Determine the order of magnitude of the following small number by entering the appropriate exponent n. below: , 37!] km m 10\" km . I View Available Hintls} Overview of Order of Magnitude The order of magnitude is an approximation of the size of a number. It is represented by 10" where n is an integer. You can determine the order of magnitude of a number by rounding it to the nearest power of 10. For example, consider the value 3, 500 meter = 3.5 x 10* meter. The 3.5 rounds down to 1, so the order of magnitude of 3, 500 meter is 1 x 10* meter, or 10* meter. Similarly, consider 7, 500 meter = 7.5 x 10* meter. The 7.5 rounds up to 10, so the order of magnitude of 7, 500 meter is 10 x 10* meter, or 10# meter. Below are a few important properties of powers of 10. When you multiply powers of 10, you add the exponents, for example: 105 x 108 = 10648 = 1014 103 x 10 4 = 1034 = 10-1When you divide powers of 10, you subtract the exponents, for example: 107 : 103 = 107-3 =10* 102 : 106 = 102 6 = 10 4 When you have a power of 10 raised to a power, you multiply the exponents, for example: (105)2 = 105*2 = 1010 (10 3)4 = 10 -3x4 = 10-12 The biggest advantage of mastering the skill of order of magnitude is that it allows you to quickly estimate the answer to a problem when only a rough approximation is needed. Below are the three steps: 1. Convert all of the numbers to an order of magnitude as shown above. 2. Multiply (or divide) the orders of magnitude by adding (or subtracting) the exponents as needed. 3. Combine the units appropriately