What is (3 × 10^4)(2.5 × 10^3)? Step by Step

Step by step

The question

Question: work out (3 × 10⁴) × (2.5 × 10³).

(3 × 10⁴) × (2.5 × 10³)

There are four choices.

First we solve it, the normal way.

Then we pick.

1 Group the parts

Times can go in any order.

So we put the numbers together, and the powers of 10 together.

= 3 × 2.5 × 10⁴ × 10³

2 Work out each part

3 times 2.5 is 7.5.

3 × 2.5 = 7.5

We write 7.5 for the numbers.

= 7.5 × 10⁴ × 10³

The rule: when we multiply powers of the same number, here 10, we add the powers.

4 plus 3.

That is 7.

10⁴ × 10³ = 10^{4 + 3}

= 10⁷

So the answer is 7.5 × 10⁷.

= 7.5 × 10⁷

3 Check

Let's check the answer is in scientific notation.

7.5 is from 1 to under 10, and it is times a power of 10.

Yes!

7.5 is from 1 to under 10, times 10⁷

4 Pick the choice

Our answer is 7.5 × 10⁷.

That is choice C.

C) 7.5 × 10⁷

5 Why not the others

A is 7.5 × 10¹.

Wrong: took the powers away: when we multiply, we add them.

A) 7.5 × 10¹ ✗ took the powers away: when we multiply, we add them

B is 5.5 × 10⁷.

Wrong: added 3 and 2.5 instead of multiplying.

B) 5.5 × 10⁷ ✗ added 3 and 2.5 instead of multiplying

D is 7.5 × 10¹².

Wrong: multiplied the powers: we add them.

D) 7.5 × 10¹² ✗ multiplied the powers: we add them

Let's look back.

First: group the parts.

Then: work out each part.

Then: check.

Then: pick the choice.

Last: why not the others.

Answer