To determine which of the expressions is correct, we need to multiply the numbers in scientific notation and ensure the results are also expressed correctly in scientific notation.
Let's evaluate each option:
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Option: ($2.9 \times 10^8$) ($1.3 \times 10^7$)
\[ (2.9 \times 1.3) \times (10^8 \times 10^7) = 3.77 \times 10^{15} \]
Calculation: \[ 2.9 \times 1.3 = 3.77 \quad \text{and} \quad 10^8 \times 10^7 = 10^{15} \]
So, the first option is correct.
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Option: ($4.6 \times 10^5$) ($2.1 \times 10^4$)
\[ (4.6 \times 2.1) \times (10^5 \times 10^4) = 9.66 \times 10^9 \]
Calculation: \[ 4.6 \times 2.1 = 9.66 \quad \text{and} \quad 10^5 \times 10^4 = 10^9 \]
This does not match the indicated result of \(2.5 \times 10\). So, this option is incorrect.
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Option: ($9.9 \times 10^7$) ($5.8 \times 10^6$)
\[ (9.9 \times 5.8) \times (10^7 \times 10^6) = 57.42 \times 10^{13} \]
Calculation: \[ 9.9 \times 5.8 = 57.42 \quad \text{and} \quad 10^7 \times 10^6 = 10^{13} \]
We must express \(57.42\) in scientific notation: \[ 57.42 = 5.742 \times 10^1 \] So: \[ 57.42 \times 10^{13} = 5.742 \times 10^{14} \]
This does not match \(5.72 \times 10^{13}\), so this option is incorrect.
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Option: ($8.8 \times 10^8$) ($4.2 \times 10^7$)
\[ (8.8 \times 4.2) \times (10^8 \times 10^7) = 36.96 \times 10^{15} \]
Calculation: \[ 8.8 \times 4.2 = 36.96 \quad \text{and} \quad 10^8 \times 10^7 = 10^{15} \]
We must express \(36.96\) in scientific notation: \[ 36.96 = 3.696 \times 10^1 \] So: \[ 36.96 \times 10^{15} = 3.696 \times 10^{16} \]
This does not match \(13 \times 10^{15}\), so this option is incorrect.
The only correct option from the list is:
- ($2.9 \times 10^8$) ($1.3 \times 10^7$) = 3.77×10^{15}
1 answer