Final answer:
Divide the coefficients 2.4 by 8 to get 0.3 and subtract the exponents of the powers of ten, 13 minus 7, to get 6, resulting in 0.3 × 10⁶.
Step-by-step explanation:
The division of 2.4 × 10¹³ by 8 × 10⁷ involves both dividing the coefficients (2.4 and 8) and subtracting the exponents of the powers of ten (13 and 7). Firstly, we divide the coefficients:
2.4 divided by 8 equals 0.3. Next, we apply the rule for dividing powers of ten, which is to subtract the exponent in the denominator from that in the numerator:
13 - 7 equals 6. Combining these results, we get 0.3 × 10⁶.
Another approach is to convert the division into a multiplication by inverting the divisor. We rewrite 8 × 10⁷ as 0.125 × 10⁻⁷ and multiply it with 2.4 × 10¹³, effectively combining the steps of division of coefficients and addition of exponents to achieve the same result.