Question

How do you evaluate `(- 0.012) ^ { 2}`?

Answer 1

`0.000144`

Explanation:

`(-0.012)^2=-0.012xx-0.012`

Solving

`-0.012`

`xx-0.012`

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`\color(fuchsia)(\cancel(-))0\color(red)(.)000144\color(blue)(.)`

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Reasoning

• Canceling out the negative: Two negative values multiplied together equal a positive result (in pink).
• Moving decimal places: First multiply the digits, and list the answer to those (in blue). Then count total amount of numbers after the decimal point in the equation, and move accordingly (in red).

  You will count 3 decimal places for each `-0.012`, which is equal to 6 decimal places. This means that the 144, including those numbers, will be SIX decimal places after the point. To get that, add 3 0's and then the 144 after the point. You get `0.000144`

Answer 2

If the decimal places are giving you a problem try this approach.

`0.000144`

Explanation:

`0.0012` is the same as `12xx1/1000`

So we can put off dealing with the decimal point until the very end.

So write as `(-12xx1/1000)^2`

This is the same as `(-12)^2xx(1/1000)^2`

Multiply 2 negatives and you have a positive giving:

`+144xx(1/1000)^2`

Giving:

`144xx1/1000000color(white)("dd")-> 144xx1/(1000,000)`

Now we deal with the decimal point.

`0.000144`

This is the same as `1.44xx1/(10000) color(white)("dd")->1.44xx10^(-4)`