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Evaluate and write the answer in scientific notation: \newline(1.48×103)(7×104)÷8.2×1012(1.48\times10^{3})(7\times10^{4})\div8.2\times10^{12}

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Evaluate definite integrals using the chain ruleright chevron icon

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Q. Evaluate and write the answer in scientific notation: \newline(1.48×103)(7×104)÷8.2×1012(1.48\times10^{3})(7\times10^{4})\div8.2\times10^{12}
  1. Multiply and Add Exponents: Multiply the coefficients 1.481.48 and 77 and add the exponents of 1010 (3(3 and 4)4).\newlineCalculation: (1.48×7)×10(3+4)(1.48 \times 7) \times 10^{(3+4)}\newlineMath error check: Multiplication and addition are basic operations, and there is no error here.
  2. Multiply Coefficients: Perform the multiplication of the coefficients.\newlineCalculation: 1.48×7=10.361.48 \times 7 = 10.36\newlineMath error check: Multiplication is correct.
  3. Add Exponents: Add the exponents of 1010.\newlineCalculation: 103+4=10710^{3+4} = 10^7\newlineMath error check: Addition of exponents is correct.
  4. Combine Results: Combine the results from steps 22 and 33 to get the result of the multiplication part of the expression.\newlineCalculation: 10.36×10710.36 \times 10^7\newlineMath error check: Combination of results is correct.
  5. Divide by Divisor: Divide the result from step 44 by the divisor 8.2×10128.2\times10^{12}.\newlineCalculation: (10.36×107)÷(8.2×1012)(10.36 \times 10^7) \div (8.2 \times 10^{12})\newlineMath error check: Setting up the division is correct.
  6. Divide Coefficients: Divide the coefficients (10.3610.36 and 8.28.2) and subtract the exponents of 1010 (1212 from 77).\newlineCalculation: (10.36÷8.2)×10(7−12)(10.36 \div 8.2) \times 10^{(7-12)}\newlineMath error check: Division and subtraction are basic operations, and there is no error here.
  7. Perform Division: Perform the division of the coefficients.\newlineCalculation: 10.36÷8.2≈1.2634110.36 \div 8.2 \approx 1.26341 (rounded to five decimal places for intermediate calculation)\newlineMath error check: Division is correct.
  8. Subtract Exponents: Subtract the exponents of 1010.\newlineCalculation: 107−12=10−510^{7-12} = 10^{-5}\newlineMath error check: Subtraction of exponents is correct.
  9. Combine Results: Combine the results from steps 77 and 88 to get the result of the division part of the expression.\newlineCalculation: 1.26341×10−51.26341 \times 10^{-5}\newlineMath error check: Combination of results is correct.
  10. Write Final Result: Write the final result in scientific notation, rounding to two decimal places as is customary in scientific notation.\newlineCalculation: 1.26×10−51.26 \times 10^{-5}\newlineMath error check: Rounding is correct.

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