For the ISEE and other standardized tests with math sections, estimation is your friend. Estimation and rounding will reduce the amount of time you spend making calculations, which allows more time to complete difficult questions.
Rounding a number up or down will make it easier to calculate, but it is important that the estimated number be as close in value to the original number as possible. In general, you choose a specific place value to estimate, using the next lowest place value (to the right of it) as your guide. If you want to estimate a number at the second place value, then the third place value is your guide; if you’re estimating the third place value, then you use the fourth place value for your guide and so on.
There are two simple rules for rounding a specific place value:
The process for rounding decimals and rounding whole numbers is slightly different. For rounding whole numbers, you take the place value you want to estimate and use the next lowest place value. If the next lowest place value is 5 or greater, add one to the estimated place value and change all digits to right to 0. If the next lowest place value is less than 5, do not change the estimated place value, but still change all digits to the right to 0.
For decimals, you take the place value you want to estimate and use the next lowest place value. If the next lowest place value is 5 or greater, add one to the estimated place value and discard all digits to the right. If the next lowest place value is less than 5, do not change the estimated place value, but still drop all digits to the right.
For example, let’s say you are asked to find the product of 3,980 and 3,150, and you have 4 possible choices for the answer.
Without a calculator, this may be difficult to multiply. However, if you can estimate these values, you might find the problem easier to crack:
3,980 × 3,150 = ?
When you want to estimate a number closer to the original number’s value, look at the three highest place values. Think about how much your estimation will change the original number:
As we can see in the above examples, rounding to the first place value gives us a less precise estimate, which may alter your answer to a significant degree.
Answers to Practice Problems