First, students will learn how to convert decimal numbers, that are powers of ten, between scientific notation and standard form. As examples, \(0.001 = 10^{-2}\) and \(10,000 = 10^4.\) Here's a good video. Then students will learn how to convert arbitrary decimal numbers between scientific notation and standard form. For example, \(5.7 \cdot 10^4 = 57{,}000.\)
Note: In the UK, they call scientific notation standard form (source).
Concude by giving your students this challenge:
George and Jim want to buy a chocolate bar. George would need 2 cents more to buy it. Jim would need 50 cents more. When they put their money together, it's still not enough to buy the chocolate bar. How much does it cost?
Here's one solution: Let \(c\) be the cost of the chocolate bar, \(g\) the amount of money George has, \(j\) the amount Jim has. Then we have \(g = c - 2\) and \(j = c - 50.\) We know their money combined isn't enough to buy the chocolate bar, so \((c - 2) + (c - 50) \lt c.\) Solving the inequality, we find \(c \lt 52\) cents. But \(g = c - 50\) and \(g \ge 0,\) so \(c \ge 50.\) Thus, the cost of the chocolate bar is either 50, or 51 cents. Another, albeit, less favorable solution, is to use guess and check, as seen here.
Note: The problem comes from here. I have adapted it for Americans, rephrased the question slightly, and succinctly explained the solution.