Calculate the Product: 3.12 × 109 Step-by-Step

Q: Why do I multiply 312 × 109 instead of 3.12 × 109 directly?

It's much easier to multiply whole numbers first! By treating 3.12 as 312, you avoid decimal confusion during multiplication. Just remember to put the decimal back at the end.

Q: How do I know where to put the decimal point?

Count the decimal places in your original numbers. $ 3.12 $ has 2 decimal places, and 109 has 0. So your answer needs 2 decimal places: 34008 becomes 340.08.

Q: What if I get confused with the place value?

Try this trick: cover up the decimal point, multiply normally, then count from the right to place your decimal. For 34008 with 2 places: 340.08

Q: Can I use a different method to solve this?

Yes! You could use the distributive property: $ 3.12 \times 109 = 3.12 \times (100 + 9) = 312 + 28.08 = 340.08 $. Both methods work!

Q: How can I check if 340.08 is reasonable?

Estimate first! $ 3 \times 100 = 300 $, so your answer should be close to 300. Since 340.08 is near 300, it makes sense. Always estimate before calculating!

Decimal Multiplication with Place Value Adjustment

$3.12\times109=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Multiply each digit by each digit, and place in the appropriate position

00:14 Calculate and place, add the tens digit when necessary

00:37 Move to the next digit, calculate and place in the appropriate position

00:40 Any number multiplied by 0 always equals 0

00:50 Move to the next digit, calculate and place in the appropriate position

00:53 Any number multiplied by 1 always equals itself

01:00 Combine the results

01:07 Sum up the digits after the decimal point

01:13 Based on this sum, place the decimal point

01:18 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

$3.12\times109=$

Step-by-step solution

To solve $3.12 \times 109$ , we proceed as follows:

Step 1: Multiply the numbers as if they were whole numbers. Multiply $312$ by $109$ .
Step 2: Calculate $312 \times 109$ :
- $312 \times 100 = 31200$
- $312 \times 9 = 2808$
- Add the two results: $31200 + 2808 = 34008$ .
Step 3: Adjust for decimal places. Since $3.12$ has two decimal places, divide $34008$ by $100$ to get $340.08$ .

Therefore, the solution to the multiplication is $340.08$ .

Final Answer

$340.08$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply as whole numbers, then adjust decimal places
Technique: 312 × 109 = 34008, then move 2 places left
Check: Count decimal places: 3.12 has 2, so 34008 → 340.08 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to adjust for decimal places
Don't just multiply 312 × 109 = 34008 and stop there! This gives 34008 instead of 340.08 - way too big. Always count the decimal places in the original numbers and move the decimal point that many places to the left in your final answer.

Practice Quiz

Test your knowledge with interactive questions

$\text{0}.07\times10=$

FAQ

Everything you need to know about this question

Why do I multiply 312 × 109 instead of 3.12 × 109 directly?

It's much easier to multiply whole numbers first! By treating 3.12 as 312, you avoid decimal confusion during multiplication. Just remember to put the decimal back at the end.

How do I know where to put the decimal point?

Count the decimal places in your original numbers. $3.12$ has 2 decimal places, and 109 has 0. So your answer needs 2 decimal places: 34008 becomes 340.08.

What if I get confused with the place value?

Try this trick: cover up the decimal point, multiply normally, then count from the right to place your decimal. For 34008 with 2 places: 340.08

Can I use a different method to solve this?

Yes! You could use the distributive property: $3.12 \times 109 = 3.12 \times (100 + 9) = 312 + 28.08 = 340.08$ . Both methods work!

How can I check if 340.08 is reasonable?

Estimate first! $3 \times 100 = 300$ , so your answer should be close to 300. Since 340.08 is near 300, it makes sense. Always estimate before calculating!

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