Adding large numbers without using a calculator takes some effort. However, in some circumstances, it is sufficient to find an estimate for a particular sum. Computing an estimate is usually faster and easier than solving the original problem.
To estimate the answer to an addition problem, we round the numbers first and then add them.
To illustrate this, let's find an estimate for the value of
Let's start by rounding both numbers to the nearest ten:
Then, we calculate the sum
Therefore,
The symbol means "is approximately equal to."
The estimate we've obtained is pretty close to the actual value of the sum. In fact,
In this example, we rounded to the nearest ten. In the next example, we'll estimate a sum by rounding both numbers to the nearest hundred.
There are currently trees in the park. Workers will plant more trees this week. By rounding each value to the nearest hundred, estimate how many trees will be in the park when the workers are finished.
To estimate how many trees will be in the park when the workers are finished, we need to find an approximation for the sum
First, we round both numbers to the nearest hundred:
Next, we calculate the sum
So, we have
Therefore, there will be approximately trees in the park when the workers are finished.
Estimate the sum $271 + 596$ by rounding each number to the nearest ten.
|
a
|
$870$ |
|
b
|
$860$ |
|
c
|
$770$ |
|
d
|
$780$ |
|
e
|
$880$ |
Estimate the sum $432 + 208$ by rounding each number to the nearest hundred.
|
a
|
$600$ |
|
b
|
$630$ |
|
c
|
$800$ |
|
d
|
$650$ |
|
e
|
$700$ |
Estimate the sum by rounding each number to the nearest thousand.
First, we round both numbers to the nearest thousand:
Next, we calculate the sum
Therefore, is approximately
Estimate the sum $4,618 + 9,952$ by rounding each number to the nearest hundred.
|
a
|
$14,500$ |
|
b
|
$14,600$ |
|
c
|
$13,000$ |
|
d
|
$14,000$ |
|
e
|
$13,900$ |
Estimate the sum $6,710 + 788$ by rounding each number to the nearest hundred.
|
a
|
$1,300$ |
|
b
|
$7,600$ |
|
c
|
$7,700$ |
|
d
|
$1,200$ |
|
e
|
$7,500$ |
Estimate the sum by rounding each number to the nearest hundred thousand.
First, we round both numbers to the nearest hundred- thousand:
Next, we calculate the sum Therefore, is approximately
Estimate the sum $456,341 + 7,230,002$ by rounding each number to the nearest hundred thousand.
|
a
|
$13,000,000$ |
|
b
|
$7,600,000$ |
|
c
|
$12,000,000$ |
|
d
|
$7,500,000$ |
|
e
|
$7,700,000$ |
Estimate the sum $7,104,671 + 3,835,490$ by rounding each number to the nearest million.
|
a
|
$11,000,000$ |
|
b
|
$10,000,000$ |
|
c
|
$12,000,000$ |
|
d
|
$1,200,000$ |
|
e
|
$10,100,000$ |