How do we actually calculate this?

[Maxim19]

Hello!

I'd like to know how do we calculate manually this following operation :

[(1-2.8)^2*1+(2-2.8)^2*3+(3-2.8)^2*2+(4-2.8)^2*2+(5-2.8)^2*1]/10=?

More specifically I'm interested in knowing how do we break down the numbers in brackets that are to the power of two such as (1-2.8)^2*1+(2-2.8)^2*3 etc, because no matter in what way I try to do it by myself without the help of a calculator the results do not coincide unfortunately.

Your help would be greatly appreciated!

 

[ksdhart2]

Given that everything involved here is "actual" numbers and not variables, what's stopping you from just cranking it through on pen & paper? Begin by discarding the *1's as multiplying by 1 does nothing:

\(\displaystyle \frac{(1-2.8)^2+(2-2.8)^2 \cdot 3+(3-2.8)^2 \cdot 2+(4-2.8)^2 \cdot 2+(5-2.8)^2}{10}\)

Then evaluate it step-by-step, according to PEMDAS. The first step is to resolve anything in Parentheses. Let's do that now:

\(\displaystyle \frac{(-1.8)^2+(-0.8)^2 \cdot 3+0.2^2 \cdot 2+1.2^2 \cdot 2+2.2^2}{10}\)

The next step is to resolve any Exponents. Your turn to try. What do you get here? As a hint, consider what exponents mean, specifically when the power is an integer. A refresher on exponents can be found here if needed

 

[Maxim19]

Given that everything involved here is "actual" numbers and not variables, what's stopping you from just cranking it through on pen & paper? Begin by discarding the *1's as multiplying by 1 does nothing:

\(\displaystyle \frac{(1-2.8)^2+(2-2.8)^2 \cdot 3+(3-2.8)^2 \cdot 2+(4-2.8)^2 \cdot 2+(5-2.8)^2}{10}\)

Then evaluate it step-by-step, according to PEMDAS. The first step is to resolve anything in Parentheses. Let's do that now:

\(\displaystyle \frac{(-1.8)^2+(-0.8)^2 \cdot 3+0.2^2 \cdot 2+1.2^2 \cdot 2+2.2^2}{10}\)

The next step is to resolve any Exponents. Your turn to try. What do you get here? As a hint, consider what exponents mean, specifically when the power is an integer. A refresher on exponents can be found here if needed

Thank you it helped a lot!

 

[Denis]

I'd like to know how do we calculate manually this following operation :

[(1-2.8)^2*1+(2-2.8)^2*3+(3-2.8)^2*2+(4-2.8)^2*2+(5-2.8)^2*1]/10=?

More specifically I'm interested in knowing how do we break down the numbers in brackets
that are to the power of two such as (1-2.8)^2*1+(2-2.8)^2*3 etc, because no matter in what
way I try to do it by myself without the help of a calculator the results do not coincide unfortunately.

WHAT are you really asking?
How to calculate (as example) 3 * (2 - 2.8)^2 BY HAND ?
WHY?