Rounding numbers is an important skill to learn when you have math equations or calculation problems in the real world. Although less accurate than unrounded numbers, rounded results are easier to calculate and imagine. You can round whole numbers, decimals, and fractions by keeping a few key tips in mind when working on equations or math problems. You can also use a calculator or an Excel spreadsheet to round numbers and check rounding results again.
Step
Method 1 of 6: Understanding Rounding
Step 1. Round the number to make it easier to calculate
If you have a number with a decimal number that is long enough, of course it will be difficult when you need to calculate it. Such numbers are also difficult to calculate in the real world (eg when you are budgeting or shopping). Therefore, rounding is a method of getting the approximate number of a number and making it easier to calculate.
You can imagine rounding like a mathematical approximation
Step 2. Determine the place value you want to round
When rounding a number, you can round to any place value. The smaller the place value to which you are rounded, the more accurate your rounding result will be.
For example, you have the number "813, 265". You can round to a place value of hundreds, tens, ones, tenths, or hundredths
Step 3. Observe the digits to the right of the place value you want to round
For example, if you want to round in the tens place, look at the numbers in the ones place. Rounding will be done based on the place value so it is very important that you remember this step or rule.
On the number “813, 265”, let's say you want to round to the tenth place. This means you need to look at the numbers in the hundredth position
Step 4. Do not change the number if the number in the place value on the right side is less than “5”
If the smallest digit after the place value you want to round is less than “5” (e.g. “0”, “1”, “2”, “3”, or “4”), leave the digit in the benchmark place value as is. This means that the number next to the place value will be “0” so you can omit or delete it at the end of the number. This process is known as rounding down.
For example, if you want to round “0.74” to the nearest tenth, look at the number next to the tenth place (“4”). Since “4” is less than “5”, you can keep or keep “7” and remove “4” from the number so that the rounding result becomes “0, 7”
Step 5. Increase the number if the number in the place value on the right is greater than “5”
If the smallest digit after the place value you want to round is greater than “5” (e.g. “5”, “6”, “7”, “8”, or “9”), add “1” to the number in the place value. benchmark. As before, any other numbers to the right of the digit or place value of the rounding benchmark will be “0” so they can be deleted or omitted. This process is known as rounding up.
For example, you have the number "35". If you want to round it to the nearest ten, observe the smallest place value after it (“5”). To round a number, add “1” to the number in the benchmark place value (tens or “3”). Therefore, the result of rounding the number “35” to the nearest ten is 40
Method 2 of 6: Rounding Decimal Numbers
Step 1. Determine the place value for the rounding benchmark
The place value can be stated or determined by your teacher if you are working on a math problem. You can also find out based on the context and the series of numbers used. For example, when rounding money, you may need to round to the nearest thousands or hundreds place value. When rounding off an object's weight, round to the nearest kilograms place.
- The less number of precision required, the more or farther the rounding can be done (to a larger place value).
- For more precise numbers, it is necessary to round to the smaller place value.
- If you must round a fraction, convert it to a decimal number before rounding.
Step 2. Identify the place value you want to set as a rounding benchmark
Let's say you have the number “10, 7659” and want to round it to the nearest thousandth digit (“5” in the thousandth place), or the third digit to the right of the comma. You can also think of it as rounding a number to five significant digits. Therefore, focus on the number “5” for now.
Step 3. Look for the number to the right of the rounding benchmark place value
Just observe a single digit to the right of the benchmark place value. In the example above, you can see the number “9” next to the number “5”. The number “9” will determine whether you need to round the number “5” up or down.
Step 4. Add one to the number in the standard place value if the number to the right of the place value is “5” (or more)
This process is known as rounding up because the number in the place value you want to round becomes larger than the original number. The number " 5 " which is a natural number needs to be changed to " 6 ". All the numbers to the left of the original “5” will remain unchanged, and the numbers on the right side can be omitted (you can imagine them as zeros). Therefore, if you round the number “10.7659” from the digit or number “5”, the number will be rounded up to “6” so the final rounding result is “10, 766”.
