Decimal Point Placement: Solve 0.45 × 3.14 = 1413

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

Add zeros to the left of your number! For example, if you need 4 decimal places but only have 3 digits (like 413), write it as 0413, then place the decimal: $ 0.0413 $.

Q: How do I remember which direction to count decimal places?

Always count from the right side moving left! Think of it like this: the decimal point 'walks' from the right, taking as many steps as you counted from both original numbers.

Q: Can I check my answer without a calculator?

Yes! Use estimation: $ 0.45 \times 3.14 $ is close to $ 0.5 \times 3 = 1.5 $. Your answer should be near 1.5, so 1.413 makes sense!

Q: What if I forget to count decimal places in one number?

You'll get the wrong answer every time! Both numbers matter. Even if one number seems 'easier' like 3.14, you still must count its 2 decimal places and add them to the other number's decimal places.

Decimal Multiplication with Place Value Positioning

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

$0.45\times3.14=1413$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Convert decimal numbers to fractions

00:07 Write the number as a whole number in the numerator, and multiply by 10 in the denominator

00:10 Add zeros to the denominator according to the number of digits after the decimal point:

00:14 Move to the second term, use the same method

00:24 Make sure to multiply numerator by numerator and denominator by denominator

00:38 Calculate the multiplications

00:47 Now write the numerator as a whole number

00:53 For the zeros in the denominator, position the decimal point

01:02 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:

$0.45\times3.14=1413$

Step-by-step solution

To solve this problem, we need to determine the correct position of the decimal point in the product $1413$ , which results from multiplying $0.45$ by $3.14$ .

Step 1: Count the decimal places in each factor. The number $0.45$ has 2 decimal places, and $3.14$ has 2 decimal places.
Step 2: Sum the decimal places from each factor. The total number of decimal places is $2 + 2 = 4$ .
Step 3: Place the decimal point in the result $1413$ such that there are 4 digits following the decimal.

Therefore, the decimal point should be placed to give us $1.413$ .

Given the provided choices, the correct option is: $1.413$ .

Thus, the corrected and correctly formatted multiplication result is $1.413$ .

Final Answer

$1.413$

Key Points to Remember

Essential concepts to master this topic

Rule: Total decimal places equals sum of both factors' decimal places
Technique: Count 0.45 (2 places) + 3.14 (2 places) = 4 total places
Check: Verify 1.413 makes sense: 0.5 × 3 ≈ 1.5, close to 1.413 ✓

Common Mistakes

Avoid these frequent errors

Placing decimal point by visual estimation
Don't guess where the decimal goes based on how it 'looks right' = wrong answer every time! Visual placement ignores the mathematical rule and leads to answers like 14.13 or 141.3. Always count the total decimal places from both factors and place the decimal exactly that many places 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 can't I just multiply the numbers and guess where the decimal goes?

Guessing leads to wrong answers! The decimal placement follows a specific rule: count decimal places in both numbers, add them together, then place the decimal that many places from the right in your answer.

What if my answer has fewer digits than decimal places needed?

Add zeros to the left of your number! For example, if you need 4 decimal places but only have 3 digits (like 413), write it as 0413, then place the decimal: $0.0413$ .

How do I remember which direction to count decimal places?

Always count from the right side moving left! Think of it like this: the decimal point 'walks' from the right, taking as many steps as you counted from both original numbers.

Can I check my answer without a calculator?

Yes! Use estimation: $0.45 \times 3.14$ is close to $0.5 \times 3 = 1.5$ . Your answer should be near 1.5, so 1.413 makes sense!

What if I forget to count decimal places in one number?

You'll get the wrong answer every time! Both numbers matter. Even if one number seems 'easier' like 3.14, you still must count its 2 decimal places and add them to the other number's decimal places.

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