1998 CEMC Pascal Problems/Problem 9

Problem

What is one-half of $1.2 \times 10^{30}$ ?

$\text{ (A) }\ 6.0 \times 10^{30} \qquad\text{ (B) }\ 6.0 \times 10^{29} \qquad\text{ (C) }\ 0.6 \times 5^{30} \qquad\text{ (D) }\ 1.2 \times 10^{15} \qquad\text{ (E) }\ 1.2 \times 5^{30}$

Solution

We can use the fact that $a^{b + c} = a^{b} \times a^{c}$ , and $\frac{1.2}{2} = 0.6$ :

$\frac{1.2 \times 10^{30}}{2} = \frac{1.2}{2} \times 10^{30} = 0.6 \times 10^{30}$

$=0.6 \times 10^{29 + 1} = 0.6 \times 10^{1} \times 10^{29} = \boxed {\textbf {(B) } 6.0 \times 10^{29}}$

~anabel.disher

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1998 CEMC Pascal Problems/Problem 9

Problem

Solution