Solve: Placing the Decimal Point in 2.5 × 0.13 = 0325

Q: What if I forget to count decimal places in one of the numbers?

You'll get the wrong answer! Both numbers matter. In 2.5 × 0.13, missing the 2 places in 0.13 would give you only 1 decimal place instead of the correct 3.

Q: Does the leading zero in 0.325 matter?

Yes, for clarity! Writing 0.325 instead of just .325 makes it clear you have a decimal less than 1. It's good mathematical practice and prevents confusion.

Q: How do I know if 0325 should become 0.325 or 0.0325?

Count the decimal places! $ 2.5 $ has 1 place, $ 0.13 $ has 2 places. Total = 3 places, so count 3 positions from the right in 0325 to get 0.325.

Decimal Multiplication with Place Value Positioning

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

$2.5\times0.13=0325$

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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 the total number of digits after the decimal point

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

00:12 We'll move the decimal point by the sum of digits

00:15 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:

$2.5\times0.13=0325$

Step-by-step solution

To solve this problem, we'll determine the placement of the decimal point, adhering to the total number of decimal places rule in multiplication:

Step 1: Identify the decimal places in the numbers.
- $2.5$ has 1 decimal place.
- $0.13$ has 2 decimal places.
Step 2: Calculate the total decimal places in the product:
- Total: $1 + 2 = 3$ decimal places.
Step 3: Apply the decimal places to the product $0325$ :
- Insert decimal point into $0325$ such that it reflects 3 decimal places:

Position the decimal to achieve $0.325$ .

Therefore, the correct placement of the decimal point results in the answer $\text{0}.325$ , matching the given correct answer.

Final Answer

$\text{0}.325$

Key Points to Remember

Essential concepts to master this topic

Decimal Rule: Count total decimal places in both factors
Technique: Add decimal places: 2.5 (1 place) + 0.13 (2 places) = 3 total
Check: Verify 0.325 by counting rightward from 0325: three places ✓

Common Mistakes

Avoid these frequent errors

Placing decimal point by guessing or visual estimation
Don't look at 0325 and guess where the decimal goes = wrong placement like 03.25! This ignores the mathematical rule and leads to answers off by factors of 10 or 100. Always count the exact number of decimal places from both original numbers first.

Practice Quiz

Test your knowledge with interactive questions

$0.1 \times 0.008 =$

FAQ

Everything you need to know about this question

Why can't I just estimate where the decimal point should go?

Estimating leads to major errors! The decimal placement rule is mathematical and precise. With $2.5 \times 0.13$ , you need exactly 3 decimal places, giving 0.325, not a guess like 3.25.

What if I forget to count decimal places in one of the numbers?

You'll get the wrong answer! Both numbers matter. In 2.5 × 0.13, missing the 2 places in 0.13 would give you only 1 decimal place instead of the correct 3.

Does the leading zero in 0.325 matter?

Yes, for clarity! Writing 0.325 instead of just .325 makes it clear you have a decimal less than 1. It's good mathematical practice and prevents confusion.

How do I know if 0325 should become 0.325 or 0.0325?

Count the decimal places! $2.5$ has 1 place, $0.13$ has 2 places. Total = 3 places, so count 3 positions from the right in 0325 to get 0.325.

What if my answer has trailing zeros after the decimal?

You can usually drop trailing zeros after the decimal point. For example, 0.250 becomes 0.25. But always check your specific problem to see if exact precision is required.

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