Question

a microgram is equal to 1×10⁻⁶ grams. how many times greater than a microgram is 1×10² grams?

Explanation:

Step1: Set up the ratio

To find out how many times greater $1\times10^{2}$ grams is than $1\times 10^{-6}$ grams, we divide the larger quantity by the smaller one. The ratio is $\frac{1\times 10^{2}}{1\times 10^{-6}}$.

Step2: Use exponent - rule for division

According to the rule $\frac{a^{m}}{a^{n}}=a^{m - n}$, when $a = 10$, $m = 2$ and $n=-6$, we have $10^{2-(-6)}=10^{2 + 6}$.

Step3: Calculate the exponent

$2+6 = 8$, so $10^{2+6}=10^{8}$. And since the coefficient is $\frac{1}{1}=1$, the result is $1\times 10^{8}$.

Answer:

$1\times 10^{8}$ (corresponding to the orange - colored option)