The Difference Between Rounding and EstimatingÂ
Rounding and estimating are math strategies used for approximating a number. To estimate means to make a rough guess or calculation. To round means to simplify a known number by scaling it slightly up or down. Rounding is a type of estimating. Both methods can help you make educated approximations and can be used in everyday life for tasks related to money, time or distance.
How to Round Numbers
Rounding means decreasing the amount of digits in a number but keeping the number close to its original value. To round a number, decide on the digit you want to round to. Look at the digit to the right of that rounding digit. If the number is 5 or greater, bump the rounding digit up one number. If it is less than 5, drop it down one number. In a decimal, remove all of the digits after the rounding digit. For example, if you want to round 7.38 to the nearest 10th, the answer would be 7.4. In a whole number, change all digits to the right of the rounding digit to zeros. If you want to round 62 to the nearest 10, for instance, the answer would be 60.
How to Estimate
Estimating is different than rounding because it is a broader form of approximation. Estimation is used when coming up with a brand-new number instead of modifying an existing one. For example, a person might estimate how long it would take him to mow the lawn, how far it is to a friend's house or how many feet of carpet are needed to cover the floor of a particular room. Estimations are based on prior knowledge and given information. They are not exact measurements. If your usual jogging pace is between a nine- and 11-minute mile, for example, and the supermarket is two miles away, you might estimate that it would take you roughly 20 minutes to jog to the supermarket.
SPECIFIC TYPES OF ESTIMATING
There are different methods for estimation that are useful for different types of problems. The three most useful methods are the rounding, front-end and clustering methods.
Rounding Method
Rounding is one common method used for estimating. Determine the place value to use for the particular problem you want to estimate. For example, if you wanted to estimate the total cost of several different grocery items, you would want to round to the nearest tens place because it is money. If working with extremely large numbers, you might want to round to the nearest one million. Round up by one if the digit to the left of the digit you're rounding to is five or larger. Round down by one if it is four or less. For example, if you are rounding to the nearest 10 and your number is 33, you would round to 30. Now that your numbers end in zero, you can easily do mental math to solve the problem, whether that requires adding, subtracting, multiplying or dividing.
Front-end Method
If all the numbers in the problem contain the same number of digits, you can use the front-end method of estimation. Add up the first digit of each number in the problem, without rounding them. For example, if you need to estimate the value of 3,293 + 4,432 + 6,191 you would add 3 + 4 + 6 = 13. Modify your answer by adding zeroes to have the same number of digits in the numbers. In this example, there are four digits, so you would add two zeroes and end up with an estimation of 1,300.
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Clustering Method
To use the clustering method of estimation, find the best common number that ends in zero that the numbers in your problem cluster around. For example, you might have to add the numbers 29 plus 33 plus 27 plus 28 plus 35. All the numbers seem to cluster around 30. Substitute the cluster number, in this case 30, for each number. You can now use mental math to determine that 30 + 30 + 30 + 30 + 30 gives you an estimation of 150.
Uses of Estimation in Mathematics
Estimation is used in mathematics before you do a problem to help you solve it faster and easier, and after you solve a problem to help you determine whether your answer is reasonable. Estimation is also useful when you only need an approximate amount instead of a precise value.
How to Round to the Underlined Place Value Position
In mathematics, it is often difficult to work with large or complex numbers. When you don't need an accurate answer but just an estimation, rounding is a useful practice. Rounding makes numbers easier to work with by reducing the digits in the number while keeping the value similar to the original number. You can round a number to any place value depending on how much you want to change the original value of the number. You can use the rounded number in a math problem to get an approximate answer.
Determine which place value you are going to round the number to. Underline the digit in that place value position. For example, if you want to round to the nearest hundred, underline the digit in the hundreds place. When rounding the number 2,365 to the nearest hundred, underline the 3 because it is in the hundreds place.
Look at the digit to the right of your underlined numeral. Determine if it is greater than or equal to 5. If so, you will round your underlined digit up. If the digit to the right of your underlined numeral is less than 5, you will round your number down. In the example 2,365, look at the digit to the right of the hundreds place, which is 6. Since this is greater than 5, you will round up.When rounding up, add 1 to your underlined numeral and then change all of the digits to the right of the underlined numeral to zeros. In the example 2,365, you will change the 3 to a 4 and change the 6 and 5 to zeros, so your rounded number would be 2,400.
When rounding down, the underlined numeral stays the same and all of the digits to the right of it change to zeros. For example, to round the number 4,623 to the nearest hundred, your result will be 4,600 because the digit to the right of the hundreds place is less than 5.