Multiplying in scientific notation
The question
(1.2 × 10⁻³) × (8 × 10²)
(1.2 × 10⁻³) × (8 × 10²)
(1.2 × 10⁻³) × (8 × 10²)
1.2×8=9.6
−3+2=−1
9.6 × 10⁻¹
1 ≤ 9.6 < 10
(1.2 × 10⁻³) × (8 × 10²)=9.6 × 10⁻¹
- Handle the two parts separately: the coefficients multiply and the powers add.
- Multiply the coefficients: 1.2 × 8 = 9.6.
- Now the powers. Multiplying powers of the same base adds the exponents: −3 + 2 = −1. So the powers give 10⁻¹.
- Put them together: 9.6 × 10⁻¹. Check it: a coefficient has to be at least 1 and less than 10, and 9.6 is.
- So the answer is 9.6 × 10⁻¹ — 1.2 × 8 = 9.6 and the powers give 10⁻¹.
How it works.
- 01
Handle the two parts separately: the coefficients multiply and the powers add.
- 02
Multiply the coefficients: 1.2 × 8 = 9.6.
- 03
Now the powers. Multiplying powers of the same base adds the exponents: −3 + 2 = −1. So the powers give 10⁻¹.
- 04
Put them together: 9.6 × 10⁻¹. Check it: a coefficient has to be at least 1 and less than 10, and 9.6 is.
- 05
So the answer is 9.6 × 10⁻¹ — 1.2 × 8 = 9.6 and the powers give 10⁻¹.