Final answer:
The division problem 1.2x10⁹ ÷ 3x10² = 4x10⁶ is solved by dividing the base numbers and subtracting the exponents of the powers of ten. The correct result, using the rules of scientific notation, is indeed 4x10⁶.
Step-by-step explanation:
The student's question is asking how to solve the division problem involving numbers expressed in scientific notation: 1.2x10⁹ ÷ 3x10² = 4x10⁶. To solve the problem, we apply the rule of division for numbers in scientific notation.
First, separate the division into two parts - one for the base numbers, and one for the powers of ten:
(1.2 ÷ 3) x (10⁹ ÷ 10²)
Then we perform the division for the base numbers:
0.4 (since 1.2 ÷ 3 equals 0.4)
Next, we subtract the exponents of 10 according to the rule for dividing powers of ten:
10⁷ (since 9 - 2 equals 7)
Putting it all together:
0.4 x 10⁷
But we're given the answer is 4x10⁶, so let's check our result. We can write 0.4 as 4 x 0.1, which is 4 x 10⁻¹, thus:
4 x 10⁻¹ x 10⁷ = 4 x 10⁶ (because -1 + 7 equals 6)
This confirms the initial equation is correct: 1.2x10⁹ ÷ 3x10² = 4x10⁶.