Question

Write 'T' for true and 'F' for false for each of the following.

(i) 645 in standard form is 6.45 × 10².
(ii) 27000 in standard form is 27 × 10^3.
(iii) (3⁰ + 4⁰ + 5⁰) = 12.
(iv) Reciprocal of 5⁶ is 6⁵.
(v) If 5⁻¹ × x = 8⁻¹, then x = $\frac{8}{5}$.

Answer 1

(i) True
645 = 6.45 x 10² [since the decimal point is moved 2 places to the left]

(ii) False
27000 = 2.7 x 10⁴ [since the decimal point is moved 4 places to the left]

(iii) False
(3⁰ + 4⁰ + 5⁰) = 1 [since a⁰ = 1 for every integer a]

(iv) False
Reciprocal of 5⁶ = Reciprocal of ${\left(\frac{5}{1}\right)}^6={\left(\frac{1}{5}\right)}^6$

(v) False
5⁻¹ × x = 8⁻¹
⇒ $\frac{1}{5}\times x=\frac{1}{8}$
⇒ x = $\left(\frac{1}{8}\times 5\right)=\frac{5}{8}$