**where each side is 1.00 meter in length. To compute the area, we would certainly multiply side by side.Below, when the conversion of a square unit is carried out, each of the 2 sides will an initial be converted and then, multiplied together.Example #1:**convert 1.00 m2 to cm2.

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**Solution:**In bespeak to deal with this problem, you must see that there are TWO political parties to the 1.00 m2 area and that each SIDE need to be converted to cm.1) take into consideration that 1.00 m2 as a square that is 1.00 m on each side. Its area is our 1.00 m2:

**1.00 m x 1.00 m = 1.00 m22) What we must do next is transform each meter come centimeter:1.00 m = 100 cm3) Now, we replace each meter worth of our square v the equivalent centimeter value:100 cm x 100 cm = 1.00 m24) Now, multiply the end the 100 x 100 and replace the 1.00 m2 with the equivalent cm2 value1.00 x 104 cm2 = 1.00 m2Example #2:**take into consideration 1.00 km2. Convert it come μm2 (square micrometers).

**Solution:**1) consider 1.00 km2 together a square:

**1.00 kilometres x 1.00 km = 1.00 km22) convert kilo- come its indistinguishable in units of micro-:1 kilometres = 109μmIf you execute not know exactly how (or psychic how) to transform metric units, you require to discover that techniqe to carry out the over conversion.3) Replace kilometres with its tantamount μm measurement:(1.00 x 109μm) x (1.00 x 109μm) = 1.00 km24) Multiply the end the left-hand side:1.00 x 1018μm2 = 1.00 km2Example #3:**convert 1.0 mg/cm2 come kg/m2

**Solution:**I will convert very first the numerator, then the denominator.In the numerator, girlfriend must transform from mg to kg, like this:

**1.0 mg time (___ kg / ___mg)1.0 mg times (1 kg / ___mg) 1.0 mg time (1 kg / 106 mg) 6 is the pure exponential "distance" from milli- come kilo-1.0 mg times (1 kg / 106 mg) = 1.0 x 10-6 kgThis method we now have actually 1.0 x 10-6 kg/cm2 and also now we emphasis on the denominator (and neglect the kg portion).Think of 1 cm2 together a square like this:1 centimeter by 1 cmWhat we have to do is transform cm come m, a reasonably easy conversion:1 cm = 0.01 mLet"s replace cm with m:0.01 m x 0.01 m = 10-4 m2 (this is what 1 cm2 is in m2)Now, replace the cm2 unit:1.0 x 10-6 kg / 10-4 m2and simplify:1.0 x 10-2 kg / m2 = 0.010 kg / m2Example #4:**calculate the massive in pounds that a uniform column of water 34.6 ft high having actually an area that 1.00 in2 in ~ its base.

**34.6 ft times 12 customs / ft = 415.2 inThe formula for volume that a cylinder is πr2hsince πr2 = the area, we have actually this:415.2 inch times 1.00 in2 = 415.2 in3Now, we need to compute the conversion from inch cubed to cm cubed:1 in3 = 1 in time 1 in times 1 in1 in3 = 2.54 centimeter times 2.54 cm times 2.54 centimeter = 16.387 cm3415.2 in3 times 16.387 cm3 / 1 in3 = 6804 cm36804 cm3 time 1.00 g/cm3 = 6804 g6804 g time 1 lb / 454 g = 15.0 lbsExample #5:**5 m2 = ____ cm2

**Solution:**

**m = centimeter x 102 m2 = (cm x 102)2m2 = cm2 x 1045 m2 = 5 x 104 cm25 m2 = 50000 cm2Example #6:**5 cm2 = ____ m2

**Solution:**

**cm = m x 10¯2 cm2 = (m x 10¯2)2cm2 = m2 x 10¯45 cm2 = 5 x 10¯4 m25 cm2 = 0.0005 m2Example #7:**A house has an area that 195 m2. (a) transform the area to km2.

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(b) transform the area to ft2?

**Solution to (a):**1) Think that the 195 m2 as a rectangle 195 m by 1 m.2) Now, transform each measurement come km:

**<(195 m) (1 kilometres / 1000 m)> x <(1 m) (1 km / 1000 m)>0.195 m x 0.001 m = 0.000195 km2 (or 1.95 x 10¯4 km2)3) The counter can additionally be presented this way:(1 km)2195 m2x––––––– = 1.95 x 10¯4 km2(103 m)2**

Solution to (b):Think the the 195 m2 together a rectangle 195 m through 1 m together you review the following.I"m walking to transform each metric amount come feet, but I an initial need to do a little bit of explanation.I have memorized the adhering to two conversions:

**1 m = 39.3701 inches12 customs = 1 footFirst, I"m going to convert 195 m:(195 m) (39.3701 customs / m) (1 foot / 12 inch) = 639.764 feetSecond, convert the 1 m value:39.3701 inch1 foot1 mx–––––––––––x–––––– = 3.28084167 feet1 m12 inch**

Last, multiply the 2 values:(639.764 feet) (3.28084167 feet) = 2098.964 ft2Three sig figs would be the many reasonable answer, so 2.10 x 103 ft2.This is since 2100 has actually two SF (not enough) and 2100. Has four SF (too many).Example #8:How many 1 cm squares would certainly it require to construct a square that is 2 m on each side?

**Solution:**1) The area in meters squared is:

**(2 m) (2 m) = 4 m22) convert square meters to square cm:(4 m2) (100 cm / 1 m)2 = 40000 cm23) Written one more way:(100 cm)24 m2x–––––––– = 40000 cm2(1 m)2**

Example #9:How plenty of square picometers room there in 8.47 x 10¯6 Mm2?

**Solution:**1) Here"s one way:

**(1018 pm)28.47 x 10¯6 Mm2x–––––––– = 8.47 x 1030 pm2(1 Mm)2**

2) Here"s another method (note just how I go with meters):(106 m)2(1012 pm)28.47 x 10¯6 Mm2x––––––––x–––––––– = 8.47 x 1030 pm2(1 Mm)2(1 m)2

Example #10:How plenty of square picometer room there in 7.71 x 10¯6 square nanometer?

**Solution:**(103 pm)27.71 x 10¯6 nm2x–––––––– = 7.71 pm2(1 nm)2