Decimal Multiplication: Finding the Correct Decimal Point in 3.5 × 2.4 = 840

Decimal Multiplication with Place Value Rules

Look at the following exercise and determine the correct place of the decimal point:

3.5×2.4=840 3.5\times2.4=840

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:09 First, look for the decimal point.
00:12 Next, count the digits that are after it.
00:15 Based on this count, place the decimal point in your answer.
00:19 Shift the decimal point by that number of digits.
00:23 And there you go! That's how we find the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the following exercise and determine the correct place of the decimal point:

3.5×2.4=840 3.5\times2.4=840

2

Step-by-step solution

In the number -3.5, there is one digit after the decimal point: 5.

In the number 2.4, there is one digit after the decimal point: 4.

In other words, we have two digits after the decimal point.

Therefore we will move the decimal point two places to the left to get our answer: 8.40.

3

Final Answer

8.40 \text{8}.40

Key Points to Remember

Essential concepts to master this topic
  • Rule: Count total decimal places in both factors before multiplying
  • Technique: Move decimal point left 2 places: 840 becomes 8.40
  • Check: Verify 3.5 × 2.4 ≈ 4 × 2 = 8, so 8.40 is reasonable ✓

Common Mistakes

Avoid these frequent errors
  • Placing decimal point by estimating or guessing position
    Don't guess where the decimal goes based on what 'looks right' = completely wrong answers! This leads to results that are 10 or 100 times too big or small. Always count the total decimal places in both factors and move the decimal that many places left.

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 count decimal places in both numbers?

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When multiplying decimals, the total decimal places in your answer equals the sum of decimal places in both factors. 3.5 3.5 has 1 place, 2.4 2.4 has 1 place, so your answer needs 1 + 1 = 2 places.

What if I forget to move the decimal point?

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You'll get an answer that's way too big! For example, getting 840 instead of 8.40 means your answer is 100 times larger than it should be. Always double-check by estimating.

How can I check if my decimal placement is right?

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Use estimation! Round 3.5×2.4 3.5 \times 2.4 to 4×2=8 4 \times 2 = 8 . Since 8.40 is close to 8, it's correct. If you got 84.0 or 0.84, those are too far from your estimate!

Do I always move the decimal point to the left?

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Yes, always left! When you multiply whole numbers first (like 35 × 24 = 840), you get a bigger number. Moving the decimal left makes it smaller to match the original decimal factors.

What if one number doesn't have a decimal point?

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Whole numbers like 5 actually have an invisible decimal: 5.0. So 5×2.3 5 \times 2.3 has 0 + 1 = 1 total decimal place in the answer.

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