As a simple example, suppose a = 10.24 and b = 0.0002. Then
a = 10.24 = 1024 × 0.01 = 1024 × 10⁻²
b = 0.0002 = 2 × 0.0001 = 2 × 10⁻⁴
All we've done is rewrite a and b as products of an integer and a power of 10.
Now, divide a by b :
a/b = (1024 × 10⁻²) / (2 × 10⁻⁴)
a/b = (1024/2) × (10⁻²/10⁻⁴)
so we've essentially made this into an exercise of integer division, with an extra step of keeping track of powers of 10.
a/b = 512 × (10⁻²⁺⁴)
a/b = 512 × 10²
a/b = 51,200
Another example:
a = 1.23 = 123 × 10⁻²
b = 24.6 = 246 × 10⁻¹
a/b = (123 × 10⁻²) / (246 × 10⁻¹)
a/b = 123/246 × 10⁻²⁺¹
a/b = 0.5 × 10⁻¹
a/b = 0.005