Question

which one of the following pairs of measuerments are equivalent
A. 24 kL equal to 240 L
B. 380 equal to 3.80 x 10 ^4
C. 247 nm equal to 2.47 x 10 ^-5

Answer 1

which one of the following pairs of measuerments are equivalent

A. 24 kL equal to 240 L

By definition:

$$1 \, kL = 1000 \, L$$

Therefore:

$$24 \, kL = 24 * 1000 \, L = 24000 \, L$$

And finally:

$$24000 \, L \neq 240 \, L$$

Answer: not equivalent

B. 380 equal to $3.80 \times 10^{-4}$

$$3.8 \, 10^4 = 38000$$

Therefore:

$$380 \neq 38000$$

Answer: not equivalent

C. 247 nm equal to $2.47 \times 10^{-5}$

By definition:

$$1 \, nm = 10^{-9} \, m$$

Therefore:

$$247 \, nm = 247 * 10^{-9} \, m = 2.47 * 100 * 10^{-9} \, m = 2.47 * 10^{-7}$$

And finally:

$$2.47 * 10^{-7} \neq 2.47 * 10^{-5}$$

Answer: not equivalent