Step by step
The question
Question: work out 2 × 10⁵ divided by 8 × 10².
2 × 1058 × 102
1 Group the parts
We divide the numbers, and we divide the powers of 10.
= 28 × 105102
2 Work out each part
2 divided by 8 is 0.25.
2 ÷ 8 = 0.25
We write 0.25 for the numbers.
= 0.25 × 105102
The rule: same base, divide, take away the powers.
5 minus 2 is 3.
105102 = 105 − 2 = 103
Now we have 0.25 × 10³.
= 0.25 × 103
3 Fix the number
0.25 is less than 1.
0.25 is 2.5 divided by 10, that is 2.5 × 10⁻¹.
0.25 = 2.5 × 10−1
We write 2.5 × 10⁻¹ in place of 0.25.
= 2.5 × 10−1 × 103
Add the powers: −1 plus 3 is 2.
10−1 × 103 = 10−1 + 3 = 102
So the answer is 2.5 × 10².
= 2.5 × 102
4 Check
Let's check the answer is in scientific notation.
2.5 is from 1 to under 10, and it is times a power of 10.
Yes!
2.5 is from 1 to under 10, times 102
Let's look back.
First: group the parts.
Then: work out each part.
Then: fix the number.
Last: check.
Answer
= 2.5 × 102