Answer
(a) Scientific notation: $5 \times 10^{-9}$ $m$
Appropriate prefix: $5$ $nm$
(b) Scientific notation: $4.0075017 \times 10^{7}$ $m$
Appropriate prefix: $40.075017$ $Mm
Work Step by Step
\geq\frac{x}{y}(a)
To write the quantity in scientific notation, we have to move the decimal point to the right of the first number different number.
In 0.000000005, this number is "5"; therefore, we should put the decimal point to the right of it.
5. Notice that we had to move the point by 9 times to the right; therefore, we should put a "$\times 10^{-9}$" at the end.
$5 \times 10^{-9}$ $m$
Now, identify the closest prefix to $10^{-9}$: it is nano "n." Therefore:
$5$ $nm$ (nanometers)
(b)
In 40,075,017 the first non-neutral number is "4"; therefore, we should put the decimal point between it and the zero.
$4.0075017$. Notice that we moved the decimal point by 7 times to the left; therefore, we should put a "$\times 10^7$" at the end.
$4.0075017 \times 10^{7}$ $m$
Identify the closest prefix to $10^7$; it is mega "M", which has the value of $10^6$. Therefore:
$4.0075017 \times \frac{10^7}{10^6}$ $Mm$ (Megameters)
$4.0075017 \times 10$ $Mm$ (Megameters)
$40.075017$ $Mm$ (Megameters)
