The image contains a series of multiplication and division problems involving numbers in scientific notation. I am asked to solve each of them.

ArithmeticScientific NotationExponentsMultiplicationDivision
2025/4/8

1. Problem Description

The image contains a series of multiplication and division problems involving numbers in scientific notation. I am asked to solve each of them.

2. Solution Steps

1. $(1.8 \times 10^6) \times (3.5 \times 10^3)$

Multiply the coefficients and add the exponents:
(1.8×3.5)×(106+3)=6.3×109(1.8 \times 3.5) \times (10^{6+3}) = 6.3 \times 10^9

2. $(4.2 \times 10^6) \div (3 \times 10^3)$

Divide the coefficients and subtract the exponents:
(4.2÷3)×(1063)=1.4×103(4.2 \div 3) \times (10^{6-3}) = 1.4 \times 10^3

3. $(3.08 \times 10^5) \times (2.5 \times 10^{-11})$

Multiply the coefficients and add the exponents:
(3.08×2.5)×(105+(11))=7.7×106(3.08 \times 2.5) \times (10^{5 + (-11)}) = 7.7 \times 10^{-6}

4. $(5.5 \times 10^7) \times (4 \times 10^{10})$

Multiply the coefficients and add the exponents:
(5.5×4)×(107+10)=22×1017=2.2×1018(5.5 \times 4) \times (10^{7+10}) = 22 \times 10^{17} = 2.2 \times 10^{18}

5. $(1.7 \times 10^{-4}) \div (8 \times 10^{-7})$

Divide the coefficients and subtract the exponents:
(1.7÷8)×(104(7))=0.2125×103=2.125×102(1.7 \div 8) \times (10^{-4 - (-7)}) = 0.2125 \times 10^{3} = 2.125 \times 10^2

6. $(9.3 \times 10^{-3}) \times (1.9 \times 10^{-9})$

Multiply the coefficients and add the exponents:
(9.3×1.9)×(103+(9))=17.67×1012=1.767×1011(9.3 \times 1.9) \times (10^{-3+(-9)}) = 17.67 \times 10^{-12} = 1.767 \times 10^{-11}

7. $(9.6 \times 10^8) \div (4 \times 10^{13})$

Divide the coefficients and subtract the exponents:
(9.6÷4)×(10813)=2.4×105(9.6 \div 4) \times (10^{8-13}) = 2.4 \times 10^{-5}

8. $(4.7 \times 10^{-6}) \times (2.1 \times 10^9)$

Multiply the coefficients and add the exponents:
(4.7×2.1)×(106+9)=9.87×103(4.7 \times 2.1) \times (10^{-6+9}) = 9.87 \times 10^3

9. $(9.2 \times 10^7) \div (4 \times 10^{-9})$

Divide the coefficients and subtract the exponents:
(9.2÷4)×(107(9))=2.3×1016(9.2 \div 4) \times (10^{7-(-9)}) = 2.3 \times 10^{16}
1

0. $(6 \times 10^{13}) \div (8 \times 10^4)$

Divide the coefficients and subtract the exponents:
(6÷8)×(10134)=0.75×109=7.5×108(6 \div 8) \times (10^{13-4}) = 0.75 \times 10^9 = 7.5 \times 10^8
1

1. $(6.4 \times 10^9) \times (8.2 \times 10^{-2})$

Multiply the coefficients and add the exponents:
(6.4×8.2)×(109+(2))=52.48×107=5.248×108(6.4 \times 8.2) \times (10^{9+(-2)}) = 52.48 \times 10^7 = 5.248 \times 10^8
1

2. $(1.302 \times 10^8) \div (3.1 \times 10^{15})$

Divide the coefficients and subtract the exponents:
(1.302÷3.1)×(10815)=0.42×107=4.2×108(1.302 \div 3.1) \times (10^{8-15}) = 0.42 \times 10^{-7} = 4.2 \times 10^{-8}

3. Final Answer

1. $6.3 \times 10^9$

2. $1.4 \times 10^3$

3. $7.7 \times 10^{-6}$

4. $2.2 \times 10^{18}$

5. $2.125 \times 10^2$

6. $1.767 \times 10^{-11}$

7. $2.4 \times 10^{-5}$

8. $9.87 \times 10^3$

9. $2.3 \times 10^{16}$

1

0. $7.5 \times 10^8$

1

1. $5.248 \times 10^8$

1

2. $4.2 \times 10^{-8}$