Question

Write the following as full (decimal) numbers without prefixes on the units: (a) 177.3 mm, (b) 26 mV, (c) 537 mg. (d) 36.5 ps, (e) 52.5 nm.

Answer 1

• a) 0.177 300 m
• b) 0.026 V
• c) 0.537 g
• d) 0.000 000 000 036 500 s
• e) 0.000 000 052 500 m

Step-by-step explanation:

To find the full numbers, we just need to know the decimal representation of the unit prefix.

We know that milli- is one thousandth, this is

`10^-3 = 0.001`

So, we can obtain the first three numbers simply by taking this multiple:

a.

`177.3 \  mm = 177.3 \  10 ^ {-3}  \ m = 177.3 *  0.001  \ m =  0.177 \ 300  \ m`

b.

`26 \  mV = 26 \  10 ^ {-3}  \ V = 26 *  0.001  \ V =  0.026  \ V`

c.

`537 \  mg = 537 \  10 ^ {-3}  \ g = 537 *  0.001  \ g =  0.537  \ g`

pico- is one trillionth, this is

`10^(-12) = 0.000 \ 000 \ 000\  001`

so

d.

`36.5 \  ps = 36.5  \  10 ^ {-12}  \ s = 36.5 *  0.000 \ 000 \ 000 \ 001  \ s =   0.000 \ 000 \ 000 \ 036  \ 500 s`

finally, nano- is one "one billionth", this is

`10^(-9) = 0.000 \ 000 \   001`

`52.5 \ nm = 52.5  \  10 ^ {-9}  \ m = 52.5 *  0.000 \ 000 \ 001  \ m =   0.000 \  000 \ 052  \ 500 s`