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:**

- If the next lowest place value is 5 or greater, you round that place value up.
- If the next lowest place value is 4 or lower, you round that place value down.

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 = ?**

A) 11,340,000

B) 12,537,000

C) 13,900,000

D) 14,672,000

**Solution**

- 3,980 can be rounded up to 4,000.
- 3,150 can be rounded up to 3,200.
- The product of 4,000 and 3,200 is 12,800,00.
- The closest answer choice to this number is B - 12,537,000

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:

- If the estimation of the highest place value results in a very different number, look to the next highest place value.
- Generally, estimating the second highest place value will result in a number that is truer to the essence of the original.

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.

- Round the following decimals the nearest hundredth.
- 0.01767
- 0.35512
- 0.8334

- Round the following numbers to the 2nd highest place value.
- 2,859
- 99,481
- 853,402

- Round 78,746,910 to the 1st, 2nd, and 3rd place value. Which estimation seems best to use?
- What is the product of 3,788 and 8,956?
- a) 33,925,300
- b) 37,655,650
- c) 42,478,300
- d) 54,240,760

- Which of the following is NOT a valid estimation of 72.4565?
- a) 72.45
- b) 70
- c) 72.5
- d) 72.457

**Answers to Practice Problems**

- Question 1
- 0.02
- 0.36
- 0.83

- Question 2
- 2,900
- 99,000
- 850,000

- Question 3
- 1st place value = 80,000,000
- 2nd place value = 79,000,000
- 3rd place value = 78,700,000
- The 2nd place value seems like the best estimation to use, which is often the case.
- This is true because it alters the value the least, while maintaining more information.

- A
- A

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