Solve: Find the Product of 102×10×10 Using Powers of Ten

Q: Why do I multiply 10 × 10 first instead of going left to right?

You can work left to right or right to left with multiplication! The explanation shows right to left because $ 10 \times 10 = 100 $ is easier to see, then $ 102 \times 100 $ follows the pattern.

Q: What if I get confused about where to put the comma?

In large numbers, put commas every three digits from the right. So 10200 becomes 10,200 with a comma separating thousands.

Q: Does this zero-adding trick work with any number times 10 or 100?

Yes! Multiplying by 10 adds one zero, by 100 adds two zeros, by 1,000 adds three zeros. This is the power of ten pattern.

Q: How can I check my answer without doing the full calculation again?

Use estimation: 102 is about 100, and $ 100 \times 100 = 10,000 $. Your answer 10,200 should be close to this estimate!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:02 We will use the commutative law and solve this multiplication first, then continue

00:06 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$102\times10\times10=$

2

Step-by-step solution

According to the order of operations rules, since the exercise has only multiplication, we can solve it from right to left, as this is the simpler exercise:

$10\times10=100$

Now we will get the exercise:

$102\times100=$

Since this is a multiplication exercise where we multiply by 100, without calculation we can simply take the two zeros of the 100 and add them to the result we got in the previous exercise.

It's important to make sure to write the decimal point in the correct place.

Now we will get the number:

$10,200$

3

Final Answer

$10,200$

Key Points to Remember

Essential concepts to master this topic

Rule: When multiplying by 10, add one zero to the number
Technique: $10 \times 10 = 100$ , then $102 \times 100 = 10,200$
Check: Count zeros: two tens give 100, so 102 becomes 10,200 ✓

Common Mistakes

Avoid these frequent errors

Adding zeros incorrectly when multiplying by powers of ten
Don't just add one zero when multiplying 102 by two tens = wrong answer like 1,020! This misses that 10 × 10 = 100 (two zeros). Always first calculate the powers of ten, then multiply by adding the correct number of zeros.

Practice Quiz

Test your knowledge with interactive questions

$$ 13+5+5= $$ ?

FAQ

Everything you need to know about this question

Why do I multiply 10 × 10 first instead of going left to right?

+

You can work left to right or right to left with multiplication! The explanation shows right to left because $10 \times 10 = 100$ is easier to see, then $102 \times 100$ follows the pattern.

How do I know how many zeros to add when multiplying by 100?

+

Count the zeros in the number you're multiplying by! Since 100 has two zeros, you add two zeros to 102, making it 10,200.

What if I get confused about where to put the comma?

+

In large numbers, put commas every three digits from the right. So 10200 becomes 10,200 with a comma separating thousands.

Does this zero-adding trick work with any number times 10 or 100?

+

Yes! Multiplying by 10 adds one zero, by 100 adds two zeros, by 1,000 adds three zeros. This is the power of ten pattern.

How can I check my answer without doing the full calculation again?

+

Use estimation: 102 is about 100, and $100 \times 100 = 10,000$ . Your answer 10,200 should be close to this estimate!

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Solve: Find the Product of 102×10×10 Using Powers of Ten

Multiplication with Powers of Ten

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