200/3 * 10^-2 = 2/3?

[CeciliaZ609]

Hi,

I am trying to solve #3 on the All the Quant Companion, Ch. 1. It states that 200/3 times 10 ^ -2 is equal to 2/3. I am struggling to understand this.

[Sage Pearce-Higgins]

Let's unpack this one. A negative exponent means a reciprocal, i.e. 1/something. So 10^-2 is 1/10^2 which is 1/100. If you multiply fractions, multiply the top parts and the bottom parts, so that 200/3 * 1/100 = 200/300, which simplifies down to 2/3. If that's unclear, let me know which step is problematic.

You can also find more about this in the Foundations of Math book.