Huang Clarke
01/02/2023 · Primary School
9. What is the value of \( n \) in the equation \( 1.9 \times 10^{7}=\left(1 \times 10^{5}\right)\left(1.9 \times 10^{n}\right) \) ?
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Tutor-Verified Answer
Step-by-step Solution
Solve the equation \( 1.9 \times 10^{7}=(1 \times 10^{5})(1.9 \times 10^{n}) \).
Solve the equation by following steps:
- step0: Solve for \(n\):
\(1.9\times 10^{7}=10^{5}\left(1.9\times 10^{n}\right)\)
- step1: Remove the parentheses:
\(1.9\times 10^{7}=10^{5}\times 1.9\times 10^{n}\)
- step2: Multiply:
\(1.9\times 10^{7}=1.9\times 10^{5+n}\)
- step3: Swap the sides:
\(1.9\times 10^{5+n}=1.9\times 10^{7}\)
- step4: Divide both sides:
\(\frac{1.9\times 10^{5+n}}{1.9}=\frac{1.9\times 10^{7}}{1.9}\)
- step5: Divide the numbers:
\(10^{5+n}=10^{7}\)
- step6: Set the exponents equal:
\(5+n=7\)
- step7: Move the constant to the right side:
\(n=7-5\)
- step8: Subtract the numbers:
\(n=2\)
The value of \( n \) in the equation \( 1.9 \times 10^{7}=\left(1 \times 10^{5}\right)\left(1.9 \times 10^{n}\right) \) is \( n=2 \).
Quick Answer
\( n=2 \)
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