Estimating Sums

At times whenever we add two large numbers, you do not wish to find out the precise sum. You only wish to get a fast estimate.

A sum can be estimated fast via rounding each addend and then adding these together. Now we’ll demonstrate a few quite easy steps to see the way to estimate a sum. 

Related Topics

• Estimating and Rounding
• Estimating Products
• Rounding Numbers

Way to estimate sums to the closest tenth

To estimate s sum to the tenth you must follow these three steps:

STEP one: Round the summands to the closest tenth. Don’t forget:

If a numeral ends in \(0, 1, 2, 3\) or \(4\), it gets rounded down ?

If a numeral ends in \(5, 6, 7, 8\) or \(9\), it gets rounded up  ?

Tip: Unless it is stated differently, you constantly round numbers to the maximum feasible place value.

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STEP two: Add the rounded numerals

STEP three: Looking at the overall quantity of rounding, \(3\) things could occur:

• If  it’s rounded one quantity up as well as one down, the resulting sum is a proper estimation.
• If both the summands were rounded up and then the result of this rounding is more than \(5\), you take \(10\) from this estimate.
• If both the summands were rounded down and the quantity of the rounding is more than \(5\), you add \(10\) to this estimate.

Estimating Sums – Example 1:

Estimate sum by rounding each added to the nearest ten.

\(43+58=\)___

Solution:

First, round \(43\) to the closest ten. Check out the numeral on the right of the tens position. It is \(3\) and this number is lower than \(5\). So, \(43\) is rounded down to \(40\). Do the same for \(58\). Then \(58\) is rounded up to \(60\). Now add two result together: \(40+60=100\)

Estimating Sums – Example 2:

Estimate sum by rounding each added to the nearest ten.

\(75+32=\)___

Solution:

First, round \(75\) to the closest ten. Check out the numeral on the right of the tens position. It is \(5\). So, \(75\) is rounded up to \(80\). Do the same for \(32\). Then \(32\) is rounded down to \(30\). Now add two result together: \(80+30=110\)

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Exercises for Estimating Sums

Estimate sum by rounding each added to the nearest ten.

1. \(\color{blue}{14+35}\)
2. \(\color{blue}{ 46+77 }\)
3. \(\color{blue}{83+38 }\)
4. \(\color{blue}{ 71+95 }\)

1. \(\color{blue}{50}\)
2. \(\color{blue}{ 130 }\)
3. \(\color{blue}{120 }\)
4. \(\color{blue}{ 170 }\)