Calculate the Product: 5.11 × 110 Decimal Multiplication

Q: Why do we ignore the decimal point during multiplication?

Ignoring the decimal temporarily makes multiplication much easier because you can use regular whole number multiplication. Just remember to put the decimal back in the correct position at the end!

Q: How do I know where to place the decimal in my answer?

Count the total decimal places in both numbers you're multiplying. 5.11 has 2 decimal places, 110 has 0, so your answer needs 2 + 0 = 2 decimal places from the right.

Q: What if I multiply and get trailing zeros?

Keep the trailing zeros if they're significant! For example, if your calculation gives 562.10, you can write it as 562.1, but both are mathematically correct.

Q: Can I use the same method for any decimal multiplication?

Yes! This method works for any decimal multiplication: ignore decimals, multiply normally, then count total decimal places to position your final decimal point.

Q: What if my answer has more decimal places than expected?

Double-check your counting! Make sure you counted all decimal places in both original numbers. If you still get unexpected results, verify your whole number multiplication first.

Decimal Multiplication with Place Value Positioning

$5.11\times110=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Multiply each digit by each digit, and place in the appropriate position

00:08 Any number multiplied by 0 is always equal to 0

00:19 Move to the next digit, calculate and place in the appropriate position

00:23 Any number multiplied by 1 is always equal to itself

00:26 Move to the next digit, calculate and place in the appropriate position

00:35 Add up the results

00:42 Sum up all digits after the decimal point

00:47 Based on this sum, we'll place the decimal point

00:52 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$5.11\times110=$

Step-by-step solution

To solve this problem, we'll multiply the decimal number 5.11 by the integer 110. To do this, we'll follow these main steps:

Step 1: Treat the decimal number 5.11 temporarily as 511 by ignoring the decimal point. This helps us simplify the multiplication process.
Step 2: Multiply 511 by 110, as if they were whole numbers:

$511 \times 110$

Step 3: Calculate the product:

$511 \times 110 = 56210$

Step 4: Since the original problem involved a decimal (two decimal places in number 5.11), adjust the product to account for these two decimal places by dividing by 100:

$56210 \div 100 = 562.1$

Therefore, the solution to the problem is $562.1$ .

Final Answer

$562.1$

Key Points to Remember

Essential concepts to master this topic

Decimal Rule: Count total decimal places in both factors
Technique: Multiply 511 × 110 = 56210, then place decimal
Check: 5.11 has 2 decimal places, so 56210 becomes 562.1 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to count decimal places in the final answer
Don't just multiply 511 × 110 = 56210 and leave it as a whole number! This ignores the original decimal completely and gives 56210 instead of 562.1. Always count the decimal places in your factors (5.11 has 2 places) and move the decimal point that many places left in your final answer.

Practice Quiz

Test your knowledge with interactive questions

$0.26\times10=$

FAQ

Everything you need to know about this question

Why do we ignore the decimal point during multiplication?

Ignoring the decimal temporarily makes multiplication much easier because you can use regular whole number multiplication. Just remember to put the decimal back in the correct position at the end!

How do I know where to place the decimal in my answer?

Count the total decimal places in both numbers you're multiplying. 5.11 has 2 decimal places, 110 has 0, so your answer needs 2 + 0 = 2 decimal places from the right.

What if I multiply and get trailing zeros?

Keep the trailing zeros if they're significant! For example, if your calculation gives 562.10, you can write it as 562.1, but both are mathematically correct.

Can I use the same method for any decimal multiplication?

Yes! This method works for any decimal multiplication: ignore decimals, multiply normally, then count total decimal places to position your final decimal point.

What if my answer has more decimal places than expected?

Double-check your counting! Make sure you counted all decimal places in both original numbers. If you still get unexpected results, verify your whole number multiplication first.

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