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Express the following quantities using prefixes.
(a) 5000 g (b) 2000000 W
(c) $52\times1Tt0kg$ (d) 225$\times10^{-8s}$
{(a)5kg (b) 2 MW (c) 5.2 µg (d) 2.25µs }
Solution:
(a) 5000 g
= $5 \times 1000g$
= $5 \times 1kg (Since 1000g = 1kg)$
= 5kg
(b) 2000,000 w
=$2 \times 1000000$
= $2 \times 10^{6}W (10^{6} = 1 Mega)$
= 2 MW
(c) $52 \times 10^{-10} kg$
= $5.2 \times l0\times 10^{-10}kg$
= $5.2 \times 10^{-9} kg$
= $5.2 \times10^{-9} \times 1000g$ (Since 1 kg = 1000 g)
= $5.2\times 10^{-9} \times 10^{3} g$
= $5.2\times 10^{-9} \times 10^{-6} g$
= $5.2 µg (10^{-6} = 1micro(µ))$
(d) $225 \times 10^{-8} s$
= $225\times10^{2} \times 10^{-8} s$
= $2.25 \times 10^{-6} s$
= $2.25 µs (10^{-6} = 1micro(µ))$
How do the prefixes micro, nano, and pico relate to each other?
Solution:
As we know
$micro = µ = 10^{-6}$
$nano = n = 10^{-9}$
$pico = p = 10^{-12}$
The relation between micro, nano and pico can be written as.
$micro = 10^{-6}$
$nano = 10^{-6} \times 10^{-3} = 10^{-6}$ micro
pico = $10^{-6} \times10^{-6} = 10^{-6}$ micro
Your hair grows at the rate of 1 mm per day. Find their growth rate
in nm $s^{-1}. (11.57 nm s^{-1})$
Solution:
Growth rate Of hair in nm $s^{-1}$ = Imm per day
Growth rate of hair in one day = $24\times 60 \times$ 60 s
(Since 1 mm $10^{-3} m and one day = 24 \times 60 \times 60 s)$, hence
1 mm per day = $I\times 10^{-3} m \times \frac{1}{24} \times 60 \times$ 60 s
= $I \times 10^{-3} m \times \frac{1}{8400} m s^{-1}$
= $I \times10^{-3} m\times 0.00001157$
= $I \times 10^{-3} m \times1157 \times 10^{-8} ms^{-I}$
= $1157 \times 10^{-2}m \times 10^{-9}ms^{-1}$
=$11.57 \times10^{-9} ms^{-1}$
1 mm per day =$11.57 nms^{-1}$
(because $10^{-9} ms^{-1} = 1n ms^{-1})$.
