Knowing how to round a number is a very important skill for solving mathematical equations, but also for dealing with everyday real life problems. While a rounded number is by definition less accurate than its corresponding unrounded value, it is much easier to work with rounded numbers and be able to visualize them in your mind and perform the necessary calculations. You can round up whole, decimal and fractional numbers with a few simple tips in mind. However, you can rely on modern tools like a calculator or a spreadsheet like Excel to make all the work easier for you.
Steps
Method 1 of 6: Understanding the Rounding Rules
Step 1. The purpose of rounding the numbers is to make them easier to manage by simplifying in turn all the calculations that will have to be performed
If you have a number consisting of many decimal places, it can be very difficult to manage it within an equation. It is equally difficult to work with numbers of this type to solve problems you may encounter in real life, for example while shopping or other purchases. Rounding a number gives an approximate value of that number which makes it much easier to perform mathematical calculations.
You can think of rounding as a mathematical estimate of a certain numerical value
Step 2. Find the digit of the number to which the rounding is to be applied
A number can be rounded off from any digit that composes it. Obviously, rounding a value to a less significant figure will give a more precise approximation.
For example, the number 813, 265 can be rounded to any of the first 5 digits
Step 3. Look at the figure located to the right of the one you need to round
For example, if you need to round a value to the tens, you will need to focus on the number corresponding to the units. The latter will be the value on which the rounding operation will be based, so it is very important.
For example, assume that you need to round the number 813, 265 to the tenth. In this case you will have to focus on the value assumed by the figure that indicates the cents
Step 4. The rounded value should not be changed if the digit from which the number truncation starts is less than 5
If the rounding digit is less than 5 (0, 1, 2, 3, or 4), the last digit of the rounded number will remain unchanged. This means that all digits following the one where you have decided to round will have a null value and can be truncated. In this case, a rounding down is carried out.
For example, suppose you want to round the number 0, 74 to the tenth, you will have to pay attention to the next decimal digit, which in this case is 4. Since 4 is less than 5, the value of the digit relative to the tenths will not be changed and all the following digits will be truncated and the final result will be 0, 7
Step 5. Increase the value of the figure to be rounded by one unit if the value of the next one is greater than 5
If the rounding digit is greater than 5 (5, 6, 7, 8 or 9), you will need to increment the last digit of the rounded number by one. Also in this case, as in the previous one, all the digits following the one in which the rounding was performed will be truncated. In this case, rounding up is carried out.
Take the number 35 as an example. If you need to round it up to the nearest tens, you will need to evaluate the value indicated by the unit figure, which in this case is 5. To round up, you need to add one unit to the tens digit and truncate the ones. Rounding 35 to the nearest ten gives you 40
Method 2 of 6: Round the Decimal Numbers
Step 1. Determine the decimal place where the rounding is to be performed
If you are working on a math problem, your teacher will tell you where to round. Alternatively, depending on the context and numbers you are working on, you can set where you want to round yourself. For example, if you need to round a monetary amount, you will most likely want to round it to the hundredth or tenth. When you need to round a weight value, you need to round it towards the nearest unit of measurement (kilograms, grams, etc.).
- The lower the precision required by the data, the greater the rounding can be (i.e. it can be rounded to a more significant digit).
- The higher the precision required by the data, the less rounding will be (i.e. you will have to round to less significant digits).
- If you need to round a fraction, you will first need to convert it to a decimal number.
Step 2. Identify the digit to apply rounding to
For example, assume that you have to round the decimal number 10, 7659 to the thousandth, you will have to round the 5, which is the digit that represents the thousandths, the third to the right starting from the decimal separator. In other words, you are rounding to five significant digits. In this case, focus your attention on the digit 5 of the number under consideration.
Step 3. Now move your attention to the digit on the right of the number you need to round
Continuing with the previous example, next to the 5 you will find a 9. The latter is the figure that will determine how you need to round the 5: down or up.
Step 4. If the figure you are looking at is greater than or equal to 5, you will need to round the value up by adding one unit
In this case, rounding up is performed, since the value you will get will be larger than the original. In the example above you need to round off the 5 which will become a 6. All remaining numbers of the original value present after 5 will be truncated, while those on the left will remain unchanged. If you have to round the decimal number 10, 7659 to the thousandth, you will get 10, 766 as a result.
