What is the area, 1mm^2, in square metres, and in scientific notation? Why?

Answer 1

There are one thousand millimetres in one metre. To create a square metre, you would have a square which has sides of a length of one metre each. To determine the area of the square, you multiply the length by the width. In metres, this would be 1m x 1m which creates 1m². In millimetres, this would be 1000mm x 1000mm which gives you 1,000,000mm².

Scientific notation is generally in this notation: n x 10^e where n is the base number and e is the exponent. Generally n is one integer followed by decimals, however, since we're dealing with a round number, all we need is the integer 1. The 1 is in the millionth place which is 10^6 (just could the places after the first number). Therefore, that answer is 1 x 10^6mm².

Conversely, to invert that for your question, there are .001 metres in a millimetre. Using the same logic you can also come up with the scientific notation of such by knowing that 1 x 10^-1 = 0.1. .001x.001 = .000001, ergo, your answer in scientific notation is 1 x 10^-6m².

Another interesting feature related to scientific notation is that to multiply similar exponents (exponents with the same base) you simply add them together. If you took your original number of metres and put it in scientific notation, you would have 1 x 10^-3m. If you square this, you basically have 1 x 10^-3m x 1 x 10^-3m. If you just add the exponents together (-3+-3, or -3-3) you have, again, 1 x 10^-6m.

Answer 2

1mm^2 = 10^-6 m^2 since 1mm = 10^-3m and you must square

10^-6 is written 1E-6 E- means 10^-

Answer 3

(0.001)*(0.001) = 0.000001 = 10^-6

There are 0.001 millimeters in a meter. So squaring that gives you the number of square millimeters in a square meter.