  Math Topics
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# Estimates

You can use a simpler version of the one-step method to make quick estimates for the new price when you’re in a store that is having a sale, and it’s not important to get the new price exactly down to the penny. If the old price doesn’t end in a zero, you can round to the nearest ten or hundred first, depending on the scenario, and then use the method.

Rule

### EstimatingtheNewPrice

If you know the the old price and the discount is $n\phantom{\rule{0.17em}{0ex}}\text{%}$, then you have to pay $p\phantom{\rule{0.17em}{0ex}}\text{%}=100\phantom{\rule{0.17em}{0ex}}\text{%}-n\phantom{\rule{0.17em}{0ex}}\text{%}$ of the old price. You can estimate the new price like this:

• Round the old price to the nearest 100 dollars. How many hundred dollar bills are there in the rounded price?

• Multiply $p$ dollars by the number of hundred dollar bills, and you have your estimate.

Example 1

A PlayStation 5 used to cost \$$430$, but is now discounted by $20$ %. You round the price down to \$$400$. You have to pay $80$ % of the old price, which is $80\phantom{\rule{0.17em}{0ex}}\text{%}×\text{}100=\text{}80$ for each hundred dollar bill in the estimate for the old price. As this is just an estimate, you don’t consider the extra \$$30$ for now.

That means the estimated price is

 $\text{}80×4=\text{}320$

You continue with Example 1, and make the estimate a bit more accurate:

Example 2

The estimate is a bit more accurate if you add the \$$30$ you left behind earlier:

 $\text{}80×4+\text{}30=\text{}320+\text{}30=\text{}350$

If you use a calculator to find the exact answer of \$$344$, you will see that it’s a bit lower than your estimate. The reason why this happens is that the exact calculation also gives you a discount on the \$$30$ you left behind when you rounded.