Question

How many times larger is 8 *108 than 4 *1027?

A) 200 times
B) 2,000,000 times
C) 2,000 times
D) 20,000 times

Answer 1

8 × 108 is not larger than 4 × 1027; in fact, it is much smaller. The correct computation shows that 8 × 108 is 2 × 10-19 times the size of 4 × 1027, rather than 200, 2,000, 20,000, or 2,000,000 times larger.

Step-by-step explanation:

Comparing Powers of Ten

To determine how many times larger 8 × 108 is than 4 × 1027, one needs to divide the former by the latter. This calculation involves comparing the powers of tens and the coefficients. The calculation process is as follows:

1. Set up the division expression: (8 × 108) ÷ (4 × 1027).
2. Divide the coefficients: 8 ÷ 4 = 2.
3. Subtract the exponents of the powers of tens: 8 - 27 = -19.
4. Simplify the expression: 2 × 10-19.

The final result shows us that 8 × 108 is 2 × 10-19 times larger than 4 × 1027, meaning it is actually much smaller, not larger. Therefore, none of the provided options (A to D) are correct.

This calculation emphasizes the importance of powers of ten and their role in scientific notation, which is commonly used to express very large or very small numbers efficiently.