Worked examples
The question
Question: write 4.5 × 10⁴ as a normal number.
4.5 × 104
1 Read the power
10⁴ is 10000.
Times 10000 makes the number bigger, so the point moves 4 places to the right.
104 = 10000
right 4 places
2 Move the point
There are not enough digits after the point.
We write 3 zeros at the end.
Zeros there do not change the number.
= 4.5000
The point is at the end now, so we leave it out.
So 4.5 × 10⁴ = 45000.
= 45000
Careful!
The power is not the number of zeros.
It is how many places the point moves.
4.5 already has 1 digit after the point.
Careful: not 450000 ✗
3 Check
Let's check: times 10000.
4.5 times 10000 is 45000.
It works!
4.5 × 10000 = 45000
Let's look back.
First: read the power.
Then: move the point.
Last: check.
▶ Watch it solved
The question
Question: write 3.2 × 10⁻⁴ as a normal number.
3.2 × 10−4
1 Read the power
10⁻⁴ is 1/10000.
That divides by 10000: the number gets smaller, so the point moves 4 places to the left.
10−4 = 110000
left 4 places
2 Move the point
There are no digits in front of it.
We write 4 zeros in front.
Zeros there do not change the number.
= 00003.2
A 0 goes in front of the point.
So 3.2 × 10⁻⁴ = 0.00032.
= 0.00032
Careful!
The power is not the number of zeros after the point.
It is how many places the point moves.
Careful: not 0.000032 ✗
3 Check
Let's check: divide by 10000.
3.2 divided by 10000 is 0.00032.
It works!
3.2 ÷ 10000 = 0.00032
Let's look back.
First: read the power.
Then: move the point.
Last: check.
▶ Watch it solved
The question
Question: write 1.2 × 10⁻⁷ as a normal number.
1.2 × 10−7
1 Read the power
10⁻⁷ is 1/10000000.
That divides by 10000000: the number gets smaller, so the point moves 7 places to the left.
10−7 = 110000000
left 7 places
2 Move the point
There are no digits in front of it.
We write 7 zeros in front.
Zeros there do not change the number.
= 00000001.2
A 0 goes in front of the point.
So 1.2 × 10⁻⁷ = 0.00000012.
= 0.00000012
Careful!
The power is not the number of zeros after the point.
It is how many places the point moves.
Careful: not 0.000000012 ✗
3 Check
Let's check: divide by 10000000.
1.2 divided by 10000000 is 0.00000012.
It works!
1.2 ÷ 10000000 = 0.00000012
Let's look back.
First: read the power.
Then: move the point.
Last: check.
▶ Watch it solved
