Final answer:
The order of magnitude is the exponent in scientific notation. For the numbers given, 5.1 x 10⁴ has an order of magnitude of 10⁴, and 1.63 x 10⁻¹⁰ has an order of magnitude of 10⁻¹⁰.
Step-by-step explanation:
The order of magnitude of a number is the power of 10 when the number is expressed in scientific notation. The base 10 logarithm is used to determine the order of magnitude, rounding to the nearest whole number. For instance, the order of magnitude of 450 is 10³ because log10450 ≈ 2.653, which rounds to 3. Let's calculate the order of magnitude for your numbers.
The number 5.1 x 10⁴ is already in scientific notation, and thus its order of magnitude is 10⁴.
For the number 1.63 x 10⁻¹⁰, the exponent of 10 is -10. Therefore, the order of magnitude is 10⁻¹⁰.
In conclusion, the orders of magnitude for the given numbers are 10⁴ and 10⁻¹⁰ respectively.