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

\( 51.4:10= \)

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

Step-by-step solutions included
Exercise #1

0.26×10= 0.26\times10=

Step-by-Step Solution

We will solve the problem by multiplying 0.260.26 by 1010. When multiplying a decimal by 1010, the decimal point moves one place to the right.

Let's follow the steps:

  • Recognize our initial number: 0.260.26.
  • To multiply by 1010, shift the decimal point one position to the right. This changes 0.260.26 to 2.62.6.

Therefore, multiplying 0.260.26 by 1010 gives us the result 2.62.6.

The solution to the problem is 2.6 2.6 .

Answer:

2.6 2.6

Video Solution
Exercise #2

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 #3

1.004×10= 1.004\times10=

Step-by-Step Solution

To solve this problem, we'll follow this straightforward approach:

  • Since we are multiplying by 1010, we need to shift the decimal point in the number 1.0041.004 one place to the right.

Now, let's perform the calculation:

The number 1.0041.004 has a decimal point after the first digit, and when we shift the decimal one place to the right, it moves between 00 and 00, resulting in 10.0410.04.

Therefore, the product of 1.0041.004 multiplied by 1010 is 10.0410.04.

Thus, the solution to the problem is 10.04 10.04 .

Answer:

10.04 10.04

Video Solution
Exercise #4

111.1:10= 111.1:10=

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

Video Solution
Exercise #5

2.7×10= 2.7\times10=

Step-by-Step Solution

To solve this problem, we'll use the property that states: when we multiply a decimal number by 1010, we move its decimal point one place to the right.

Let's work through the steps:

  • Step 1: Identify the number and its decimal place. The number 2.72.7 has a decimal point between 22 and 77.
  • Step 2: Since we are multiplying by 1010, move the decimal point one place to the right. Moving the decimal point means 2.72.7 becomes 27.27..
  • Step 3: Write down the resulting number. After moving the decimal point, the number is 2727.

Therefore, the product of 2.7×102.7 \times 10 is 2727.

Answer:

27 27

Video Solution

Frequently Asked Questions

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

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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?

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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?

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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?

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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?

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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?

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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?

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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?

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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.

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