- Even if the number 5 is the central value of the range of numbers 1 ÷ 9, it is normally a common rule that the presence of a subsequent digit is necessary to perform a rounding up. However, in the final scrutiny phase, your professors may not adopt this general rule to decide your grade in individual subjects.
- National and international bodies such as NIST may adopt rounding methods other than the standard ones: if the figure to be rounded is 5, check the value of the figures on its right. If any of these are non-zero, then rounding up is done. If all the digits following the one to be rounded are zero or there are no other digits, then a rounding up in the case of an odd value or down in the case of an even value will be performed.
Step 5. Perform a round down if the next digit after the one to round is less than 5
If the value of the figure on the right of the one to be rounded is less than 5, the latter will remain unchanged. In this case we speak of rounding down and the value of the figure to be rounded will remain unchanged from the original. In other words, you will only need to perform a truncation and not a modification of the original number. For example, if you have to round the number 10, 7653 to the thousandth, you will get the number 10, 765, since the rounding figure is a 3 and is less than 5.
- In this case, since the rounded number will have all digits unchanged from the original, but it will have been truncated, it will be smaller than the initial value. For this reason we speak of rounding down.
- The previous two steps are referred to on most office calculators as "5/4 rounding". Normally there is a selector that must be positioned on item "5/4" for the device to make the rounding as described.
Method 3 of 6: Round the Integers
Step 1. Round an integer to the nearest ten
In this case, focus on the figure on the right of the one representing the tens. The digit in question is the second starting from the last digit on the right which is relative to the units. For example, if you need to round the number 12, you will need to focus on 2. At this point, if the number relating to the units, in this case the 2, is less than 5, you will have to round down, while if it is equal or greater than 5 you will need to round up. Some examples of this type of rounding:
- 12 will become 10 (rounding down);
- 114 will become 110 (rounding down);
- 57 will become 60 (rounding up);
- 1.334 will become 1.330 (rounding down);
- 1,488 will become 1,490 (rounding up);
- 97 will become 100 (rounding up).
Step 2. Round an integer to the nearest hundred
To perform this rounding follow the same process described in the previous step. Look at the figure of the whole number relative to the hundreds, that is the third starting from the right. For example, in number 1.234 you will have to refer to 2. At this point, to decide how to make the rounding (down or up), refer to the figure placed on the right of the one in question, that is the tens. At the end of the rounding, the tens and ones digits will both become zero. Here are some examples of this type of rounding:
- 7,891 will become 7,900 (rounding up);
- 15,753 will become 15,800 (rounding up);
- 99,961 will become 100,000 (rounding up);
- 3,350 will become 3,400 (rounding up);
- 450 will become 500 (rounding up);
Step 3. Round an integer to the nearest thousand
Also in this case you will have to apply the same principle seen in the previous two steps. Identify the figure relating to the thousands which is the fourth starting from the right, i.e. the one on the left of the figure corresponding to the hundreds, then examine the value of the latter to decide whether to round up or down. If the hundreds figure is less than 5, you will need to round down; if it is equal to or greater than 5, you will have to round up. Here are some examples of this type of rounding:
- 8,800 will become 9,000 (rounding up);
- 1,015 will become 1,000 (round down);
- 12, 450 will become 12, 000 (rounding down);
- 333, 878 will become 334,000 (rounding up);
- 400, 400 will become 400, 000 (rounding down);
Method 4 of 6: Round Numbers Based on the Number of Significant Digits
Step 1. Understand the meaning of "significant figure"
By "significant digit" we refer to all the digits of a number that contain useful information, "important" or "significant", of the number itself. This means that any zero digit placed to the right of an integer or to the left of a decimal number can be neglected, as it has no significant value. Zeroes between significant digits are also significant. To calculate the number of significant digits present within a numerical value, you will simply have to count those present starting from the right and moving to the left. Some examples that will help you understand the process better:
- The number 1,239 has 4 significant digits;
- The number 134, 9 has 4 significant digits;
- The number 0, 0165 has 3 significant digits;
Step 2. Round a numeric value by a specific number of significant digits
The approach to use depends on the type of problem to be solved. For example, if you need to round a number that has two significant digits, you need to identify the second significant digit and analyze the one placed immediately on the right to figure out whether to round up or down. Here are some examples that better explain the process to be adopted:
- The number 1, 239 rounded to 3 significant digits will become 1, 24. In this case the figure following the one to be rounded is equal to 9, which is greater than 5, so we will adopt a rounding up.
