Step by step
The question
Question: work out (6 × 10⁵) × (7 × 10³).
(6 × 105) × (7 × 103)
1 Group the parts
Times can go in any order.
So we put the numbers together, and the powers of 10 together.
= 6 × 7 × 105 × 103
2 Work out each part
6 times 7 is 42.
6 × 7 = 42
We write 42 for the numbers.
= 42 × 105 × 103
The rule: same base, times, add the powers.
5 plus 3 is 8.
105 × 103 = 105 + 3 = 108
Now we have 42 × 10⁸.
= 42 × 108
3 Fix the number
42 is not under 10.
42 is 4.2 times 10, that is 4.2 × 10¹.
42 = 4.2 × 101
We write 4.2 × 10¹ in place of 42.
= 4.2 × 101 × 108
Add the powers: 1 plus 8 is 9.
101 × 108 = 101 + 8 = 109
So the answer is 4.2 × 10⁹.
= 4.2 × 109
4 Check
Let's check the answer is in scientific notation.
4.2 is from 1 to under 10, and it is times a power of 10.
Yes!
4.2 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
= 4.2 × 109