Question

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 1

Answer with explanation:

We have to estimate the sum of

→7.95 + 8.11 + 78.5 + 8.05 + 79.4 + 0.815

When Rounded to nearest tens

7.95 → 8.00

8.11→ 8.00

78.5→79

8.05→8.00

79.4→79.0

0.815→1

So,estimation of the above rational numbers with addition as an operation is done,the result is

→8 + 8 + 80 + 8 + 80 + 0.8 = 184.8, is not correct ,because in the expression it is not clear , the numbers are neither exactly rounded to nearest tens or tenths.

for example ,79.4 when rounded to nearest tens → 79,but in the expression 80 is written,which is not correct.

Similarly,when rounded to nearest tens, 0.815 → 1, but in the expression 0.8 is written,which is confusing.

Similarly,when rounded to nearest tens ,78.5 →79 , but in the expression 80, is written,which is incorrect.

Answer 2

The numbers are not clustered around a common number. Two of the numbers are very large and one is very small.