- Even though the number "5" is between the numbers "1" to "9", people generally agree that the number "5" needs another number before it to be rounded up. However, this agreement or principle may not apply to teachers when they add final grades to your report card!
- Standards bodies such as NIST use a different method. When the standard number to be rounded is “5”, pay attention to the number to the right. If the number is not “0”, round up. If the number is “0” or there are no other digits, round up if the standard digit is an odd number, or down if the standard digit is an even number.
Step 5. Round the number down if the number on the right side is less than “5”
If the number on the right side of the rounding benchmark place value is less than “5”, the number on the benchmark place value will remain the same. Even though it is called rounding down, in this process the number in the place value will not change; You can't change it to a smaller number. For example, if you have the number “10, 7653”, you can round it down to “10, 765” because the number “3” next to “5” is smaller than “5”.
- By keeping the number at the default place value and changing the numbers to the right of it to “0”, the final rounding result will be less than the original number. Therefore, it can be said that the whole number was rounded down.
- The above two steps are represented as rounding “5/4” on most tabletop calculators. Usually, you can find a toggle or slider that can be moved to the “5/4” rounding position to get the rounding result.
Method 3 of 6: Rounding Numbers (Integer)
Step 1. Round a number to the nearest digit or tens place
To do this, observe the number to the right of the tens digit (the place value of the rounding benchmark). The digits or tens are the second digit of the last digit, before the ones digit (in the number “12”, for example, the place value of the units is occupied by the number “2”). If the number in the units place is less than “5”, keep the number in the standard place value. If the number is greater than or equal to “5”, add “1” to the number in the standard place value. Here are some examples you can study:
- ”12” “10”
- ”114” “110”
- ”57” “60”
- ”1.334” “1.330”
- ”1.488” “1.490”
- ”97” “100”
Step 2. Round the number to the nearest digit or hundreds place
Follow the same rules for rounding numbers to the nearest hundreds digit or place. Observe the hundreds place value (the third from the last digit), just to the left of the tens digit. For example, in the number “1.234”, the number “2” is the hundreds digit) After that, use the number on the right side (the tens digit) to check whether you need to round up or down, then make the following numbers “0”. Here are some examples you can study:
- ”7.891” -- > “7.900”
- ”15.753” “15.800”
- ”99.961” “100.000”
- ”3.350” “3.400”
- ”450” “500”
Step 3. Round the number to the nearest digit or thousands place
The same rules apply to questions like this. You just need to know how to recognize the digits or the thousands place value, which is the fourth number from the right. After that, check the number in the hundreds digit or place (to the right of the thousands digit). If the number in the hundreds digit is less than “5”, round down. If the number is greater than or equal to “5”, round up. Here are some examples you can study:
- ”8.800” “9.000”
- ”1.015” “1.000”
- ”12.450” “12.000”
- ”333.878” “334.000”
- ”400.400” “400.000”
Method 4 of 6: Rounding Numbers to Significant Digits
Step 1. Understand the significant digits
You can think of significant digits as “interesting” or “significant” digits that give you useful information about a number. This means that all zeros on the right side of the integer or on the left side of the decimal can be ignored because zero only serves as a "place filler". To find the number of significant digits in a number, simply count the number of digits from left to right. Here are some examples:
- “1, 239” has 4 significant digits.
- “134, 9” has 4 significant digits.
- “0.0165” has 3 significant digits.
Step 2. Round the number to a number of significant digits
The number of digits will depend on the problem you are working on. If you're asked to round a number to two significant digits, for example, you'll need to identify the second significant digit and look at the number to the right of it to see if you need to round up or down. Here are some examples:
- “1, 239” can be rounded up to 3 significant digits to “1, 24”. This is because the third significant digit is “3” and the number to the right is “9”. The number "9" is greater than "5" so rounding is done up.
- “134, 9” can be rounded to 1 significant digit to “100”. This is because the first significant digit is “1” and the number to the right is “3”. The number "3" is smaller than "5" so rounding is done down.
