Step by step
The question
Question: work out (3.2 × 10⁵) × (4 × 10³).
(3.2 × 105) × (4 × 103)
1 Group the parts
Times can go in any order.
So we put the numbers together, and the powers of 10 together.
= 3.2 × 4 × 105 × 103
2 Work out each part
3.2 times 4 is 12.8.
3.2 × 4 = 12.8
We write 12.8 for the numbers.
= 12.8 × 105 × 103
The rule: when we multiply powers of the same number, here 10, we add the powers.
5 plus 3.
That is 8.
105 × 103 = 105 + 3
= 108
Now we have 12.8 × 10⁸.
= 12.8 × 108
3 Fix the number
12.8 is not under 10.
12.8 is 1.28 times 10, that is 1.28 × 10¹.
12.8 = 1.28 × 101
We write 1.28 × 10¹ in place of 12.8.
= 1.28 × 101 × 108
Add the powers: 1 plus 8 is 9.
101 × 108 = 101 + 8
= 109
So the answer is 1.28 × 10⁹.
= 1.28 × 109
4 Check
Let's check the answer is in scientific notation.
1.28 is from 1 to under 10, and it is times a power of 10.
Yes!
1.28 is from 1 to under 10, times 109
Let's look back.
First: group the parts.
Then: work out each part.
Then: fix the number.
Last: check.
Answer
= 1.28 × 109