# Can I Extrapolate 3.4 Defects Per Million to 34 Defects Per 10 Million or 3400 Defects Per Billion?

To help you better understand the nature of this question; let us consider a very simple example.  Let us suppose that we go to the store – looking for fresh apples.  Once there, we notice a sign that reads “3 apples for \$1.00.”

Based on this sign, we ask the storekeeper: “If I want to buy 6 apples, will it cost me \$2.00?”  To this question, he replied: “Yes.”  Let us now consider these two ratios:

Apples: 6
Cost: \$2.00

Apples: 3
Cost: \$1.00

By way of observational reasoning, we may now infer that 1 apple would cost \$0.33 and 12 apples would cost \$4.00.  In each case, the ratio is 3 to 1.  For every three apples, you must pay one dollar.  This is called a “linear relationship.”  It is also called a “proportional relationship” because each case is proportional to the next case (as well as the previous case).

Now, let us switch from “apples to defects” and change “cost to opportunities.”  In this manner, the answer to your question will be revealed.

Defects .0000034
Opportunities: 1

Defects .000034
Opportunities: 10

Defects .00034
Opportunities: 100

Defects .0034
Opportunities: 1,000

Defects .034
Opportunities: 10,000

Defects .34
Opportunities: 100,000

Defects 3.4
Opportunities: 1,000,000

Defects 34
Opportunities: 10,000,000

Defects 340
Opportunities: 100,000,000

Defects 3,400
Opportunities: 1,000,000,000

Pick any one of these ratios and compare it to the one that follows.   Doing so will reveal the next ratio to be 10X of the previous.  In other words, we just multiply the “defects” and “opportunities” by 10 to find the next ratio.  Of course, such an extrapolation could go on to the limit of infinity (forever).