We can estimate decimal division by rounding each decimal to the nearest whole number and dividing the resulting numbers.
For example, suppose we wish to estimate the quotient of the following division problem.
One way to proceed is first to round both quantities to the nearest whole number:
So, we can form an estimate of by evaluating
Computing the quotient of this simplified problem gives
Therefore, is approximately equal to We can write this symbolically as follows:
The symbol means "is approximately equal to."
By rounding the dividend to the nearest whole number, estimate the value of
First, we round the dividend to the nearest whole number:
Hence, we need to find the value of Computing the quotient, we get:
Hence,
Therefore, is approximately equal to
Estimate the value of $16.4 \div 3.6$ by rounding each number to the nearest whole number.
a
|
$4$ |
b
|
$5$ |
c
|
$3$ |
d
|
$2$ |
e
|
$1$ |
By rounding the dividend to the nearest whole number, estimate the value of $96.2 \div 4.$
a
|
$22$ |
b
|
$25$ |
c
|
$24$ |
d
|
$26$ |
e
|
$23$ |
Estimate by rounding the divisor to the nearest hundred.
First, we round the divisor to the nearest hundred:
Now, we need to compute
There are two zeros in so we move the decimal point two places to the left:
Therefore, is approximately equal to
Estimate $4.3 \div 11.1$ by rounding the divisor to the nearest ten.
a
|
$11.4$ |
b
|
$0.43$ |
c
|
$43$ |
d
|
$0.34$ |
e
|
$0.043$ |
Estimate $6.4 \div 97.7$ by rounding the divisor to the nearest hundred.
a
|
$6.4$ |
b
|
$64$ |
c
|
$0.064$ |
d
|
$0.64$ |
e
|
$9.77$ |
Estimate $1455 \div 990$ by rounding the divisor to the nearest thousand.
a
|
$14.55$ |
b
|
$0.1455$ |
c
|
$145.5$ |
d
|
$1450$ |
e
|
$1.455$ |
Estimate the value of by rounding each number to the nearest whole number.
We round both numbers to the nearest whole number:
Now, we need to find the value of
So, we go through the long division procedure as usual:
Therefore, is approximately equal to
By rounding the divisor to the nearest whole number, estimate the value of $124 \div 4.15.$
a
|
$31$ |
b
|
$30$ |
c
|
$32$ |
d
|
$35$ |
e
|
$33$ |
Estimate the value of $374.5 \div 5.05$ by rounding each number to the nearest whole number. Round your final answer to the nearest whole number.
a
|
$77$ |
b
|
$89$ |
c
|
$73$ |
d
|
$75$ |
e
|
$71$ |
Estimate the value of by rounding each number to the nearest whole number. Round your final answer to the nearest whole number.
We round both numbers to the nearest whole number:
Now, we need to find the value of
So, we go through the long division procedure as usual:
Therefore,
The remainder is closer to than to the divisor So, to round to the nearest whole number, we must round down:
Therefore, is approximately equal to
Estimate the value of $262.5 \div 3.09$ by rounding each number to the nearest whole number. Round your final answer to the nearest whole number.
a
|
$90$ |
b
|
$86$ |
c
|
$89$ |
d
|
$87$ |
e
|
$88$ |
Estimate the value of $284.9 \div 8.53$ by rounding each number to the nearest whole number. Round your final answer to the nearest whole number.
a
|
$32$ |
b
|
$34$ |
c
|
$33$ |
d
|
$35$ |
e
|
$31$ |