Question
Compare the following numbers.
$2.7 \times 10^{12} ; 1.5 \times 10^8$
$2.7 \times 10^{12} ; 1.5 \times 10^8$
✓
Answer
We have, $2.7 \times 10^{12}, 1.5 \times 10^8$
$2.7 \times 10^{12}=2.7 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10^7$
$=\frac{27}{10} \times 10 \times 10 \times 10 \times 10 \times 10 \times 10^7$
$=270000 \times 10^7$
and $1.5 \times 10^8=\frac{15}{10} \times 10 \times 10^7=15 \times 10^7$
$\because \quad 270000>15$
$\therefore \quad 270000 \times 10^7>15 \times 10^7$
or $\quad 2.7 \times 10^{12}>1.5 \times 10^8$
Hence, $2.7 \times 10^{12}$ is greater than $1.5 \times 10^8$.
$2.7 \times 10^{12}=2.7 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10^7$
$=\frac{27}{10} \times 10 \times 10 \times 10 \times 10 \times 10 \times 10^7$
$=270000 \times 10^7$
and $1.5 \times 10^8=\frac{15}{10} \times 10 \times 10^7=15 \times 10^7$
$\because \quad 270000>15$
$\therefore \quad 270000 \times 10^7>15 \times 10^7$
or $\quad 2.7 \times 10^{12}>1.5 \times 10^8$
Hence, $2.7 \times 10^{12}$ is greater than $1.5 \times 10^8$.
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