Step by step
The question
Question: work out (8 × 10⁴) × (6 × 10⁻⁷).
(8 × 104) × (6 × 10−7)
1 Group the parts
Times can go in any order.
So we put the numbers together, and the powers of 10 together.
= 8 × 6 × 104 × 10−7
2 Work out each part
8 times 6 is 48.
8 × 6 = 48
We write 48 for the numbers.
= 48 × 104 × 10−7
The rule: when we multiply powers of the same number, here 10, we add the powers.
4 plus −7: adding a minus is taking away.
That is −3.
104 × 10−7 = 104 + (−7)
= 10−3
Now we have 48 × 10⁻³.
= 48 × 10−3
3 Fix the number
48 is not under 10.
48 is 4.8 times 10, that is 4.8 × 10¹.
48 = 4.8 × 101
We write 4.8 × 10¹ in place of 48.
= 4.8 × 101 × 10−3
Add the powers: 1 plus −3 is −2.
101 × 10−3 = 101 + (−3)
= 10−2
So the answer is 4.8 × 10⁻².
= 4.8 × 10−2
4 Check
Let's check the answer is in scientific notation.
4.8 is from 1 to under 10, and it is times a power of 10.
Yes!
4.8 is from 1 to under 10, times 10−2
Let's look back.
First: group the parts.
Then: work out each part.
Then: fix the number.
Last: check.
Answer
= 4.8 × 10−2