Dividing in scientific notation
The question
(3 × 10²) ÷ (7.5 × 10⁻⁵)
(3 × 10²) ÷ (7.5 × 10⁻⁵)
(3 × 10²) ÷ (7.5 × 10⁻⁵)
3÷7.5=0.4
2−−5=7
0.4 × 10⁷
0.4 < 1
0.4 × 10⁷
→4 × 10⁶
(3 × 10²) ÷ (7.5 × 10⁻⁵)=4 × 10⁶
- Handle the two parts separately: the coefficients divide and the powers subtract.
- 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. Check it: a coefficient has to be at least 1 and less than 10, and 0.4 is not.
- 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.
- 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
Handle the two parts separately: the coefficients divide and the powers subtract.
- 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. Check it: a coefficient has to be at least 1 and less than 10, and 0.4 is not.
- 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.
- 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.