Teacher2Teacher 
Q&A #1154 
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From: Xun Chen <chen@dataq.com> To: Teacher2Teacher Public Discussion Date: 2001092421:27:50 Subject: Front end estimmation can be very misleading sometimes Hi, there, My daughter came home today with the following question: Use frontend digits to give a range for each sum. $2909.94 + $14.53 + $3.83 The teacher wrote down the answers to it as: Range of 2013 to 3024 Where I assume she use 2000+10+3 for the lower rage, and (2000+1000)+(10+10)+(3+1) for the higher range. But, on page 24 of her math text book "Exploring Mathematics", about the frontend digit estimation, it is said that the lower end of the range is derived from the whole number of the exact number, while the higher end of the range is from the sum of one and whole number of the exact number. When it mentions whole number, it didn¡¯t say we should round it to a certain place differently according to each individual number. To show an extreme case, considering $100000000.32 + $1, if we use the teacher's method, we will simple come up with a range of $100000001 as the lower end, and $200000002 as the higher end. Yes, the real number is indeed inside this range, but it does not give a suitable picture of the range. My believe is that if we have to use this socalled frontend estimate range, the numbers should be in a same order, or we shouldn't use this confusing method at all. Any suggestion on this topic. Thanks, Xun Chen
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