2.3.3 Standard Form, PT3 Focus Practice

Question 11:
$\text{Express }0.000064-3.5\times {10}^{-6}\text{ in standard form}\text{.}$

Solution:
$\begin{array}{l}0.000064-3.5\times {10}^{-6}\\ =6.4\times {10}^{-5}-3.5\times {10}^{-6}\\ =6.4\times {10}^{-5}-0.35\times {10}^{-5}\\ =\left(6.4-0.35\right)\times {10}^{-5}\\ =6.05\times {10}^{-5}\end{array}$

Question 12:
$\begin{array}{l}200.7\times {10}^{11}\text{ is written as }2.007\times {10}^b\text{ in the standard form}\text{.}\\ \text{State the value of }b.\end{array}$

Solution:
$\begin{array}{l}200.7\times {10}^{11}=2.007\times {10}^2\times {10}^{11}\\ =2.007\times {10}^{13}\\ b=13\end{array}$

Question 13:
Find the product of 0.1985 and 0.5.
Round off the answer correct to two significant figures.

Solution:
0.1985 × 0.5
= 0.09925
= 0.10 (two significant figures)

Question 14:
The area of a rectangular public parking area is 7.2 km² . Its width is 2400 m. The length, in m, of the parking area is

Solution:
$\begin{array}{l}\text{Area = Length }\times \text{ Width}\\ \text{Length }\times \text{ 2}\text{.400 }km\text{ = 7}\text{.2 }k{m}^2\\ \text{Length}=\frac{7.2}{2.4}\\ =3km\\ =3000m\\ =3\times {10}^{3}m\end{array}$

Question 15:
It is given that 30 solid metal cylinders each with a radius of 70 cm and a height of 300 cm, are melted to make 40 identical solid spheres.
Find the volume, in cm³ , of each solid sphere.

Solution:
$\begin{array}{l}\text{Volume of 40 spheres}\\ \text{= Volume of 30 cylinders}\\ =30\times \frac{22}{7}\times {70}^2\times 300\\ =138\text{ 6}00000{\text{ cm}}^3\\ \\ \text{Volume of 1 sphere }=\frac{138\text{ 6}00000}{40}\\ =3\text{ 465 }000{\text{ cm}}^3\\ =3.465\times {10}^6{\text{ cm}}^3\\ =3.47\times {10}^6{\text{ cm}}^3\end{array}$