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Rounding: Integers, decimal places, significant figures

Rounding: Integers, decimal places, significant figures

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Summary

Rounding: Integers, decimal places, significant figures

​​In a nutshell

There are three different types of ways to round numbers. One way of rounding involves rounding to the nearest whole number, ten, hundred, thousand or million. Other ways of rounding include rounding to the nearest decimal place or the nearest significant figure. 



Rounding to whole numbers

You can round any number to the nearest whole number, nearest ten, nearest hundred, etc. To round to the nearest whole number, look at the number after the decimal point to see whether to round up or down. To round to the nearest ten, look at the number in the units column to see whether to round up or down. 


In the same way, when rounding to the nearest hundred, thousands or millions, look at the digit to the right, or the digit that is one place value lower to see whether to round up or down. If the digit is smaller than five, round down and if the digit is five or bigger, then round up.


Example 1

Round 43.643.6 to the nearest whole number.


To round to the nearest whole number, look at the number after the decimal point. As 66 is bigger than 55, round up.


43.643.6 rounded to the nearest whole number is 44\underline{44}.​

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Example 2

Round 12 34612 \ 346 to the nearest hundred.


To round to the nearest hundred, look at the number in the tens column. As 44 is less than 55, round down.


12 34612 \ 346 rounded to the nearest hundred is 12 300\underline{12 \ 300}.​


Decimal places

To round to the nearest decimal place, look at the digit to the right, or the digit that is one place value lower to see whether to round up or down. If the digit is smaller than five, round down and if the digit is five or bigger, then round up.


Example 3

What is the value of 17.34217.342 to 22 decimal places?


To round to 22 decimal places, look at the digit in the 3rd3rd decimal place. As 22 is less than 55, round down.


17.34217.342 rounded is 17.34 (2 d.p.)\underline{17.34 \ (2 \ d.p.)}​​

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Significant figures

The first significant figure in a number is the first non-zero digit starting from the left. The second significant figure is the digit to the right, then the third significant figure is to the right again, and so on. Zero can be counted as a significant figure from the second significant figure onwards.


Example 3

What is the value of 0.0037080.003708​ to 33 significant figures?


The first significant figure starts at the digit 33. The second significant figure is 77, and the third significant figure is 00. To round to 33 significant figures, look at the next digit. As 88 is bigger than 55, round up.​​


0.0037080.003708 rounded is 0.00371 (3 s.f.)\underline{0.00371 \ (3 \ s.f.) }​​

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