Question

Consider the following operations on the number 7.02 times 10^-2. Without using a calculator, decide which would give a significantly smaller value than 7.02 times 10^-2, which would give a significantly larger value, or which would give essentially the same value.

a. 7.02 times 10^-2 + 6.10 times 1^5
b. 7.02 times 10^-2 -6.10 times 10^5
c. 7.02 times 10^2 times 6.10 times 10^5
d. 7.02 times 10^-2 + 6.10 times 10^5

Answer 1

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.