Step by step
The question
Question: work out 3 × 10⁴ divided by 6 × 10⁻².
3 × 1046 × 10−2
1 Group the parts
We divide the numbers, and we divide the powers of 10.
= 36 × 10410−2
2 Work out each part
3 divided by 6 is 0.5.
3 ÷ 6 = 0.5
We write 0.5 for the numbers.
= 0.5 × 10410−2
The rule: same base, divide, take away the powers.
4 minus −2 is 6.
10410−2 = 104 − (−2) = 106
Now we have 0.5 × 10⁶.
= 0.5 × 106
3 Fix the number
0.5 is less than 1.
0.5 is 5 divided by 10, that is 5 × 10⁻¹.
0.5 = 5 × 10−1
We write 5 × 10⁻¹ in place of 0.5.
= 5 × 10−1 × 106
Add the powers: −1 plus 6 is 5.
10−1 × 106 = 10−1 + 6 = 105
So the answer is 5 × 10⁵.
= 5 × 105
4 Check
Let's check the answer is in scientific notation.
5 is from 1 to under 10, and it is times a power of 10.
Yes!
5 is from 1 to under 10, times 105
Let's look back.
First: group the parts.
Then: work out each part.
Then: fix the number.
Last: check.
Answer
= 5 × 105