The 1-10-100 Rule is something that companies think about, so it might not seem like it would have much to do with our daily lives, but...
The 1-10-100 Rule says that the cost of a mistake goes up the farther that it goes. If a company is making a car seat, for instance, and they catch a mistake in the design, they might lose some money (whatever it takes to redo the work). That is "1" in the Rule. But if they didn't catch the mistake there and they started making the car seats and THEN they realized the problem, they would lose ten times as much money as if they caught it earlier (that's the "10"). If the mistake hadn't been discovered at the manufacturing stage and they actually sold the car seats and later realized the problem, recalling the car seats would cost much, much more (that's the "100" in the Rule). So being careful and taking your time can save a lot of problems down the road. This is true for many situations.
Let's say you're writing a paper and you pick a topic that doesn't match what the teacher has asked for. You don't realize your mistake, but if you figured it out before you started writing, it would be a "1" in terms of "cost" (inconveniencing you). It would only inconvenience you a little. If you figured it out while you were planning your paper and taking notes, it would be a "10" -- some inconvenience. If you didn't figure it out until you wrote the whole paper, that would be a "100." Checking things early on, and then double-checking, can save you a lot of inconvenience. Can you think of anything else where, the earlier you figure out the mistake, the less of a problem it is?
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