In the next questions change the given value into scientific notation ex 4 nm-> 4 x 10^-9m
A) 3.7 pm->
B) 31 km->
C) 9.8 mm->
In the next questions change the given value into scientific notation ex 4 nm-> 4 x 10^-9m
A) 3.7 pm->
B) 31 km->
C) 9.8 mm->
p stands for pico, 10^{-12;}
k is kilo, 1000 or 10^{3}
m is for milli, 0.001 or 10^{-3}
The rest shall be easy.
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} m
(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 = 31000x10^{0} 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, 10^{0} now becomes 10^{4}:
31000x10^{0} m = 3.1x10^{4} m
Thus,
31 km ≥ 3.1x10^{4} m
C) 9.8 mm ≥ ? m
1 millimeters (mm) = 0.001 m
(9.8 mm)(0.001 m/1 mm) = 0.0098 m = 0.0098x10^{0} 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, 10^{0} now becomes 10^{-3}:
0.0098x10^{0} m = 9.8x10^{-3} m
Thus,
9.8 mm ≥ 9.8x10^{-3} m