Write the expression as a number in scientific notation.

Question

the quantity 3.6 times ten to the fifth power end quantity times the quantity 1.5 times ten to the negative eighth power end quantity all divided by the quantity 2.5 times ten to the negative fourth power end quantity

a
2.6 × 107

b
2.16 × 101

c
2.16 × 10−1

d
2.6 × 10−7

Answer 1

To solve the expression

\[ \frac{(3.6 \times 10^5) \times (1.5 \times 10^{-8})}{(2.5 \times 10^{-4})} \]

we can follow these steps:

1. Multiply the numerators: \[ 3.6 \times 1.5 = 5.4 \] For the powers of ten: \[ 10^5 \times 10^{-8} = 10^{5 + (-8)} = 10^{-3} \] So the product in the numerator is: \[ 5.4 \times 10^{-3} \]

2. Now we divide by the denominator: \[ \frac{5.4 \times 10^{-3}}{2.5 \times 10^{-4}} \] First, perform the division on the numbers: \[ \frac{5.4}{2.5} = 2.16 \] For the powers of ten: \[ 10^{-3} \div 10^{-4} = 10^{-3 - (-4)} = 10^{-3 + 4} = 10^1 \]

3. Combine the results: \[ 2.16 \times 10^1 \]

Thus, the final expression in scientific notation is: \[ 2.16 \times 10^1 \]

The correct answer is: b (2.16 × 10^1).