Question

How do you round 214.0822 to the nearest tenth?

Answer 1

Hint: We are given a decimal number. We need to round this number which means to calculate the most proximal or the nearest real number to the number given. There are some rules of rounding off which we will use here. We also need to see that it has been mentioned to round off to the nearest thousandth.

Complete step by step solution:
We are given the number 214.0822. When we are required to round a decimal number to the nearest $n^{th}$ place, we want to reduce the number of digits in the given value by 1 and we do that by picking the nearest number. While rounding off whole numbers we simply pick the nearest 10’s multiple. For example, if we have the number 41 then it is nearest to 40.
We have a rule that if the number ends with 5 then it goes to the next 10’s multiple. For example, if the number is 45 then the round off will be 50. Using this we round off decimal numbers. Say the number is 1.254 and we want to round it to the nearest hundredth then we round off the last two digits i.e. 54 to the nearest 10 which will be 50 in this case and the resultant rounded number will be 1.250 which is equivalent to 1.25.
Here we have 214.0822. To round this to the nearest tenth we first pick the last two digits i.e. 22 and we near it to the closest 10 which is 20 in this case. After that we get the number as 214.082. After this we pick the next two digits and we round it off to the nearest tenth i.e. 82 turns into 80. So, we get the number 214.08 now. For final reduction, we pick 08 and nearing it to tenth we get 10. So here, the round off will be 214.10 which is equal to 214.1.

Note:
You should be aware of all the rounding rules, any rule applied wrongly will lead to an incorrect answer. The rules are fairly simple so it should not be a problem. Always remember the rule of putting the next digit when the ending digit is 5, this is where commonly the mistake happens. Moreover, be aware of which place the rounding off has to be done. Always start rounding off from the right.