Calculate the Product: 0.5 × 6.7 × 6.31 Decimal Multiplication

Sequential Decimal Multiplication with Three Factors

Solve the following problem:

0.5×6.7×6.31= 0.5\times6.7\times6.31=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's begin by solving the problem.
00:10 We'll use long multiplication. Watch closely as I explain each step.
00:21 Remember to notice where the decimal point is placed.
00:25 Zero times any number is always zero. That's an important rule.
00:31 Now, this finishes our first part of the multiplication.
00:40 Let's go over it again with long multiplication. Pay careful attention.
00:53 Don't forget to check the decimal point again.
01:26 And there you go! That's how we solve this problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following problem:

0.5×6.7×6.31= 0.5\times6.7\times6.31=

2

Step-by-step solution

Adhering to the rules of the order of operations the exercise can be solved from left to right given that it only contains multiplication

The exercise on the left hand side should be solved vertically in order to avoid confusion as shown below:

0.5×6.7=3.35 0.5\\\times6.7\\=3.35

It is important to maintain correct positioning of the exercise, with the decimal point serving as an anchor.
Then we can multiply in order, first the ones digit of the first number by the ones digit of the second number,
then the tens digit of the first number by the ones digit of the second number, and so on.

This should result in the following exercise::

3.35×6.31= 3.35\times6.31=

We will once again solve the exercise vertically whilst maintaining the decimal point and multiplying in order (ones, tens, and so on)

As shown below:

3.35×6.31=21.1385 3.35\\\times6.31\\=21.1385

3

Final Answer

21.1385 21.1385

Key Points to Remember

Essential concepts to master this topic
  • Order of Operations: Multiply from left to right with three decimal numbers
  • Technique: First calculate 0.5 × 6.7 = 3.35, then 3.35 × 6.31
  • Check: Count total decimal places: 1 + 1 + 2 = 4 places in final answer ✓

Common Mistakes

Avoid these frequent errors
  • Counting decimal places incorrectly in final answer
    Don't forget to count decimal places in each factor = wrong placement! Students often miscount 0.5 (1 place) + 6.7 (1 place) + 6.31 (2 places) = 4 total places. Always add up all decimal places from every factor to place the decimal point correctly in your final answer.

Practice Quiz

Test your knowledge with interactive questions

\( 94+12+6= \)

FAQ

Everything you need to know about this question

Do I have to multiply from left to right?

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Yes! While multiplication is commutative (order doesn't matter), working left to right with 0.5×6.7×6.31 0.5 \times 6.7 \times 6.31 helps you stay organized and avoid errors.

How do I keep track of decimal places?

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Count decimal places in each factor: 0.5 has 1, 6.7 has 1, and 6.31 has 2. Add them up: 1 + 1 + 2 = 4 places in your final answer.

Can I ignore decimals and add them back later?

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Absolutely! Multiply 5×67×631=211385 5 \times 67 \times 631 = 211385 , then place the decimal 4 places from the right: 21.1385.

What if I get a different answer doing it step by step?

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Double-check your arithmetic! First: 0.5×6.7=3.35 0.5 \times 6.7 = 3.35 . Then: 3.35×6.31=21.1385 3.35 \times 6.31 = 21.1385 . Each step must be accurate.

Why is 21.1385 correct and not 21.14?

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The exact answer is 21.1385. Only round if the problem specifically asks for it! Always give the complete answer unless told to round to a certain number of decimal places.

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