Question

What is the rough estimate and the closer estimate of \[4125 + 139 + 62\] ?

Answer 1

Hint: Estimation is a process used to simplify the calculation by rounding the numbers involved in a calculation. While rounding off the numbers to nearest hundreds, if the digit in the tens place is \[0\] , \[1\] , \[2\] , \[3\] or \[4\] we replace the digits in the tens and ones place by zero. If the digit in the tens place is \[5\] , \[6\] , \[7\] , \[8\] or \[9\] we replace the digits in the tens and ones place by zeroes. We also increase the digit in the hundreds place by \[1\] .

Complete step-by-step answer:
Before starting this question you should know what estimation means. So basically in mathematics, estimation of any number is just a guess of the actual value to make calculations easier. Now let’s see some general rules
Rules for estimating to round off to the nearest tens:
The numbers \[1\] , \[2\] , \[3\] and \[4\] are nearer to \[0\] than to \[10\] .So, we round off \[1\] , \[2\] , \[3\] and \[4\] as \[0\] .
Numbers \[6\] , \[7\] , \[8\] and \[9\] are nearer to \[10\] so we round them off as \[10\] .
Number \[5\] is equidistant from both \[0\] and \[10\] so it is a common practice to round it off as \[10\] .
Rules for estimating to round off to the nearest hundreds:
The numbers ending in \[01\] to \[49\] are rounded off downwards.
The numbers ending in \[50\] to \[99\] are rounded off upwards.
Rough estimate can be done by rounding off to nearest hundreds. Whereas closer estimates can be done by rounding off to nearest tens. .

Rough estimate : Now look at the number \[4125\] .We observe that last two digits of a number \[4125\] is \[25\] which is between \[01\] to \[49\] so we round off \[25\] as \[00\] because the nearest hundred of \[125\] is \[100\] .Hence, \[4125\] is rounded off to nearest hundreds as \[4100\] .

Next given number in the equation is \[139\] . This number ends with \[39\] which lies between \[01\] to \[49\] so we round off \[39\] as \[00\] because the nearest hundred of \[139\] is \[100\] .Hence, \[139\] is rounded off as \[100\]
Next we have \[62\] .In the hint it is given that if the digit in the tens place is \[6\] then we replace the digits in the tens and ones place by zeroes and we also increase the digit in the hundreds place by \[1\] . Hence, the number \[62\] can be rounded off to \[100\] .
Thus, the rough estimate of \[4125 + 139 + 62\] is \[4100 + 100 + 100\] which is equal to \[4300\] .

Closer estimate: We observe that in the number \[4125\] , \[5\] is at one's place and according to the rule \[5\] can be rounded off to the nearest tens as \[10\] . Therefore the number \[4125\] can be rounded off as \[4130\] .
Next we have \[139\] . In this number \[9\] is at the one place which is nearer to \[10\] .Therefore, the number \[139\] can be rounded off as \[140\] .
Now again we have the number \[62\] , in this number \[2\] is at the one's place which means \[2\] can be rounded off as \[0\] . Therefore, \[60\] is the closer estimation of \[62\] .
Thus, the closer estimate of \[4125 + 139 + 62\] is \[4130 + 140 + 60\] which is equal to \[4330\] .

Note: For students estimating is important. By this skill you are able to determine the reasonableness of the answer. Without this skill you are not able to determine if your answer is within a reasonable range or not. Estimation is not always about doing calculations, it is used to get the approximate value. If you find the last digit as 5 in any number then do not confuse how to round off it. According to the general rule, 5 will round the number up.