Step by step
The question
Question: work out (2.4 × 10⁴) × (3 × 10⁵).
(2.4 × 104) × (3 × 105)
1 Group the parts
Times can go in any order.
So we put the numbers together, and the powers of 10 together.
= 2.4 × 3 × 104 × 105
2 Work out each part
2.4 times 3 is 7.2.
2.4 × 3 = 7.2
We write 7.2 for the numbers.
= 7.2 × 104 × 105
The rule: when we multiply powers of the same number, here 10, we add the powers.
4 plus 5.
That is 9.
104 × 105 = 104 + 5
= 109
So the answer is 7.2 × 10⁹.
= 7.2 × 109
3 Check
Let's check the answer is in scientific notation.
7.2 is from 1 to under 10, and it is times a power of 10.
Yes!
7.2 is from 1 to under 10, times 109
Let's look back.
First: group the parts.
Then: work out each part.
Last: check.
Answer
= 7.2 × 109