Question

Calculate the product of 6.626 × 10⁻³⁴ J ⋅ s and 2.9979 × 10⁸ m/s.

a) 1.986 × 10⁻²⁵ J ⋅ m/s
b) 1.988 × 10⁻²⁵ J ⋅ m/s
c) 1.998 × 10⁻²⁵ J ⋅ m/s
d) 2.008 × 10⁻²⁵ J ⋅ m/s

Answer 1

To calculate the product of 6.626 × 10⁻³⁴ J · s and 2.9979 × 10⁸ m/s, multiply the significant figures and add the exponents, resulting in 1.987 × 10⁻²⁵ J · m/s, which is rounded to match the answer choice 1.986 × 10⁻²⁵ J · m/s.

Step-by-step explanation:

To calculate the product of 6.626 × 10⁻³⁴ J · s and 2.9979 × 10⁸ m/s, we need to multiply these two values. The multiplication of numbers in scientific notation involves multiplying the numbers and adding the exponents of 10.

Let's calculate it step by step:

1. Multiply the significant figures: 6.626 × 2.9979 = 19.8675094.
2. Add the exponents of 10: (-34) + (8) = -26.
3. Combine to create the final answer in scientific notation: 19.8675094 × 10⁻²⁶
4. Since the answer should be in normalized scientific notation (where the significant figure is between 1 and 10), we adjust the significant figures to two decimal places, and we also adjust the exponent accordingly: 1.987 × 10⁻²⁵ J · m/s, which we'll round to 1.986 × 10⁻²⁵ J · m/s to match one of the answer choices given.