Final answer:
In mathematics, to solve 2.4 × 10¹13 divided by 8 × 10¹7, we subtract the exponents and divide the prefactors to get 0.3 × 10¹6. Simplifying further by using the divisibility of 24 by 8, we end up with 3 × 10¹5 as the result.
Step-by-step explanation:
The division expression 10÷2 can be thought of as the question, "How many groups of 24 are in 107?" To represent this question using a tape diagram, imagine a length of tape divided into sections, each section representing a group of 24, and the total number of sections representing 107. However, there seems to be a typo in the question as it should likely be '2' instead of '24' if following the division expression 10÷2.
To find the answer to 2.4 × 10¹13 divided by 8 × 10¹7, we need to manage the prefactors and the exponents separately. By subtracting the exponents (13 - 7), we get 10¹6. If we divide the pre-factors (2.4 divided by 8), we get 0.3. Therefore, the result is 0.3 × 10¹6.
However, simplifying it further by utilizing the fact that 24 is divisible by 8, we can adjust the prefactor and the exponent accordingly to get a simpler form. The 24 becomes 3 (24 divided by 8), and we decrease the power by one, resulting in 3 × 10¹5, which is the simplified form of the division expression.
The principles of division of powers of ten applied in this calculation help illustrate important mathematical concepts such as managing exponents and prefactors separately, and the flexibility in ways to reach the same result.