1. **State the problem:** We have populations of four countries: England, Wales, Scotland, and Northern Ireland, given in scientific notation and ordinary numbers. We want to understand the total population of Wales, Scotland, and Northern Ireland combined, and the predicted percentage increase in the UK population. 2. **List the populations:** - England: $5.60 \times 10^{7}$ (which is 56,000,000) - Wales: $3.14 \times 10^{6}$ - Scotland: $5.44 \times 10^{6}$ - Northern Ireland: $1.88 \times 10^{6}$ 3. **Calculate the combined population of Wales, Scotland, and Northern Ireland:** $$ 3.14 \times 10^{6} + 5.44 \times 10^{6} + 1.88 \times 10^{6} = (3.14 + 5.44 + 1.88) \times 10^{6} = 10.46 \times 10^{6} = 1.046 \times 10^{7} $$ 4. **Compare with given combined population:** The problem states the combined population as $1.05 \times 10^{7}$, which is approximately equal to our calculated $1.046 \times 10^{7}$, confirming the data. 5. **Calculate the total UK population:** $$ \text{Total UK population} = \text{England} + \text{Wales + Scotland + Northern Ireland} = 5.60 \times 10^{7} + 1.05 \times 10^{7} = 6.65 \times 10^{7} $$ 6. **Calculate the predicted increase in population:** Given the predicted percentage increase is 11.02%, the increase in population is: $$ \text{Increase} = 6.65 \times 10^{7} \times \frac{11.02}{100} = 6.65 \times 10^{7} \times 0.1102 = 7.33 \times 10^{6} $$ 7. **Calculate the new predicted population:** $$ \text{New population} = 6.65 \times 10^{7} + 7.33 \times 10^{6} = 7.38 \times 10^{7} $$ **Final answers:** - Combined population of Wales, Scotland, and Northern Ireland: approximately $1.05 \times 10^{7}$ - Total UK population: $6.65 \times 10^{7}$ - Predicted increase in population: $7.33 \times 10^{6}$ - New predicted UK population: $7.38 \times 10^{7}$