Step by step
The question
Question: work out (1.2 × 10⁵) × (3 × 10⁻⁸).
(1.2 × 105) × (3 × 10−8)
1 Group the parts
Times can go in any order.
So we put the numbers together, and the powers of 10 together.
= 1.2 × 3 × 105 × 10−8
2 Work out each part
1.2 times 3 is 3.6.
1.2 × 3 = 3.6
We write 3.6 for the numbers.
= 3.6 × 105 × 10−8
The rule: same base, times, add the powers.
5 plus −8 is −3.
105 × 10−8 = 105 + (−8) = 10−3
So the answer is 3.6 × 10⁻³.
= 3.6 × 10−3
3 Check
Let's check the answer is in scientific notation.
3.6 is from 1 to under 10, and it is times a power of 10.
Yes!
3.6 is from 1 to under 10, times 10−3
Let's look back.
First: group the parts.
Then: work out each part.
Last: check.
Answer
= 3.6 × 10−3