Answer: (a). Significantly Larger value
(b). Significantly Smaller value
(c). Significantly Larger value
(d). Significantly Smaller value
Explanation:
This is quite a dicey question to analyze, let us not get too carried away with the simplicity of the mathematical signs involved.
Given that 7.02 × 10⁻² is the number to be compared with.
(a). 7.02 × 10⁻² + 6.10 × 10⁵
from this, we can see a very large number being added to the base number involved, although the base number is carrying a negative power, it does not affect the other greatly.
ANS: the sum would give a significantly larger value
(b). 7.02 × 10⁻² - 6.10 × 10⁵
Here, we can see a very large number subtracted from the base number having a negative power.
the subtraction of this numbers gives a Significantly smaller value than the base number i.e. 7.02 × 10⁻²
ANS: Significantly smaller value
(c). 7.02 × 10⁻² × 6.10 × 10⁵
we would solve this from our basic knowledge of indices
where ⇒ (10ᵃ × 10ᵇ = 10ᵃ⁺ᵇ)
we have,
7.02 × 10⁻² × 6.10 × 10⁵ = (7.02 × 6.10) × 10⁻²⁺⁵ = (7.02 × 6.10) × 10³
this final value (multiplication value) gives a Significantly larger value.
ANS: Significantly larger value
(d). 7.02 × 10⁻² ÷ 6.10 × 10⁵
Also, we apply the indices rule for Division
where ⇒ (10ᵃ ÷ 10ᵇ = 10ᵃ⁻ᵇ)
i.e. 7.02 × 10⁻² ÷ 6.10 × 10⁵ = (7.02 × 6.10) × 10⁻²⁻⁺⁵ = (7.02 × 6.10) × 10⁻⁷
this final value gives a Significantly Smaller value
ANS: Significantly Smaller value
cheers i hope this helps.
