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The order of operations allows you to evaluate mathematical expressions and equations. Without it, math would be ambiguous — it would be like trying to speak a language that had no word order. Building bridges, giving doses of medicine, and launching rockets would become inconsistent and dangerous because people would calculate differently. The order of operations provides a common framework for everyone to use!
Use this information to solve questions 1-3. You can use the order of operations to manipulate numbers into whatever format is most convenient to you at any given time. There are plenty of situations in which you can solve a problem quicker by hand than with a calculator. Some skills you might use include converting between decimals and fractions as well as scaling numbers up or down.
If \(0.02 = \frac{2}{x}\), what is x?
The least common denominator of \( \frac{6}{25}, \frac{1}{15}, \frac{2}{21} \) is:
\(9^2 * 27^3\) can be written as 3 to which power?
Understanding notations
Use this information to solve question 4. Very large or very small numbers can get unwieldy, increasing the chance for you to make a mistake when using them in calculations. Scientific notation allows you to express these numbers compactly while also allowing you to compare their sizes at a glance. Nearly every scientific field uses scientific notation in some way, so being familiar with it is very important.
What is the sum of \(5.23*10^5\) and \(1.7*10^4\)?
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Master Questions: Solving expressions/equations
Use this information to solve questions 5-7. Arithmetic is used all the time in rearranging equations. For example in physics, arithmetic can be used to help determine the relationship between light and temperature. This is particularly useful when trying to measure the temperature of stars in the distant universe. Let’s use this same relationship to look at body temperature.
The Stefan-Boltzmann equation gives the amount of energy emitted by a body at a given temperature: \(\mathrm{L=A \sigma T^4}\) with \(\sigma= 5.67*10^{-8}\), A = surface area, T is temperature in Kelvin, and L is energy in watts. If the average adult has a surface area of \(1.7m^2\) of skin, and their average body temperature is 306K, then what is the average energy per second radiated by a human?
Wien’s displacement law gives a relationship between the temperature of a body, and the most abundant wavelength of light it emits: \( \mathrm{\lambda*T= 2.89*10^{-3} m*K}\) where T is temperature in Kelvin and \( \lambda \) is wavelength in meters. If the average human body temperature is 306K, then what is the wavelength in \( \mu m \) of light the human body emits most. (\( \mathrm{1\mu m = 10^{-6} m}\))
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Using the table above, what part of the electromagnetic spectrum does this wavelength fall in?
Manipulating expressions/equations
Use this information to solve questions 8-9. In math and science, you don’t always have a choice as to what information you can measure. As such, being able to manipulate equations to solve for whatever variable you need to is outstandingly important. Furthermore, rearranging equations can help you control what you’re doing.
In physics, the average velocity of particles in a gas can be approximated with the following formula: \(\bar{v} = \sqrt{\frac{3RT}{M_m}}\). What is T in terms of \(\bar{v},M_m, \mathrm{and} R\)?
The virial theorem relates the kinetic (T) and potential energy (U) of a system. For a galaxy, the virial theorem can be expressed as: 2T + U = 0
If \(T=\frac{Mv^2}{2}\) and \(U=\frac{-GM^2}{R}\), solve the virial theorem for M.
Fun
Use this information to solve question 10.
You can also use the order of operations for fun. It will help you solve those viral riddles you see on your timelines!
1+2+3+4+5+6*0+7+8+9=?