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->

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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

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