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Sagot :
Let's break down this problem step-by-step:
### Part (a)
Write the population of England as an ordinary number.
Given:
[tex]\[ \text{Population of England} = 5.60 \times 10^7 \][/tex]
In ordinary number format:
[tex]\[ 5.60 \times 10^7 = 56,000,000 \][/tex]
### Part (b)
Work out the population of Wales, Scotland, and Northern Ireland. Give your answer in standard form.
Given populations:
- Wales: [tex]\( 3.14 \times 10^6 \)[/tex]
- Scotland: [tex]\( 5.44 \times 10^6 \)[/tex]
- Northern Ireland: [tex]\( 1.88 \times 10^6 \)[/tex]
Step-by-step calculation:
1. Add up the populations:
[tex]\[ 3.14 \times 10^6 + 5.44 \times 10^6 + 1.88 \times 10^6 \][/tex]
2. Combine like terms:
[tex]\[ (3.14 + 5.44 + 1.88) \times 10^6 = 10.46 \times 10^6 \][/tex]
3. Convert 10.46 to standard form:
[tex]\[ 10.46 \times 10^6 = 1.046 \times 10^7 \][/tex]
So, the population of Wales, Scotland, and Northern Ireland combined in standard form is:
[tex]\[ 1.046 \times 10^7 \][/tex]
### Part (c)
Calculate the predicted percentage increase in the UK population from 2018 to 2041. Give your answer correct to 2 significant figures.
1. Calculate the total UK population in 2018:
[tex]\[ \text{Total population in 2018} = \text{Population of England} + \text{Combined population of Wales, Scotland, and Northern Ireland} \][/tex]
[tex]\[ = 5.60 \times 10^7 + 1.046 \times 10^7 \][/tex]
2. Convert these to ordinary numbers:
[tex]\[ 5.60 \times 10^7 = 56,000,000 \][/tex]
[tex]\[ 1.046 \times 10^7 = 10,460,000 \][/tex]
3. Add the populations:
[tex]\[ 56,000,000 + 10,460,000 = 66,460,000 \][/tex]
4. The predicted population in 2041 is 72.9 million:
[tex]\[ \text{Predicted population in 2041} = 72,900,000 \][/tex]
5. Calculate the percentage increase:
[tex]\[ \text{Percentage increase} = \left( \frac{\text{Predicted population in 2041} - \text{Total population in 2018}}{\text{Total population in 2018}} \right) \times 100 \][/tex]
[tex]\[ = \left( \frac{72,900,000 - 66,460,000}{66,460,000} \right) \times 100 \][/tex]
[tex]\[ = \left( \frac{6,440,000}{66,460,000} \right) \times 100 \][/tex]
[tex]\[ \approx 9.69 \% \][/tex]
6. Round to 2 significant figures:
[tex]\[ 9.69 \% \approx 9.7 \% \][/tex]
So, the predicted percentage increase in the UK population from 2018 to 2041 is:
[tex]\[ 9.7\% \][/tex]
### Part (a)
Write the population of England as an ordinary number.
Given:
[tex]\[ \text{Population of England} = 5.60 \times 10^7 \][/tex]
In ordinary number format:
[tex]\[ 5.60 \times 10^7 = 56,000,000 \][/tex]
### Part (b)
Work out the population of Wales, Scotland, and Northern Ireland. Give your answer in standard form.
Given populations:
- Wales: [tex]\( 3.14 \times 10^6 \)[/tex]
- Scotland: [tex]\( 5.44 \times 10^6 \)[/tex]
- Northern Ireland: [tex]\( 1.88 \times 10^6 \)[/tex]
Step-by-step calculation:
1. Add up the populations:
[tex]\[ 3.14 \times 10^6 + 5.44 \times 10^6 + 1.88 \times 10^6 \][/tex]
2. Combine like terms:
[tex]\[ (3.14 + 5.44 + 1.88) \times 10^6 = 10.46 \times 10^6 \][/tex]
3. Convert 10.46 to standard form:
[tex]\[ 10.46 \times 10^6 = 1.046 \times 10^7 \][/tex]
So, the population of Wales, Scotland, and Northern Ireland combined in standard form is:
[tex]\[ 1.046 \times 10^7 \][/tex]
### Part (c)
Calculate the predicted percentage increase in the UK population from 2018 to 2041. Give your answer correct to 2 significant figures.
1. Calculate the total UK population in 2018:
[tex]\[ \text{Total population in 2018} = \text{Population of England} + \text{Combined population of Wales, Scotland, and Northern Ireland} \][/tex]
[tex]\[ = 5.60 \times 10^7 + 1.046 \times 10^7 \][/tex]
2. Convert these to ordinary numbers:
[tex]\[ 5.60 \times 10^7 = 56,000,000 \][/tex]
[tex]\[ 1.046 \times 10^7 = 10,460,000 \][/tex]
3. Add the populations:
[tex]\[ 56,000,000 + 10,460,000 = 66,460,000 \][/tex]
4. The predicted population in 2041 is 72.9 million:
[tex]\[ \text{Predicted population in 2041} = 72,900,000 \][/tex]
5. Calculate the percentage increase:
[tex]\[ \text{Percentage increase} = \left( \frac{\text{Predicted population in 2041} - \text{Total population in 2018}}{\text{Total population in 2018}} \right) \times 100 \][/tex]
[tex]\[ = \left( \frac{72,900,000 - 66,460,000}{66,460,000} \right) \times 100 \][/tex]
[tex]\[ = \left( \frac{6,440,000}{66,460,000} \right) \times 100 \][/tex]
[tex]\[ \approx 9.69 \% \][/tex]
6. Round to 2 significant figures:
[tex]\[ 9.69 \% \approx 9.7 \% \][/tex]
So, the predicted percentage increase in the UK population from 2018 to 2041 is:
[tex]\[ 9.7\% \][/tex]
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