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QuestionMultiply. Write in scientific notation, and then write the result in standard forn 1.4.1) (−3.4×10−7)×(8.4×105)=\left(-3.4 \times 10^{-7}\right) \times\left(8.4 \times 10^{5}\right)= 1.4.2) (70×10−4)×(60×106)=\left(70 \times 10^{-4}\right) \times\left(60 \times 10^{6}\right)=
Divide. Write in scientific notation, and then write the result in standard form. 1.4.3) 4.10×10−2(−2.05×104)=\frac{4.10 \times 10^{-2}}{\left(-2.05 \times 10^{4}\right)}= 1.4.4) 1.14×1073.8×10−3=\frac{1.14 \times 10^{7}}{3.8 \times 10^{-3}}=

Studdy Solution

STEP 1

1. The expressions involve multiplication and division of numbers expressed in scientific notation.
2. Scientific notation follows the form a×10ba \times 10^b, where aa is a real number (the significand) and bb is an integer (the exponent).
3. When multiplying numbers in scientific notation, we multiply the significands and add the exponents.
4. When dividing numbers in scientific notation, we divide the significands and subtract the exponents.
5. The final results should be expressed in both scientific notation and standard form.

STEP 2

1. Multiply the given numbers in scientific notation and express the result in scientific notation.
2. Convert the result from scientific notation to standard form.
3. Divide the given numbers in scientific notation and express the result in scientific notation.
4. Convert the result from scientific notation to standard form.

STEP 3

Multiply the significands and add the exponents for (−3.4×10−7)×(8.4×105)\left(-3.4 \times 10^{-7}\right) \times \left(8.4 \times 10^{5}\right).
(−3.4×8.4)×(10−7+5)=−28.56×10−2 \left(-3.4 \times 8.4\right) \times \left(10^{-7 + 5}\right) = -28.56 \times 10^{-2}

STEP 4

Convert −28.56×10−2-28.56 \times 10^{-2} to proper scientific notation.
−28.56×10−2=−2.856×101×10−2=−2.856×10−1 -28.56 \times 10^{-2} = -2.856 \times 10^{1} \times 10^{-2} = -2.856 \times 10^{-1}

STEP 5

Convert −2.856×10−1-2.856 \times 10^{-1} to standard form.
−2.856×10−1=−0.2856 -2.856 \times 10^{-1} = -0.2856

STEP 6

Multiply the significands and add the exponents for (70×10−4)×(60×106)\left(70 \times 10^{-4}\right) \times \left(60 \times 10^{6}\right).
(70×60)×(10−4+6)=4200×102 \left(70 \times 60\right) \times \left(10^{-4 + 6}\right) = 4200 \times 10^{2}

STEP 7

Convert 4200×1024200 \times 10^{2} to proper scientific notation.
4200×102=4.2×103×102=4.2×105 4200 \times 10^{2} = 4.2 \times 10^{3} \times 10^{2} = 4.2 \times 10^{5}

STEP 8

Convert 4.2×1054.2 \times 10^{5} to standard form.
4.2×105=420000 4.2 \times 10^{5} = 420000

STEP 9

Divide the significands and subtract the exponents for 4.10×10−2(−2.05×104)\frac{4.10 \times 10^{-2}}{\left(-2.05 \times 10^{4}\right)}.
4.10−2.05×10−2−4=−2×10−6 \frac{4.10}{-2.05} \times 10^{-2 - 4} = -2 \times 10^{-6}

STEP 10

Convert −2×10−6-2 \times 10^{-6} to standard form.
−2×10−6=−0.000002 -2 \times 10^{-6} = -0.000002

STEP 11

Divide the significands and subtract the exponents for 1.14×1073.8×10−3\frac{1.14 \times 10^{7}}{3.8 \times 10^{-3}}.
1.143.8×107−(−3)=0.3×1010 \frac{1.14}{3.8} \times 10^{7 - (-3)} = 0.3 \times 10^{10}

STEP 12

Convert 0.3×10100.3 \times 10^{10} to proper scientific notation and standard form.
0.3×1010=3×10−1×1010=3×109 0.3 \times 10^{10} = 3 \times 10^{-1} \times 10^{10} = 3 \times 10^{9}
3×109=3000000000 3 \times 10^{9} = 3000000000
Solution: 1.4.1) Scientific notation: −2.856×10−1-2.856 \times 10^{-1}, Standard form: −0.2856-0.2856.
1.4.2) Scientific notation: 4.2×1054.2 \times 10^{5}, Standard form: 420000420000.
1.4.3) Scientific notation: −2×10−6-2 \times 10^{-6}, Standard form: −0.000002-0.000002.
1.4.4) Scientific notation: 3×1093 \times 10^{9}, Standard form: 30000000003000000000.

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