Answer
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Hint:
We are required to round off the given number to the nearest 10m. To do that we will first check that the given number lies between which two whole numbers. Then we will calculate the difference of the given number to each whole number between which it lies. We will round off the given number to the nearest 10 to that whole number which will be closer to it.
Complete step by step solution:
We are given \[78.25\] m and we have to round off this number to the nearest 10 m. This means that we have to round off the given number to the nearest whole number. So, we will first determine the whole numbers between which \[78.25\] lies.
We can see that \[78.25\] is greater than 78 and also, we know that \[78.25\] is lesser than 79. Hence, \[78.25\] lies between the whole numbers 78 and 79. This means that \[78 < 78.25 < 79\].
Now to determine the round-off value, we can calculate the difference of \[78.25\] with both the whole numbers. The difference of \[78.25\] with whichever whole number will be lesser, the value of \[78.25\] will be closer to that number, hence, it will be rounded off to that number.
Let us calculate the difference between \[78.25\] and 78.
\[78.25 - 78 = 0.25\]
Let us calculate the difference between 79 and \[78.25\].
\[79 - 78.25 = 0.75\]
Now we know that \[0.25 < 0.75\].
Hence, \[78.25\] is closer to 78.
According to the rules of rounding off, when rounding to the nearest 10 value, we see the tens digit. If the tens digit is greater than 5, then the ones place is rounded off to 0, and the tens place is rounded off to one more than the given number.
In 78, the tens place is 7. We know that 7 is greater than 5. Hence, following the rule of rounding off, the one's place will become 0. The tens place will become one more than the given number, i.e., one more than 7. Hence, the tens place will become 8. So the number will become 80.
Hence, \[78.25\] m rounded off to the nearest 10 m is 80 m.
Since our answer matches with option (C), hence, it is the correct option.
Note:
We might make a mistake by rounding off \[78.25\] m to 78 m. This is because we are required to round it off to the nearest 10 m. So, we might think that rounding off to the nearest 10 m means rounding off to the nearest whole number. However, this will be wrong because rounding off to the nearest 10 m means rounding off to the nearest multiple of ten.
Rounding off a number means to get a less precise number. This is done when the actual number has no physical significance. For example, when you go to a mall for shopping, say vegetables, you can end up with a bill like Rs. \[366.37\]. Now paying that amount is practically not possible as we do not have our currency made this way. Hence, the computer rounds off our bill to a value that is physically significant to pay.
We are required to round off the given number to the nearest 10m. To do that we will first check that the given number lies between which two whole numbers. Then we will calculate the difference of the given number to each whole number between which it lies. We will round off the given number to the nearest 10 to that whole number which will be closer to it.
Complete step by step solution:
We are given \[78.25\] m and we have to round off this number to the nearest 10 m. This means that we have to round off the given number to the nearest whole number. So, we will first determine the whole numbers between which \[78.25\] lies.
We can see that \[78.25\] is greater than 78 and also, we know that \[78.25\] is lesser than 79. Hence, \[78.25\] lies between the whole numbers 78 and 79. This means that \[78 < 78.25 < 79\].
Now to determine the round-off value, we can calculate the difference of \[78.25\] with both the whole numbers. The difference of \[78.25\] with whichever whole number will be lesser, the value of \[78.25\] will be closer to that number, hence, it will be rounded off to that number.
Let us calculate the difference between \[78.25\] and 78.
\[78.25 - 78 = 0.25\]
Let us calculate the difference between 79 and \[78.25\].
\[79 - 78.25 = 0.75\]
Now we know that \[0.25 < 0.75\].
Hence, \[78.25\] is closer to 78.
According to the rules of rounding off, when rounding to the nearest 10 value, we see the tens digit. If the tens digit is greater than 5, then the ones place is rounded off to 0, and the tens place is rounded off to one more than the given number.
In 78, the tens place is 7. We know that 7 is greater than 5. Hence, following the rule of rounding off, the one's place will become 0. The tens place will become one more than the given number, i.e., one more than 7. Hence, the tens place will become 8. So the number will become 80.
Hence, \[78.25\] m rounded off to the nearest 10 m is 80 m.
Since our answer matches with option (C), hence, it is the correct option.
Note:
We might make a mistake by rounding off \[78.25\] m to 78 m. This is because we are required to round it off to the nearest 10 m. So, we might think that rounding off to the nearest 10 m means rounding off to the nearest whole number. However, this will be wrong because rounding off to the nearest 10 m means rounding off to the nearest multiple of ten.
Rounding off a number means to get a less precise number. This is done when the actual number has no physical significance. For example, when you go to a mall for shopping, say vegetables, you can end up with a bill like Rs. \[366.37\]. Now paying that amount is practically not possible as we do not have our currency made this way. Hence, the computer rounds off our bill to a value that is physically significant to pay.
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