- The number 134, 9 rounded to a single significant digit will become 100. In this case, since the digit on the right of the hundreds, the number 1, is less than 5, a rounding down is performed.
- The number 0, 0165 rounded to 2 significant digits becomes 0, 017. This happens because the second significant digit is 6 and the number immediately following it is a 5, so you are rounding up.
Step 3. Perform a proper rounding based on the significant digits in the additions
In this case the first step is to perform the sum of the given numbers. At this point it is necessary to identify the value with the fewest significant digits of the sum and to round based on this information. Here is an example:
- 13, 214 + 234, 6 + 7, 0350 + 6, 38 = 261, 2290
- Since the second addend, the number 234, 6, has four significant digits, but only one decimal digit, it will be necessary to round according to this model.
- Now round the result of the sum to just one decimal. The result of the sum is 261, 2290 which after rounding will become 261, 2.
Step 4. Perform a proper rounding based on the significant digits in the multiplications
Start by calculating the product of the multiplication given to you. Now find the value with the number of significant digits and the lowest level of precision and use that model to make the rounding. Here is an example:
- 16, 235 × 0, 217 × 5 = 17, 614975
- Number 5 has the lowest accuracy, since it is made up of only one significant digit. This means that you will need to round the final result of the multiplication to a single significant digit.
- The result of the example multiplication is 17.614975 which after rounding will become 20.
Method 5 of 6: Using the Calculator
Step 1. Select the calculator's "round" function
If you are using a Texas Instrument model TI-84 calculator, you must press the Math key, scroll to the "NUM" section, select the "round" function and press the "OK" key.
Older models of Texas Instrument calculators may have different menus and function names than those listed
Step 2. Enter the value you want to round
The text "round (") should appear on the calculator display. Use the calculator's numeric keypad to type in the value you want to round, but do not press the "Enter" or "OK" key (or the key to perform your calculations. calculator model) for now.
If you need to round a fractional number, you will first need to convert it to a decimal value
Step 3. Enter a comma and specify the number of decimal places that the final result of the rounding should have
After entering the value to be rounded, press the calculator key to type a comma, then enter the number of decimal places that the final rounded value should have.
- When you have finished entering the function, the device display should show the following text: "round (6, 234, 1)".
- If you don't specify how the rounding should be done, you will most likely get an error message or an unexpected result.
Step 4. Insert a closing round brackets and press the key to perform the calculations
After specifying how many decimal places the final rounding value should have, type a closing parenthesis and press the calculator's "Enter" key. The result of the rounding will immediately appear on the display with the specified number of decimal places.
Method 6 of 6: Use Excel
Step 1. Click on the cell next to the one in which the value to be rounded is present
Enter all your data in the spreadsheet and make sure it is correct. Click on an empty cell next to the first number to be rounded.
This is the cell in which you will enter the formula to perform the rounding and where the result of this operation will appear
Step 2. Type the code "= ROUND (" into the Excel formula bar
In the Excel "Fx" field, located at the top of the program window, type the equal sign followed by the keyword "ROUND" (without quotation marks) and an opening parenthesis. This is the formula that will allow you to round off a numeric value.
It is a very simple formula, but it must be entered respecting the correct syntax
Step 3. Click on the cell that contains the value to be rounded
The selected cell will appear highlighted and the corresponding address will be automatically inserted into the formula you are composing. The name of the selected cell consisting of a letter and a number will appear in the Excel "Fx" bar.
For example, if you clicked on cell "A1", the following code should be present in the Excel function bar: "= ROUND (A1"
Step 4. Enter a comma followed by the number of digits that the final rounded value should have
For example, if you want the value stored in cell "A1" to be rounded to 3 decimal places, you will need to enter the code ", 3". If you want the rounding to be done to the nearest integer, simply enter a zero.
If you want the indicated value to be rounded to the next multiple of 10, enter the code ", -1"
Step 5. Enter the closing parenthesis of the formula and press the "Enter" key
To complete the formula with the correct syntax you need to add a closed round perentesis. At this point, press the "Enter" key to allow Excel to perform the calculations.
The result of the rounding will be displayed in the cell where you entered the formula
Advice
- After identifying the figure where the rounding is to be performed, underline it with a pencil or pen. In this way you will not risk confusion between the figure to be rounded and the values that follow it that will determine the final rounded number.
- There are many free services on the web that automatically round off the value provided.
