Some Basic Concepts of Chemistry

Question

Fill in the blanks in the following conversions:
(i) 1 km = ............. mm = .............. pm
(ii) 1 mg = ............... kg = ............. ng
(iii) 1 mL = ........ L = .......... dm³

Solution

(i) 1 km
$space equals space 1 km space space cross times space fraction numerator 1000 space straight m over denominator 1 space km end fraction cross times space fraction numerator 100 space cm over denominator 1 space straight m end fraction cross times space fraction numerator 10 space mm over denominator 1 space cm end fraction space equals space 10 to the power of 6 space mm$
$1 space km space equals space 1 space km space cross times space fraction numerator 1000 space straight m over denominator 1 space km end fraction cross times fraction numerator 1 space pm over denominator 10 to the power of negative 12 end exponent straight m end fraction space equals space 10 to the power of 15 pm space space space space space space space space space$
$left parenthesis ii right parenthesis space 1 space mg space equals space 1 space mg space cross times space fraction numerator 1 space straight g over denominator 1000 space mg end fraction cross times fraction numerator 1 space kg over denominator 1000 space straight g end fraction space equals space 10 to the power of negative 6 end exponent space kg 1 space mg space equals space 1 space mg space cross times fraction numerator 1 space straight g over denominator 1000 space mg end fraction cross times fraction numerator 1 space ng over denominator 10 to the power of negative 9 end exponent space straight g end fraction equals space 10 to the power of 6 ng left parenthesis iii right parenthesis space 1 space mL space equals space 1 space straight m space straight L space cross times space fraction numerator 1 space straight L over denominator 1000 space mL end fraction space equals space 10 to the power of negative 3 end exponent straight L 1 space mL space equals space 1 space cm cubed space space space space space space space space space equals space 1 space cm cubed space cross times space fraction numerator 1 space dm space cross times space 1 space dm space cross times space 1 space dm over denominator space 10 space cm space cross times space 10 space cm space cross times 10 cm end fraction space equals space 10 to the power of negative 3 end exponent space dm cubed$

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