practice

Master multiplying and dividing decimals by 10, 100, 1000 with step-by-step practice problems. Learn decimal point movement rules and boost math confidence.

📚Master Decimal Point Movement with Interactive Practice
  • Apply the decimal point movement rule for multiplying by 10, 100, 1000
  • Practice moving decimal points right for multiplication problems
  • Master moving decimal points left for division by powers of 10
  • Solve problems involving adding zeros when decimal points move
  • Build confidence with step-by-step decimal multiplication and division
  • Apply decimal point rules to real-world math scenarios

Understanding Multiplying and Dividing Decimal Fractions by 10, 100, etc.

Complete explanation with examples

In multiplications: the decimal point moves to the right as many steps as the number has zeros.
In divisions: the decimal point moves to the left as many steps as the number has zeros.

Detailed explanation

Practice Multiplying and Dividing Decimal Fractions by 10, 100, etc.

Test your knowledge with 23 quizzes

\( 0.7\times10= \)

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

Step-by-step solutions included
Exercise #1

20.1:10= 20.1:10=

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

Video Solution
Exercise #2

13.61:10= 13.61:10=

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

Video Solution
Exercise #3

12.2:10= 12.2:10=

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

Video Solution
Exercise #4

65.2:10= 65.2:10=

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

Video Solution
Exercise #5

581.8:10= 581.8:10=

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

Video Solution

Frequently Asked Questions

How do you multiply decimals by 10, 100, or 1000?

+
When multiplying decimals by 10, 100, or 1000, move the decimal point to the right as many places as there are zeros in the multiplier. For example, 0.7 × 10 = 7 (move 1 place right), and 0.486 × 100 = 48.6 (move 2 places right).

What happens when dividing decimals by 10, 100, or 1000?

+
When dividing decimals by powers of 10, move the decimal point to the left as many places as there are zeros in the divisor. For instance, 0.6 ÷ 10 = 0.06 (move 1 place left), and 0.364 ÷ 100 = 0.00364 (move 2 places left).

Why does the decimal point move when multiplying by powers of 10?

+
The decimal point moves because multiplying by 10, 100, or 1000 is equivalent to making a number 10, 100, or 1000 times larger. Moving the decimal point right increases the place value of each digit, effectively multiplying the entire number.

What do you do when there aren't enough digits to move the decimal point?

+
When there aren't enough digits, add zeros to fill the empty spaces. For multiplication, add zeros to the right if needed. For division, add zeros to the left of the decimal point, like changing 0.6 ÷ 10 to 0.06.

How do you remember which direction to move the decimal point?

+
Use this memory trick: Multiplication makes numbers bigger, so move RIGHT (positive direction). Division makes numbers smaller, so move LEFT (negative direction). Count the zeros in 10, 100, or 1000 to know how many places to move.

What are common mistakes when moving decimal points?

+
Common mistakes include: 1) Moving the decimal point in the wrong direction, 2) Counting zeros incorrectly, 3) Forgetting to add zeros when needed, 4) Not removing unnecessary zeros from the final answer. Always double-check the direction and count zeros carefully.

Can you multiply decimals by numbers like 10000 or 100000?

+
Yes! The same rule applies to any power of 10. For 10000 (4 zeros), move the decimal point 4 places right for multiplication or 4 places left for division. For example, 1.495 × 10000 = 14950.

How does this decimal rule help in real life math problems?

+
This rule is essential for converting between metric units (meters to centimeters), working with money calculations, scientific notation, and percentage problems. It's also crucial for mental math and estimation skills in everyday situations.

More Multiplying and Dividing Decimal Fractions by 10, 100, etc. Questions

Continue Your Math Journey

Practice by Question Type