4: Overall dilution

Now that you are really comfortable with working out individual dilutions … what happens if you dilute and then dilute again? For example, we could take super-strong coffee, dilute  it 1/5, and then dilute THAT by 1/10. So:

Here’s the rule:

To find the overall (or total) dilution, simply multiply the dilution at each step.  This works regardless of how many dilutions you do.

In this example, to work out how much the original coffee was diluted, multiply 1/5 by 1/10:


Once again, here’s an applet to practice finding the total dilution scheme, regardless of how the dilution scheme is expressed — as directions, as fractions, or as decimals. Click ‘!’ to check your answer — you’ll see ‘correct’ when both answers are right.

Remember, keep going until you’re very comfortable with the calculations… Oh, and do yourself a favour, use a calculator!!

Given the following series of dilutions,
what is the total dilution factor?

Start with a concentrated stock:

• Do a 0.005 dilution, then
• do a 0.01 dilution, then
• do a 0.2 dilution.

As a Fraction: 1 /

As a Decimal: