a student estimated the sum 7.95 + 8.11 + 78.5 + 8.05 + 79.4 + 0.815 as: all the numbers begin with a 7 or…

a student estimated the sum 7.95 + 8.11 + 78.5 + 8.05 + 79.4 + 0.815 as: all the numbers begin with a 7 or 8, so use cluster estimation. 8 + 8 + 80 + 8 + 80 + 0.8 = 184.8 explain why this reasoning is not accurate.

a student estimated the sum 7.95 + 8.11 + 78.5 + 8.05 + 79.4 + 0.815 as: all the numbers begin with a 7 or 8, so use cluster estimation. 8 + 8 + 80 + 8 + 80 + 0.8 = 184.8 explain why this reasoning is not accurate.

Answer

Brief Explanations:

Cluster - estimation should group numbers that are close in value. Here, the numbers have different magnitudes. For example, 0.815 is much smaller than the other numbers and 78.5 and 79.4 are in the tens while 7.95, 8.11, 8.05 are in the units. Just because they start with 7 or 8 is not a valid reason for clustering.

Answer:

The student's reasoning is not accurate because cluster - estimation requires numbers to be close in value, not just starting with the same digit. The numbers in the sum have different magnitudes and are not truly 'clustered' just based on the first - digit.