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In next question change the given value into scientific notation ex 4nm-> 4x10 ^-9

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2 Answers

The example states the following:     4 nm ≥ 4x10-9 m

   The conversion is from nanometers (nm) to meters (m). Since   1 nm = 1x10-9 m ,  4 nm was converted to m by multiplying 4 nm by 1x10-9 m/1 nm , in which the nm in the denominator and numerator cancel out leaving you with m. 

A)   3.7 pm ≥ ? m

     1 picometer (pm) = 1x10-12

      (3.7 pm)(1x10-12 m/1 pm) = 3.7x10-12 m

      3.7 pm ≥ 3.7x10-12 m

B)   31 km ≥ ? m

       1 kilometer (km) = 1000 m 

      (31 km)(1000 m/1 km) = 31000 m = 31000x100 m

      To express this in scientific notation, move the decimal point in such a way that the number is greater than or equal to 1 but less than 10. Here, the decimal point is at the end of number so we move it 4 places to the left to yield 3.1. Since we made the number smaller, we make the exponent associated with the 10 that many decimal places bigger. That is, 100 now becomes 104:

          31000x100 m = 3.1x104 m

Thus,

          31 km ≥ 3.1x104 m

C)   9.8 mm ≥ ? m

      1 millimeters (mm) = 0.001 m

      (9.8 mm)(0.001 m/1 mm) = 0.0098 m = 0.0098x100 m

     Moving the decimal point 3 places to the right to yield 9.8 makes the number bigger so we make the exponent associated with the 10 that many decimal places smaller. That is, 100 now becomes 10-3:

          0.0098x100 m = 9.8x10-3 m

 Thus,

          9.8 mm ≥ 9.8x10-3 m