Question

question 1-17
how many pg in 250 kg?
○ 2.5×10¹⁴ pg
○ 2.5×10⁻⁴ pg
○ 2.5×10⁻¹⁰ pg
○ 2.5×10¹⁷ pg

Explanation:

Step1: Recall unit conversions

We know that \(1\space kg = 10^{3}\space g\) and \(1\space g = 10^{12}\space pg\). So, to convert \(kg\) to \(pg\), we can use the chain of conversions.
First, convert \(kg\) to \(g\): \(250\space kg=250\times10^{3}\space g\)
Then, convert \(g\) to \(pg\): \(250\times10^{3}\space g = 250\times10^{3}\times10^{12}\space pg\)

Step2: Simplify the expression

Using the rule of exponents \(a^{m}\times a^{n}=a^{m + n}\), we have:
\(250\times10^{3}\times10^{12}=250\times10^{3 + 12}=250\times10^{15}\)
But \(250 = 2.5\times10^{2}\), so:
\(2.5\times10^{2}\times10^{15}=2.5\times10^{2+15}=2.5\times10^{17}\space pg\)

Answer:

\(2.5\times10^{17}\space pg\) (corresponding to the option \(2.5\times10^{17}\space pg\))