# 2.3.2 Standard Form, PT3 Focus Practice

Question 6:
(a)  Round off 0.05079 correct to three significant figures.
(b)  Find the value of 5 × 107 + 7.2 × 105 and state its answer in standard form.

Solution:
(a)  0.05079 = 0.0508 (correct to three significant figures)
(b)  5 × 107 + 7.2 × 105 = 500 × 105 + 7.2 × 105
= (500 + 7.2) × 105
= 507.2 × 105
= 5.072 × 107

Question 7:
(a)  Calculate the value of 70.2 – 3.22 × 8.4 and round off its answer correct to three significant figures.
(b)  Express $\frac{840}{0.000021}$  as a number in standard form.

Solution:
(a)  70.2 – 3.22 × 8.4 = 70.2 – 27.048
= 43.152 = 43.2 (correct to three significant figures)

(b)
$\begin{array}{l}\frac{840}{0.000021}=\frac{8.4×{10}^{2}}{2.1×{10}^{-5}}\\ \text{}=\frac{8.4}{2.1}×{10}^{2-\left(-5\right)}\\ \text{}=4×{10}^{7}\end{array}$

Question 8:
Calculate the value of 7 × (2 × 10-2)3– 4.3 × 10-5 and state its answer in standard form.

Solution:
7 × (2 × 10-2)3 – 4.3 × 10-5= 7 × 23 × (10-2)3 – 4.3 × 10-5
= 56 × 10-6 – 4.3 × 10-5
= 5.6 × 10-5 – 4.3 × 10-5
= 1.3 × 10-5

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

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

Question 10:

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