5mm:1cm- what is the scale factor?

1 cm = 10 mm

So, whats the scale factor between 5mm and 10 mm?

Scale factor is really asking "how much bigger is one measurement compared to another measurement?"

Let's make the two measurements into a fraction

$${\frac{{\mathtt{5}}}{{\mathtt{10}}}}$$

This can be reduced to:

$${\frac{{\mathtt{1}}}{{\mathtt{2}}}}$$

So 1/2 is our scale factor.

It's important to know that 2 is also the scale factor to these two objects. If you were to swap the measurements' place's in the fraction, it would still work, I'll show you:

$${\frac{{\mathtt{10}}}{{\mathtt{5}}}}$$

I just swaped their places. This can be reduced to:

$${\frac{{\mathtt{2}}}{{\mathtt{1}}}}$$

or just 2

 

So either 2 or 1/2 are our scale factors. What these numbers are saying is that one object is 2 times bigger than the other, or that the other object is 1/2 the size of the first object.

 

Here's a video explaining scale factors if you'd like to watch a video on it: http://www.virtualnerd.com/pre-algebra/ratios-proportions/similar-figures-indirect-measurement/similar-figures/find-scale-factor-similar-figures