Question

Which is the correct simplification of 2.2x10^4/8.8x10^9

Answer 1

The answer is 2.5x10^-6

2.2 x 10⁴ / 8.8 x 10⁹ can be rewritten as:
2.2 x 10⁴ / 8.8 x 10⁹ = 2.2/8.8 x 10⁴/10⁹

Using the rule xᵃ/xᵇ = xᵃ⁻ᵇ, we can express 10⁴/10⁹ as:
10⁴/10⁹ = 10⁴⁻⁹ = 10⁻⁵

Hence:
2.2/8.8 x 10⁴/10⁹ = 0.25 x 10⁻⁵

However, the scientific notation includes numbers 1-9, so we must represent 0.25 as 2.5 x 0.1

0.25 x 10⁻⁵ = 2.5 x 0.1 x 10⁻⁵ = 2.5 x 10⁻¹ x 10⁻⁵

Using the rule xᵃ * xᵇ = xᵃ⁺ᵇ, then:
2.5 x 10⁻¹ x 10⁻⁵ = 2.5 x 10⁽⁻¹⁾⁺⁽⁻⁵⁾ = 2.5 x 10⁻⁶

Now, let's go all through from the beginning:
2.2 x 10⁴ / 8.8 x 10⁹ = 2.2/8.8 x 10⁴/10⁹ = 0.25 x 10⁻⁵ = 2.5 x 10⁻⁶