Answer :
Final answer:
The garter snake, measuring 1 meter, is 6 orders of magnitude longer than the dust mite, which measures 10⁻⁶ meters.
Explanation:
To calculate how many orders of magnitude longer the garter snake is than the dust mite, we need to compare their lengths on a logarithmic scale. An order of magnitude represents a ten-fold increase or decrease in size. The dust mite measures 10⁻³ millimeters in length, which converts to 10⁻⁶ meters (1 millimeter = 10⁻³ meters). The garter snake measures 100 centimeters, which is equivalent to 1 meter (100 centimeters = 1 meter).
To find the order of magnitude difference, we can use the exponents from the scientific notation. For the garter snake, we have 1 meter, which is 10⁰ meters in scientific notation (since 10 to the power of 0 is 1). For the dust mite, we have 10⁻⁶ meters. The difference in exponent between the two measurements is then:
0 (from 10⁰) - (-6) (from 10⁻⁶) = 6
Hence, the garter snake is 6 orders of magnitude longer than the dust mite.
