Question

In 2006, the US had a Gross Domestic Product (GDP) of 1.3 x 1013. The United Kingdom had a GDP of 1.9 x 1012.
What were the combined GDPs of the US and the UK in 2006?


Laila’s Solution
Identify and Explain the error
(1.313 x 10^13) + (1.93 x 10^12)
1.313 + 1.93 = 3.243
10^13 + 10^12 = 10^25

Answer 1

To find the combined GDPs of the US and the UK in 2006, let's analyze Laila's calculation step by step and identify the error.

The GDP values given are:
- US: \(1.3 \times 10^{13}\)
- UK: \(1.9 \times 10^{12}\)

To add these two numbers together, they must be expressed in the same power of 10. The larger of the two powers is \(10^{13}\), so we will convert \(1.9 \times 10^{12}\) to the same power:

\[
1.9 \times 10^{12} = 0.19 \times 10^{13}
\]

Now we can add the two GDPs:

\[
1.3 \times 10^{13} + 0.19 \times 10^{13} = (1.3 + 0.19) \times 10^{13}
\]

Calculating that:

\[
1.3 + 0.19 = 1.49
\]

So, we have:

\[
1.49 \times 10^{13}
\]

### Laila's Error:

1. **Combining the powers of 10**:
Laila incorrectly combined the powers of 10 when adding the two GDPs. The correct approach involves keeping the power consistent during addition (in this case, both terms should be in terms of \(10^{13}\)).

2. **Numerical Addition**:
Laila's numerical addition was correct (adding \(1.313 + 1.93\)), but she did not adjust the second term to the correct exponent before adding.

### Conclusion:
The correct combined GDP of the US and the UK in 2006 is:

\[
1.49 \times 10^{13}
\]