1.3 SPM Practice (Short Questions)

Question 9:
$3.17\times {10}^{-8}-1.20\times {10}^{-9}=$

Solution:
$\begin{array}{l}3.17\times {10}^{-8}-1.20\times {10}^{-9}\\ =3.17\times {10}^{-8}-\left(0.120\times {10}^1\times {10}^{-9}\right)\\ =3.17\times {10}^{-8}-0.120\times {10}^{-8}\\ =\left(3.17-0.120\right)\times {10}^{-8}\\ =3.05\times {10}^{-8}\end{array}$

Question 10:
$\text{Express }\frac{0.096}{{\left(2\times {10}^3\right)}^3}\text{ in standard form}\text{.}$

Solution:
$\frac{0.096}{{\left(2\times {10}^3\right)}^3}=\frac{0.096}{8\times {10}^9}=1.2\times {10}^{-11}$

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)