Rounding and Estimating

Rounding- To round you need to take your number that your working with, so lets say I'm working with the number 63. If your number is 0 - 4 your going to round to a lower number, so if you want to round to your nearest tenth you look for the number after your tenths unit which is a 3, since 3 is under 4 your going to round down to 60. Say my number was 67, you're going to round up to 70, your going to do this because any number from 5 - 9, is going to be rounded up since these numbers are closer to the next tenth.


Estimating- To estimate, what I do is I round first. Lets say I want to add 56 and 32, to estimate this I round first. So, 56 rounded to the nearest tenth would be 60 because it's a greater number than 4, then we take the 32 and round it to the nearest tenth, which is 30. It's rounded to 30 because it's a lower number than 4. After you round your numbers you can add, subtract, multiply, etc. Now lets take the numbers we rounded, which is 60 and 30, add them together making 90. Since it's an estimation it is not going to be exact.

Rounding/Estimating

To estimate, first round the numbers. Then add it or subtract it.
When estimating, first decide what 
rounding will take place and look at the digit to its right.


Round it up if the number is like this;
   = 5, 6, 7, 8, 9
Change it to 0 (zero)/round it down   if the number is less  than 4

  
 For Example:
      

Estimate the sum.		Estimate the difference.
36   +44       ?	40 +40 80	52  -25   ?	50 -30  20

You  can estimate numbers to the nearest ten, hundreds, 
thousands, ten-thousands, etc.

Estimating Decimals
    
     Estimation is a good tool for making a rough calculation. There are many estimation strategies that you could use to estimate the sum of these decimals. Let's look at the front-end strategy and the rounding strategy. We will round to the nearest tenth.

Example 1:  Front-End Strategy		Rounding Strategy
Add the front digits and then adjust the estimate.		Round each decimal to a designated place value, then add to estimate the sum.
3.75      3.75               about + 4.29   + 4.29                 1    7      7 + 1 = 8		3.75   3.8 + 4.29+ 4.3 + 4.29+ 8.1
3 + 4 = 7 and .75 plus .29 is about 1. Thus, $7+ $1 = $8. The estimated sum is $8.		Rounding each decimal to the nearest tenth, we get an estimated sum of 8.1 or $8.10.

     

Note the difference between the two strategies used in Example 1: The front-end strategy uses the first digit to estimate a sum and then considers the other digits to adjust the estimate. In the rounding strategy, addition does not occur until after the numbers have been rounded. In both strategies, you must line up both decimals before proceeding.

   To round a decimal to a designated place value, first underline or mark that place. If the digit to the right of that place is 5 through 9, then round up. If the digit to the right of that place is 1 through 4, then round down, leave the digit in the designated place unchanged, and drop all digits to the right of it.

Example 2:	Estimate the sum of each pair of decimals by rounding to the specified place.
a)	Estimate 4.203 + 6.598 by rounding to the nearest hundredth.
	4.203   4.20 + 6.598+ 6.60              10.80		If the digit to the right of the place you are rounding to is 1 through 4, then round down. Thus, 4.203 is rounded down to 4.20. If the digit to the right of the place you are rounding to is 5 through 9, then round up. Thus, 6.598 is rounded up to 6.60.
b)	Estimate $12.96 + $7.19 by rounding to the nearest one.
	$12.96   $13 + $  7.19+ $  7             $20		If the digit to the right of the place you are rounding to is 5 through 9, then round up. Thus, 12.96 is rounded up to 13. If the digit to the right of the place you are rounding to is 1 through 4, then round down. Thus, 7.19 is rounded down to 7.
c)	Estimate 11.79 + 4.58 by rounding to the nearest tenth.
	11.79  11.8 +   4.58+  4 6          16.4		If the digit to the right of the place you are rounding to is 5 through 9, then round up. Thus, 11.79 is rounded up to 11.8. If the digit to the right of the place you are rounding to is 5 through 9, then round up. Thus, 4.58 is rounded up to 4.6.

    
 An overestimate is an an estimate that is too high: it exceeds the actual answer.                        An underestimate is an estimate that is too low: it is lower than the actual answer.

	Estimate	Actual Sum		Overestimate or Underestimate?
a)	+ $36.23+ $36.20 + $63.44+ $63.40 + $99.60+ $99.60	$99.67		Underestimate since $99.60 < $99.67
b)	$57.65   $  57.70 + $43.31+ $  43.30             $101.00	$100.96		Overestimate since $101.00 > $100.96
c)	$24.89   $24.90 + $72.15+ $72.20             $97.10	$97.04		Overestimate since $97.10 > $97.04