Decimal Multiplication: Place the Decimal Point in 6.13 × 2.05 = 125665

Q: Why do I add the decimal places instead of multiplying them?

This is the fundamental rule of decimal multiplication! When you multiply decimals, the total number of decimal places in the answer equals the sum of decimal places in both factors. It's like combining the precision from both numbers.

Q: What if I get confused about which direction to count?

Always count from the right side moving left! Think of it like this: start at the rightmost digit of your product and count backwards the total number of decimal places needed.

Q: How can I check if my decimal placement is reasonable?

Use estimation! Round both numbers to whole numbers and multiply: $ 6 \times 2 = 12 $. Your answer should be close to 12, so 12.5665 makes sense, but 125.665 would be way too big!

Q: What happens if my product has fewer digits than decimal places needed?

Add leading zeros! For example, if you need 4 decimal places but only have 3 digits (like 123), write it as 0123, then place the decimal: 0.0123.

Q: Do I need to memorize this rule or can I understand why it works?

Understanding is better! Think about it: $ 6.13 = \frac{613}{100} $ and $ 2.05 = \frac{205}{100} $. When you multiply fractions, you get $ \frac{613 \times 205}{100 \times 100} = \frac{125665}{10000} $, which equals 12.5665!

Decimal Placement with Multiplication Products

Given the following exercise, find the correct place of the decimal point:

$6.13\times2.05=125665$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Place the decimal point

00:04 Count all digits after the decimal point

00:08 According to this sum, we'll place the decimal point in the solution

00:13 We'll move the decimal point by the sum of digits

00:17 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

Given the following exercise, find the correct place of the decimal point:

$6.13\times2.05=125665$

Step-by-step solution

To resolve the problem of finding the correct decimal point placement in the product of $6.13$ and $2.05$ , we proceed as follows:

Step 1: Calculate the total decimal places by adding the decimal places of each number.
- The number $6.13$ has 2 decimal places.
- The number $2.05$ has 2 decimal places.
- Therefore, the total number of decimal places in the product should be $2 + 2 = 4$ .
Step 2: Place the decimal point in the product number $125665$ to achieve 4 decimal places.
- Starting from the right, count four places towards the left: $1256.65$ .
- From $1256.65$ , adjust to achieve 4 places, resulting in $12.5665$ .

Thus, the correctly positioned product is $12.5665$ .

Final Answer

$12.5665$

Key Points to Remember

Essential concepts to master this topic

Rule: Total decimal places equals sum of factor decimal places
Technique: Count 2+2=4 places from right: 125665 becomes 12.5665
Check: Estimate: 6×2=12, so 12.5665 is reasonable ✓

Common Mistakes

Avoid these frequent errors

Counting decimal places incorrectly
Don't place the decimal randomly or count from the left = completely wrong answer! This ignores the fundamental rule of decimal multiplication. Always count the total decimal places from both factors, then place the decimal that many positions from the RIGHT.

Practice Quiz

Test your knowledge with interactive questions

$0.1 \times 0.008 =$

FAQ

Everything you need to know about this question

Why do I add the decimal places instead of multiplying them?

This is the fundamental rule of decimal multiplication! When you multiply decimals, the total number of decimal places in the answer equals the sum of decimal places in both factors. It's like combining the precision from both numbers.

What if I get confused about which direction to count?

Always count from the right side moving left! Think of it like this: start at the rightmost digit of your product and count backwards the total number of decimal places needed.

How can I check if my decimal placement is reasonable?

Use estimation! Round both numbers to whole numbers and multiply: $6 \times 2 = 12$ . Your answer should be close to 12, so 12.5665 makes sense, but 125.665 would be way too big!

What happens if my product has fewer digits than decimal places needed?

Add leading zeros! For example, if you need 4 decimal places but only have 3 digits (like 123), write it as 0123, then place the decimal: 0.0123.

Do I need to memorize this rule or can I understand why it works?

Understanding is better! Think about it: $6.13 = \frac{613}{100}$ and $2.05 = \frac{205}{100}$ . When you multiply fractions, you get $\frac{613 \times 205}{100 \times 100} = \frac{125665}{10000}$ , which equals 12.5665!

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