** Rounding vs Estimating **

Rounding and estimating are two methods used for approximating a number for easier usage, when very large numbers are found. Both rounding and estimating are usually performed mentally, without the aid of writing or using a calculator. The goal of rounding and estimating is to make the numbers simpler to perform calculations mentally, without much difficulty. However, applications of both rounding and estimation have further development in mathematics.

**Rounding a Number**

When using numbers, often situation arises where using the exact number or value become tedious and difficult. In such cases, numbers are approximated to a value with reasonable accuracy, but which is much shorter, simpler and easier to use.

For example, consider the value of pi (π). Pi, which is an irrational constant, has infinite decimal places. π = 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679…… But if we employ a very large figure in the calculations, simplification and other mathematical operations become increasingly difficult. Therefore, the value of Pi is rounded to a number with fewer digits. Often the value of pi (π) is considered as 3.14 after rounding to two decimal places, which gives a reasonable accuracy.

Before rounding off a number, the round off digit has to be decided. To the right of the decimal point lies tenths, hundredths, thousandths, and so on. To the left lies ones, tens, hundreds, and so on. In rounding off, the value is approximated to the closest full place value, usually determined by choice.

Before rounding a number, a place value to round must be decided first. Often, this place is chosen in a way that minimizes the loss of information in the original number. The selected place value is normally called the * round-off digit*.

In rounding, after selecting the round-off digit, the value of the digit right to the round-off digit is considered. If the value of that digit is 5 or more, the value of the round of digit is increased by one and all the digits right to it is discarded. If the digit onto right of the round-off digit is less than five, then the round off digit is not changed; but the digits right to the round off digit is discarded.

For example, consider the number 10.25364, and rounding this number at 2nd and 3rd decimal places. If 3rd decimal place is selected as the round-off digit, the values right of it is 6(which is larger than 5). Then the round off digit is increased by one. Therefore rounding off 10.25364 to the third decimal place gives 10.254. If the second decimal place is selected as the round-off digit, the digit right to the round of digit is 3 (which is less than 5). Therefore, when the number 10.25364 is rounded to the second decimal place, the value is 10.25.

Since the value of the number is either increased or decreased during the rounding, an error is introduced. This error is called the * rounding error*. The rounding error is the difference between the rounded value and the original value.

**Estimating**

Estimating is an educated guess for achieving the approximate value for a number or a quantity. Main purpose of estimation is the ease of usage of the number. Unlike rounding, there should not be a specific place value for carrying out estimation and the resulting numbers are not precise. But often rounding is used to obtain estimated values. Averaging is also used in the estimation.

Consider a jar of candy, with each candy has a weight in the range 18-22 grams. Therefore, it is reasonable to deduce that each candy might have an average weight of 20 grams. If the weight of candy in the jar is 1 kilogram, we can estimate that there are 50 candies inside the jar. In this case averaging is used to obtain the estimation.

Also, rounding is used for estimation. Suppose you have a grocery list and you want to calculate the minimum amount you need to buy all the groceries. Since we do not know the exact prices of the goods, we assess the amount using estimated prices. Estimated price can be obtained by rounding the usual prices of the goods. If we know that the average price of a loaf of bread is $1.95, we can assume that the price is $2.00. This type of calculation allows easier usage of prices to calculate the total cost of goods and taken into account any changes in the price.

**What is the difference between Rounding and Estimating?**

• Both Rounding and estimation are done for obtaining simpler number when performing calculations mentally.

• In rounding, a number is approximated by assigning the closest full number at a specified place value. Therefore, before rounding place value to round off has to be decided.

• Estimation is an educated guess or an assessment using available data. Averaging or rounding is used to get the estimated values.