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# Find the greatest integer less than \$10.3^3\$ without using a calculator.

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Find the greatest integer less than \$10.3^3\$ without using a calculator.

Guest May 10, 2015

#1
+26640
+10

Write 10.3 as (10 + 0.3) then use the binomial expansion on (10 + 0.3)^3 to get:

10^3 + 3*10^2*0.3 + 3*10*0.3^2 + 0.3^3 or

1000 + 90 + 2.7 + 0.027 → 1092.727

Therefore the greatest integer less than 10.3^3 is 1092

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Alan  May 10, 2015
Sort:

#1
+26640
+10

Write 10.3 as (10 + 0.3) then use the binomial expansion on (10 + 0.3)^3 to get:

10^3 + 3*10^2*0.3 + 3*10*0.3^2 + 0.3^3 or

1000 + 90 + 2.7 + 0.027 → 1092.727

Therefore the greatest integer less than 10.3^3 is 1092

.

Alan  May 10, 2015
#2
+92221
0

I would not have thought to do it that way.  Thanks Alan

Melody  May 11, 2015

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