Dividing in scientific notation, step by step
Dividing in scientific notation splits into two tidy jobs: the coefficients divide, and the powers of ten subtract.
(3 × 10²) ÷ (7.5 × 10⁻⁵)
- A number in scientific notation is two things multiplied: a coefficient and a power of ten. They travel separately — the coefficients divide with each other and the powers subtract with each other — so take them one at a time.
- Divide the coefficients: 3 ÷ 7.5 = 0.4.
- Now the powers. Dividing powers of the same base SUBTRACTS the exponents: 2 − −5 = 7. So the powers give 10⁷.
- Put them together: 0.4 × 10⁷. Now CHECK it — a coefficient has to be at least 1 and less than 10, and 0.4 is not. This is a true number and it is not in scientific notation yet.
- Move one factor of ten the other way: make the coefficient ten times BIGGER and the power ten times SMALLER. 0.4 × 10 = 4, and 7 − 1 = 6. The quantity has not changed — that is why the line above was true.
- So the answer is 4 × 10⁶ — 3 ÷ 7.5 = 0.4 and the powers give 10⁷, and 0.4 is not between 1 and 10 — so it becomes 4 × 10⁶.
How it works.
- 01
A number in scientific notation is two things multiplied: a coefficient and a power of ten. They travel separately — the coefficients divide with each other and the powers subtract with each other — so take them one at a time.
- 02
Divide the coefficients: 3 ÷ 7.5 = 0.4.
- 03
Now the powers. Dividing powers of the same base SUBTRACTS the exponents: 2 − −5 = 7. So the powers give 10⁷.
- 04
Put them together: 0.4 × 10⁷. Now CHECK it — a coefficient has to be at least 1 and less than 10, and 0.4 is not. This is a true number and it is not in scientific notation yet.
- 05
Move one factor of ten the other way: make the coefficient ten times BIGGER and the power ten times SMALLER. 0.4 × 10 = 4, and 7 − 1 = 6. The quantity has not changed — that is why the line above was true.
- 06
So the answer is 4 × 10⁶ — 3 ÷ 7.5 = 0.4 and the powers give 10⁷, and 0.4 is not between 1 and 10 — so it becomes 4 × 10⁶.