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operations involving scientific notation add. write your answer in scie…

Question

operations involving scientific notation
add. write your answer in scientific notation.
1 (7.2×10^5)+(1.54×10^5)
2 (8.41×10^7)+(7.9×10^7)
3 (3.7×10^8)+(4.83×10^9)
subtract. write your answer in scientific notation.
4 (5.31×10^3)-(2.8×10^3)
5 (7.9×10^6)-(7.42×10^6)
6 (8.3×10^5)-(5.6×10^4)
multiply. write your answer in scientific notation.
7 (4.1×10^6)(2.4×10^2)
8 (3.95×10^8)(5.8×10^3)
9 (9.7×10^8)(6×10^11)
divide. write your answer in scientific notation.
10 \frac{7.4×10^8}{4×10^3}
11 \frac{1.9×10^12}{9.5×10^3}
12 \frac{3.84×10^18}{8×10^6}

Explanation:

Response
  1. Addition of \((7.2\times 10^{5})+(1.54\times 10^{5})\):
  • Explanation:
  • Step1: Factor out \(10^{5}\)
  • Using the distributive property \(a\times c + b\times c=(a + b)\times c\), where \(a = 7.2\), \(b=1.54\) and \(c = 10^{5}\), we have \((7.2 + 1.54)\times10^{5}\).
  • Step2: Calculate the sum of the coefficients
  • \(7.2+1.54 = 8.74\), so the result is \(8.74\times 10^{5}\).
  1. Addition of \((8.41\times 10^{7})+(7.9\times 10^{7})\):
  • Explanation:
  • Step1: Factor out \(10^{7}\)
  • \((8.41 + 7.9)\times10^{7}\).
  • Step2: Calculate the sum of the coefficients
  • \(8.41+7.9 = 16.31\). Since scientific - notation requires \(1\leqslant a<10\), we rewrite \(16.31\) as \(1.631\times 10^{1}\). Then \((1.631\times 10^{1})\times10^{7}=1.631\times 10^{8}\).
  1. Addition of \((3.7\times 10^{8})+(4.83\times 10^{9})\):
  • Explanation:
  • Step1: Make the exponents the same
  • Rewrite \(3.7\times 10^{8}\) as \(0.37\times 10^{9}\). Then \((0.37\times 10^{9})+(4.83\times 10^{9})=(0.37 + 4.83)\times10^{9}\).
  • Step2: Calculate the sum of the coefficients
  • \(0.37+4.83 = 5.2\), so the result is \(5.2\times 10^{9}\).
  1. Subtraction of \((5.31\times 10^{3})-(2.8\times 10^{3})\):
  • Explanation:
  • Step1: Factor out \(10^{3}\)
  • \((5.31 - 2.8)\times10^{3}\).
  • Step2: Calculate the difference of the coefficients
  • \(5.31-2.8 = 2.51\), so the result is \(2.51\times 10^{3}\).
  1. Subtraction of \((7.9\times 10^{6})-(7.42\times 10^{6})\):
  • Explanation:
  • Step1: Factor out \(10^{6}\)
  • \((7.9 - 7.42)\times10^{6}\).
  • Step2: Calculate the difference of the coefficients
  • \(7.9-7.42 = 0.48\), so the result is \(0.48\times 10^{6}\). Rewriting in proper scientific - notation, we get \(4.8\times 10^{5}\).
  1. Subtraction of \((8.3\times 10^{5})-(5.6\times 10^{4})\):
  • Explanation:
  • Step1: Make the exponents the same
  • Rewrite \(5.6\times 10^{4}\) as \(0.56\times 10^{5}\). Then \((8.3\times 10^{5})-(0.56\times 10^{5})=(8.3 - 0.56)\times10^{5}\).
  • Step2: Calculate the difference of the coefficients
  • \(8.3-0.56 = 7.74\), so the result is \(7.74\times 10^{5}\).
  1. Multiplication of \((4.1\times 10^{6})(2.4\times 10^{2})\):
  • Explanation:
  • Step1: Multiply the coefficients and add the exponents
  • \((4.1\times2.4)\times10^{6 + 2}\).
  • Step2: Calculate the product of the coefficients
  • \(4.1\times2.4 = 9.84\), so the result is \(9.84\times 10^{8}\).
  1. Multiplication of \((3.95\times 10^{8})(5.8\times 10^{3})\):
  • Explanation:
  • Step1: Multiply the coefficients and add the exponents
  • \((3.95\times5.8)\times10^{8 + 3}\).
  • Step2: Calculate the product of the coefficients
  • \(3.95\times5.8=22.91\). Rewrite \(22.91\) as \(2.291\times 10^{1}\). Then \((2.291\times 10^{1})\times10^{11}=2.291\times 10^{11}\).
  1. Multiplication of \((9.7\times 10^{8})(6\times 10^{11})\):
  • Explanation:
  • Step1: Multiply the coefficients and add the exponents
  • \((9.7\times6)\times10^{8 + 11}\).
  • Step2: Calculate the product of the coefficients
  • \(9.7\times6 = 58.2\). Rewrite \(58.2\) as \(5.82\times 10^{1}\). Then \((5.82\times 10^{1})\times10^{19}=5.82\times 10^{19}\).
  1. Division of \(\frac{7.4\times 10^{8}}{4\times 10^{3}}\):
  • Explanation:
  • **Step1: Divide the coefficients and subtract the exponen…

Answer:

  1. \(8.74\times 10^{5}\)
  2. \(1.631\times 10^{8}\)
  3. \(5.2\times 10^{9}\)
  4. \(2.51\times 10^{3}\)
  5. \(4.8\times 10^{5}\)
  6. \(7.74\times 10^{5}\)
  7. \(9.84\times 10^{8}\)
  8. \(2.291\times 10^{11}\)
  9. \(5.82\times 10^{19}\)
  10. \(1.85\times 10^{5}\)
  11. \(2\times 10^{8}\)
  12. \(4.8\times 10^{11}\)