How to Round Numbers

Rounding helps the numbers look more concise. Although the rounded numbers are less precise than the original number, in many situations we are required to round. Depending on the situation, you may need to round to decimals or whole numbers. Here are the steps to guide you through.

Table of Contents

Rounding decimals

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Specifies the value of the row of digits to be rounded. This may be required by your teacher if you are working on a math assignment, or you can determine based on the context and the units you are using. For example, when rounding money, you will usually round to the nearest thousand. When rounding off a weight, you will round to the nearest kilogram.

The less precision the number requires, the more rounding you can get (to higher rows of digits).
The more precise the number will be rounded to the lower number of digits.

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Specify the value of the row of digits to which you will round. Suppose you have the number 10.7659 , and you want to round to the digit to the thousandth place, i.e. 5 , the third digit to the right of the decimal point.

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Specifies the digit to the right of the rounded number. Consider only one digit to the right. In this case, you will consider the digit 9 next to the digit 5 . This number determines whether 5 will be rounded up or down.

Round up if the right digit is greater than or equal to 5. The rounded digit will be larger than the original digit. Your original digit of 5 will become 6 . All numbers to the left of the original 5 will remain, and the numbers to the right of it will be discarded. So the number 10.7659 will be rounded to 10.766″.

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Although 5 is the middle digit from 1 to 9, it is convention that the digit before it should be rounded up. However, this may not apply to end-of-year grades! ^{[1] X Research Source}
When the rounded digit is 5, look at the digits to the right of it. If the next digit is non-zero, round up. If all subsequent digits are 0 or no more, round up if the rounded digit is odd and round down if the rounded digit is even. ^{[2] X Research Source}

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Round down if the digit to the right is less than 5. If the digit to the right of the row of digits to be rounded is less than 5, the digit in the rounded row will stay the same. Although this process is called rounding down, it just means that the number in the rounding row stays the same; you must not change it to a lower number. In the case of a number to round to 10.7653 , you would round down to 10,765 because the digit 3 to the right of 5 is less than 5.

By keeping the digit in the rounding row unchanged and converting all numbers to the right of it to zero, the final rounded number is smaller than the original. Thus, the overall number is reduced.
The two steps above are shown on most calculators to round 5/4. You can use the slide-switch to switch to the 5/4 rounding position to get these results.

Rounding integers

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Round to nearest tens digit. To do this, simply consider the digit to the right of the tens digit of the rounded digit. The tens digit is the second digit from the last digit in a number, before the units digit. (If you have number 12, consider number 2). Then, if the number is less than 5, keep the rounded digit; if it is greater than or equal to 5 round up to one digit. Here are some examples: ^{[3] X Research Sources}^{[4] X Research Sources}

12 -> 10
114 –> 110
57 -> 60
1334 –> 1330
1488 –> 1490
97–> 100

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Round to nearest hundred digit. Follow the same steps as for rounding to the nearest hundredth digit. Consider the hundreds digit, that is, the third digit from the last digit in a number, immediately preceding the tens digit. (Out of 1234, 2 is the hundreds digit). Then use the digit to the right of the hundreds digit, i.e. the tens digit, to see if you will round up or down, converting the numbers after it to 00. Here are some examples. : ^{[5] X Research Source}

7 891 — > 7 900
15 753 –> 15 800
99 961 –> 100 000
3 350 –> 3 300
450 -> 500

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Round to nearest thousands digit. Apply the same rule as above. Just know how to identify the thousands digit, which is the fourth digit from the bottom, and then look at the digit in the hundreds place, which is the number to the right of the number. If the digit is less than 5, round down, and if it is greater than or equal to 5, round up. Here are a few examples: ^{[6] X Research Sources}

8 800 -> 9 000
1 015 –> 1 000
12 450 –> 12 000
333 878 –> 334 000
400 400 –> 400 000

Round to significant digits

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Understand what “significant digits” mean. Simply think of digits as “interesting” or “important” digits that give you useful information about a number. This means that any zeros to the right of an integer or to the left of a decimal do not count as a significant digit. To find the number of significant digits in a number, simply count the number of digits from left to right. Here are some examples: ^{[7] X Research Sources}^{[8] X Research Sources}

1,239 has 4 significant digits
134.9 has 4 significant digits
0.0165 has 3 significant digits

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Round a number to the number of significant digits. This depends on the problem you are looking at. If you want to round a number down to two significant digits, then you will need to determine the second significant digit of the number and then use the digit to the right of it to see if you will round it. down or up. Here are some examples: ^{[9] X Research Sources}

1.239 is rounded to 3 significant digits 1.24. This result is obtained because the digit to the right of the third digit (3) is 9 greater than 5.
134.9 is rounded to one significant digit of 100. This is obtained because the digit to the right of the hundreds digit (1) is 3 less than 5.
0.0165 is rounded to 2 significant digits 0.017. This result is obtained because the second significant digit is 6, and its right digit is 5 causing it to be rounded up.

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Round to the exact number of significant digits in the addition. To do this, you will first have to add up the given numbers. You would then have to find the number with the smallest number of significant digits and then round the whole answer down to that number of significant digits. Here’s how: ^{[10] X Research Sources}

13.214 + 234.6 + 7,0350 + 6.38 = 261.2290
See that the second number 234.6 is accurate to the tenth place, or four significant digits.
Round the answer so that it is accurate to the tenth place. 261.2290 becomes 261.2.

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Round to the exact number of significant digits in the multiplication. First, multiply all the given numbers. Then check to see which number is rounded to the least significant number of digits. Finally, round the final answer to match the precision of that number. Here’s how: ^{[11] X Research Source}

16.235 × 0.217 × 5 = 17.614975
Notice that the number 5 has only one significant digit. That means your final answer will also have only one significant digit.
17.614975 is rounded to one significant place to 20.

Advice

You can leave trailing zeros when rounding values to the right of the decimal point. Zeros after the decimal point do not change the value of the number so they can be deleted. However, this is not true for zeros to the left of, or before, the decimal point.
After finding the value of the row of digits to which you are going to round, underline it. This helps to minimize confusion between the digit you’re going to round with the digit to the right of it. The right digit determines the fate of the rounded digit.
One of the newest rounding methods is to round up if the value preceding it is greater than 5. Round down if the number preceding it is less than 5. If the number preceding it is equal to 5, round up ONLY if the number is generated. becomes an even number, NOT an odd number.

The importance of rounding numbers

The rounding method becomes important in problems/calculations where error plays an important part, such as calculations involving measurements made by a screw or caliper, etc. In such a situation, error is inevitable because measurement methods are performed by different users. Values with errors give results with larger errors when performing calculations. Some errors are exponential and others are exponential. As such, error should be minimized as much as possible, otherwise it will lead to unwanted confusion and meaningless accuracy. For example, if a calculation is performed between two numbers with an error range of +/- 0.003 then the third point after the decimal point is uncertain, so the third point after the decimal point in the result becomes meaningless. This can be avoided by rounding the result.

Warning

Use caution when reading digit values in decimal. The spelling of the digits to the right and to the left of the decimal point is the same, but the reading is different. To the left of the decimal point we read units, tens, hundreds, etc., but to the right of the decimal point we read tenths, percentiles, etc.

Steps