- “0.0165” can be rounded up to 2 significant digits to “0.017”. This is because the second significant digit is “6” and the number to the right is “5” so it is necessary to round up.
Step 3. Round the sum to the appropriate number of significant digits
To do rounding, you must add up the numbers in the problem first. After that, find the number with the least number of significant digits, and round the sum to that number. Here's how:
- ”13, 214” + 234, 6 + 7, 0350 + 6, 38 = 261.2290”
- The second number in the addition problem (“234, 6”) has an accuracy of up to one-tenth, so it has four significant digits.
- Round the sum until it has only tenths digits. Therefore, “261, 2290” can be rounded up to “261, 2”.
Step 4. Round the multiplication result to the appropriate number of significant digits
First, multiply all the numbers in the problem. After that, check the number that needs to be rounded to the least number of significant digits. Finally, round the final multiplication result to adjust the level of accuracy of the number. Here's how:
- ”16, 235 × 0.217 × 5 = 17, 614975”
- Keep in mind that “5” is the only number that has one significant digit. This means that the final multiplication answer can only have one significant digit.
- “17, 614975” can be rounded to one significant digit to “20”.
Method 5 of 6: Using the Calculator
Step 1. Select the “round” function on your calculator
If you are using the TI-84 calculator, click the Math button, then switch to the “NUM” option. Move the selection to the “round” function, then press the “OK” button.
Older IT calculators may have slightly different functions or menus
Step 2. Enter the number you want to round
The dialog field will display the “round(” function or code. Use the keys on the calculator to enter the number you need to round, but don't press “Enter” immediately afterward.
If you need to round a fraction, convert the fraction to a decimal number first
Step 3. Insert a comma, then enter the number of decimal places you want to set the rounding limit or limit
After entering the number you want to round, find and press the comma button on the calculator afterwards. Next, enter the number of decimal places you need to make the rounding limit.
- For example, on the calculator screen you can see a number like this: round(6234, 1).
- For calculators with Indonesian format, the display of codes or numbers on the calculator may look like this: round(6, 234, 1).
- If you don't specify the number of decimal places, you will get a very strange error code or fraction.
Step 4. End with closing brackets and press “Enter” key
After specifying the number of decimal places, enter the closing parenthesis into the equation and press the “Enter” key. The calculator will display the number that has been rounded to the point or decimal place you specify.
Method 6 of 6: Rounding Numbers in Microsoft Excel
Step 1. Click the box next to the number you want to round
Enter all the data and make sure you enter it correctly. Click the cursor in the box next to the number you need to round (as long as the box is empty).
The box that you click on will display the rounded number
Step 2. Type the formula “=ROUND(” into the equation field
In the “fx” field at the top of the screen, type an equal sign and the word “ROUND”, followed by an opening parenthesis. The equation formula will be formed so that you can enter data into it.
The formula is very simple, but make sure you don't forget any elements or punctuation
Step 3. Click the square with the number you want to round
The squares will be marked and the numbers will be entered into the equation. The square letters and numbers containing the data (in this case, the number that needs to be rounded off) will be displayed in the “fx” column.
For example, if you click the “A1” box, the “fx” column will display the following formula: “=ROUND(A1
Step 4. Type in a comma and enter the number of digits that you set as a benchmark or rounding limit
For example, if you want the number in the “A1” box to be rounded to three decimal places, type “, 3” into the column. If you want to round the data to the nearest integer, type “0”.
If you want to round to the next “10” multiplication, use “-1”
Step 5. End with closing brackets and press “Enter” key
To solve the equation, type a closing parenthesis to let Excel know that you've finished entering the formula. Press the “Enter” key so that Excel can round the number you entered.
Your answer will be displayed in the box you clicked on
Tips
- After knowing the place value that will be used as a rounding benchmark, underline the number in the place value. That way, you won't be confused when looking for the rounding benchmark digit and the digit on the right side (the number that determines the type of rounding that needs to be done).
- You can access a variety of online rounding calculators for free.
