Round Numbers

Rounding off numbers creates numbers with fewer digits (most of the time). Although rounded numbers are less precise than non-rounded numbers, they are preferred in many circumstances. You may need to round off decimals or whole numbers, depending on the situation. If you want to know how to round off numbers, just follow these steps.

Steps

Rounding Off Decimals

  1. Determine the place value to which the number is to be rounded. This can be determined by your teacher if you're working on a math problem, or you can figure it out based on the context and the sets of numbers you're using. For example when rounding money, you'd most likely want to round to the nearest hundredth, or the nearest cent. When rounding off a weight, round to the nearest pound.
    • The less precise number required, the more you can round (to higher place values).
    • More precise numbers should be rounded to lesser place values.
  2. Identify the place value that you will round the number to. If you're working with the number 10.7659, let's say you've decided to round the number to the thousandth digit, which is the 5 digit in the thousandths place, the third digit to the right of the decimal point. You can also think of this as rounding the number to five significant digits. So, focus on the digit 5 for now.
  3. Locate the number to the right of the rounding number. Just look one digit to the right. In this case, you'll find a 9 next to the 5 digit. This number will determine whether you will round the 5 digit up or down.
  4. Round the rounding digit up one digit if the digit to the right is greater than or equal to 5. This is called rounding up because the number you were rounding to becomes greater than the original number. Your original digit, 5, becomes a 6. All of the numbers to the left of the original 5 will remain the same, and the numbers to the right of it will disappear (you can think of them as becoming zeroes). So, if you're rounding the number 10.7659 to the 5 digit, it would be rounded up to a 6, making the number 10.766.
    • Though 5 is in the middle of the numbers 1-9, it is universally agreed that the digit 5 will require a number before it to be rounded up. This may not apply to your teachers when they submit final grades, though![1]
  5. Round the rounding digit down if the digit to the right is less than 5. If the number to the right of your rounding place value digit is less than 5, the rounding place value digit will remain the same. Though this process is called rounding down, it just means that the rounding digit remains the same; you should never actually change a digit to a lower number. In this case, if you're working with the number 10.7653, you would round it down to 10.765 because the digit 3 to the right of the 5 is on the low end of the scale.
    • By keeping it the same and changing all numbers to its right to 0, the final rounded number is less than the original beginning number. Thus, the number, as a whole, goes down.
    • The above two steps are represented on most desktop calculators as 5/4 rounding. There is usually a slide-switch you can move to the 5/4 rounding position to achieve these results.

Rounding Off Whole Numbers

  1. Round off a number to the nearest tens digit. To do this, simply look at the number to the right of the tens digit of the rounding number. The tens digit is the digit that is second from last in a number, before the ones digit. (If you're looking at 12, look at the number 2.) Then, if that number is less than 5, keep the rounding number the same; if it is greater than or equal to 5 round the rounding number up one digit. Here are some examples:[2][1]
    • 12 --> 10
    • 114 --> 110
    • 57 --> 60
    • 1,334 --> 1330
    • 1,488 --> 1490
    • 97--> 100
  2. Round off a number to the nearest hundreds digit. Follow the same protocol for rounding a number to the nearest hundreds digit. Check out the hundreds digit, which is the third from last in a number, just before the tens digit. (In the number 1,234, the 2 is in the hundreds digit). Then use the number to the right of the hundreds digit, the tens digit, to see if you should round that number up or down, making the numbers after it even 00s. Here are some examples:[2]
    • 7,891 -- > 7,900
    • 15,753 --> 15,800
    • 99, 961 --> 100,000
    • 3,350 --> 3,300
    • 450 --> 500
  3. Round off a number to the nearest thousands digit. The same rules apply here. Just know how to locate the thousands digit, which is fourth from the end of a number, and then check out the digit in the hundreds place, which will be to the right of that number. If the digit is less than 5, round down, and if it's greater than or equal to 5, round up. Here are a few more examples to consider:[2]
    • 8,800 --> 9,000
    • 1,015 --> 1,000
    • 12,450 --> 12,000
    • 333,878 --> 334,000
    • 400,400 --> 400,000

Rounding Numbers to Significant Digits

  1. Understand what a significant digit is. You can think of a significant digit as an "interesting" or an "important" digit that gives you useful information about a number. This means that any zeroes to the right of whole numbers or to the left of decimals can be discounted because they are placeholders. To find the number of significant digits in a number, just count the number of digits from left to right. Here are some examples:[3][1]
    • 1.239 has 4 significant digits
    • 134.9 has 4 significant digits
    • .0165 has 3 significant digits
  2. Round a number to an amount of significant digits. This depends on the problem you're working with. If you're rounding a number to two significant digits, for example, then you'll need to identify the second significant digit of the number and then use the number to the right of it to see if you should round it down or up. Here are some examples:[4]
    • 1.239 rounded to 3 significant digits is 1.24. This is because the digit to the right of the third digit, 3, is a 9, which is 5 or more.
    • 134.9 rounded to 1 significant digit is 100. This is because the digit to the right of the digit in the hundreds place, or the first digit, 1, is 3, which is less than 5.
    • 0.0165 rounded to 2 significant digits is 0.017. This is because the second significant digit is 6, and the number to the right of it, 5, makes it round up.
  3. Round to the correct number of significant digits in addition. To do this, you will first have to add up the numbers you are given. Then, you will have to find the number with the lowest amount of significant digits and then round your entire answer to that place. Here's how you do it:[3]
    • 13.214 + 234.6 + 7.0350 + 6.38 = 261.2290
    • See that the second number, 234.6, is only accurate to the tenths place, or four significant digits.
    • Round the answer so that it is only accurate to the tenths place. 261.2290 becomes 261.2.
  4. Round to the correct number of significant digits in multiplication. First, multiply all of the numbers that you are given. Then, check them to see which number is rounded to the least amount of significant digits. Finally, round your finally answer to match the level of accuracy of that number. Here's how you do it:[4]
    • 16.235 × 0.217 × 5 = 17.614975
    • Notice that the 5 number only has one significant digit. This means that your final answer will only have one significant digit as well.
    • 17.614975 rounded to one significant digit becomes 20.

Tips

  • It is acceptable to drop off the final zeros when rounding place values to the right of a decimal. Zeros after a decimal do not change the value of the number. Therefore, they may be deleted. This is not true of zeros to the left of, or before, a decimal.
  • Once you find the place value to which you are rounding, underline it. This helps minimize confusion between the digit you are rounding and the digit to its right that is determining the fate of the rounding number.
  • One last method of rounding numbers is round up if the value that precedes it is greater than 5. Round down if the number that precedes it is less than 5. If the number that precedes it is 5 round up ONLY if it will make it an even number, NOT an odd number.

Importance of rounding off

The method of rounding off becomes important in problems/calculations where errors play a significant part, such as calculations related with measurements taken using a screw gauge or vernier calipers, etc. In such circumstances, there is an uncertainty of the values due to very minute but negligible error, which occurs inevitable due to handling methods by different users. These values with errors gives results with greater errors while undergoing calculations. Some errors are additive and some are multiplicative. Thus errors are needed to be minimized as much as possible, otherwise it will lead to unwanted confusion and meaningless precision. For example, if a calculation is made between two numbers whose error range is +/- 0.003, means the third decimal point is uncertain, then the third decimal point in the result becomes meaningless, thus it can be neglected by rounding off the result by one significant figure less than the original value to avoid confusion and to make the result logical.

Warnings

  • Be cautious about carefully reading rounding place value specifications when working with decimal numbers. The name of the place values to the right and to the left of the decimal are very close in spelling. Make careful note when the suffix “th” is used at the end of the place value word. This refers to place values to the right of the decimal.

Related Articles

Sources and Citations

  1. ↑ 1.0 1.1 1.2 http://www.mathsisfun.com/rounding-numbers.html
  2. ↑ 2.0 2.1 2.2 http://www.dummies.com/how-to/content/how-to-round-numbers.html
  3. ↑ 3.0 3.1 http://www.purplemath.com/modules/rounding2.htm
  4. ↑ 4.0 4.1 http://www.purplemath.com/modules/rounding3.htm
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