The image you've uploaded explains the
conversion from parts per million (ppm) to parts per billion (ppb), but it actually shows the
definition of ppb (parts per billion), not a direct conversion formula. Let's clarify and explain this concept step by step.
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🔹 What is ppb?
ppb stands for
parts per billion, which means:
> 1 part of solute per 1 billion (10⁹) parts of solution.
The formula given in the image is:
$$
\text{ppb} = \frac{\text{Mass of Solute (g)}}{\text{Mass of Solution (g)}} \times 10^9
$$
This formula tells us how to calculate the concentration of a solute in
ppb based on mass.
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🔹 Relationship between ppm and ppb
-
1 ppm = 1 part per million = $1 \times 10^{-6}$
-
1 ppb = 1 part per billion = $1 \times 10^{-9}$
So:
$$
1 \text{ ppm} = 1000 \text{ ppb}
$$
Because:
$$
10^{-6} = 1000 \times 10^{-9}
$$
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🔹 How to Convert PPM to PPB
To convert from
ppm to ppb, use:
$$
\text{ppb} = \text{ppm} \times 1000
$$
####
✔ Example:
If a solution has a concentration of
5 ppm, then in ppb:
$$
5 \, \text{ppm} = 5 \times 1000 = 5000 \, \text{ppb}
$$
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🔹 Practical Use
These units are commonly used in environmental science, chemistry, and water quality testing to measure very low concentrations of substances (like pollutants or contaminants).
For example:
- A water sample with
0.5 ppm of lead =
500 ppb of lead.
- This helps scientists detect trace amounts accurately.
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🔹 Summary
- The image defines
ppb correctly:
$$
\text{ppb} = \left( \frac{\text{mass of solute}}{\text{mass of solution}} \right) \times 10^9
$$
- To convert
ppm → ppb: Multiply by
1000
- To convert
ppb → ppm: Divide by
1000
Let me know if you have a specific problem (e.g., "Convert 2.5 ppm to ppb") and I can solve it!
Parent Tip: Review the logic above to help your child master the concept of parts per million worksheet.
