Write the following quantities in standard form.
(a) 6400 km (b) 38000 km
(c) $300000000 ms^{-1}$ (d) seconds in a day
{(a) $6.4\times10^{3} km$ (b) $3.8\times 10^{5}$ km (c) $3 \times10^{8} ms^{-1}$ (d) $0.64\times10^{4s}$
Difficulty: Medium
Solution:
(a) 64000 km
Multiplying and dividing by “$10^{3}$”
=6400 $\frac{m}{1000}\times 10^{3}$km
=$64 \frac{m}{10} \times 10^{3}$km
=$6.4\times10^{3}$ km
(b) 38000 km
Multiplying and dividing by “$10^{5}”$
=$\frac{38000}{10^{5}} \times10^{5}km$
=$\frac{380000}{380000}\times 10^{5}km$
= $3.8 \times 10^{5}$ km
(c) 300000000 $ms^{-1}$
Multiplying and dividing by “$10^{8}$”
$\frac{300000000 ms^{-1}}{100000000}\times10^{8}km$
= $3 \times 10^{8}$ km
(d) seconds in a day
As we know
1 day =24 hours
1 hour= 60 minutes
1 minute = 60 seconds so
1 day = $24 \times 60 \times 60$ seconds
1 day = 86400 s
Multiplying and dividing by $10^{4}$
=$\frac{86400}{10000}\times10^{4} s$
=$8.4 \times10^{4} s$
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