Worked examples
The question
Question: write 45000 in scientific notation.
45000
1 What it looks like
Scientific notation is a number from 1 to under 10, times a power of 10.
a × 10n a: from 1 to under 10
2 Move the point
Moving the point 4 to the left made the number 10000 times smaller.
To make it the same again, we times by 10000.
That is 10⁴.
104 = 10000
So 45000 is 4.5000 × 10⁴.
= 4.5000 × 104
Zeros at the end, after the point, can go: 4.5000 is 4.5.
So we get 4.5 × 10⁴.
= 4.5 × 104
3 Check
Let's check: times 10000 moves the point 4 back to the right.
We get 45000 again!
4.5 × 10000 = 45000
Let's look back.
First: what it looks like.
Then: move the point.
Last: check.
▶ Watch it solved
The question
Question: work out (3 × 10⁴) × (2 × 10⁵).
(3 × 104) × (2 × 105)
1 Group the parts
Times can go in any order.
So we put the numbers together, and the powers of 10 together.
= 3 × 2 × 104 × 105
2 Work out each part
3 times 2 is 6.
3 × 2 = 6
We write 6 for the numbers.
= 6 × 104 × 105
The rule: same base, times, add the powers.
4 plus 5 is 9.
104 × 105 = 104 + 5 = 109
So the answer is 6 × 10⁹.
= 6 × 109
3 Check
Let's check the answer is in scientific notation.
6 is from 1 to under 10, and it is times a power of 10.
Yes!
6 is from 1 to under 10, times 109
Let's look back.
First: group the parts.
Then: work out each part.
Last: check.
▶ Watch it solved
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.
▶ Watch it solved
