How many significant figures are there in the following numbers: 10.78, 6.78, 0.78? If these were pH values, to how many significant figures can you express the [H]? Explain any discrepancies between your answers to the two questions.

10.78 → 4 significant figures, pH = 10.78 → [H⁺] = 1.66ₓ10⁻¹¹ M

6.78 → 3 significant figures, pH = 6.78 → [H⁺] = 1.66ₓ10⁻⁷ M

0.78 → 2 significant figures, pH = 0.78 → [H⁺] = 0.166 M

pH always can be expressed by at least 4 significant figures. The [H⁺], can be expressed by, at least 3 significant figures

Explanation:

Significant figures are the numbers of a measurement that have certainty plus a doubtful number (it is associated with the uncertainty in the measurement). For example, if we measure a paper with a ruler and the ruler measures up to centimeters we can say that the paper is 7.5 cm long, with which we know that the paper is 7 cm + 0.5 cm which we associate with uncertainty. In this case we talk about two significant figures. If the sheet measured 7.57 cm we would already be talking about a more precise measurement and in this case with 3 significant figures.

10.78 → 4 significant figures

6.78 → 3 significant figures

0.78 → 2 significant figures

To determine [H⁺], we apply 10^-pH

10⁻¹⁰°⁷⁸ = 1.66ₓ10⁻¹¹ M

10⁻⁶°⁷⁸ = 1.66ₓ10⁻⁷ M

10⁻⁰°⁷⁸ = 0.166 M