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The table shows the populations of the four countries in the UK in 2018. All values are correct to 3 significant figures.

a) Write the population of England as an ordinary number.
- England: [tex]\(56,000,000\)[/tex]

[tex]\[
\begin{tabular}{|c|c|}
\hline
Country & Population \\
\hline
England & \(5.60 \times 10^7\) \\
\hline
Wales & \(3.14 \times 10^6\) \\
\hline
Scotland & \(5.44 \times 10^6\) \\
\hline
Northern Ireland & \(1.88 \times 10^6\) \\
\hline
\end{tabular}
\][/tex]

b) Work out the population of Wales, Scotland, and Northern Ireland. Give your answer in standard form.

[tex]\(\boxed{\text{Answer}}\)[/tex]

[2 marks]

c) The total population of the UK is predicted to reach 72.9 million in 2041. Calculate the predicted percentage increase in the UK population from 2018 to 2041. Give your answer correct to 2 significant figures.

[tex]\(\boxed{\text{Answer}}\)[/tex]

Sagot :

GinnyAnswer
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]
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