This question tests operations with scientific notation: multiply/divide (apply to coefficients and exponents separately), add/subtract (adjust to same exponent first). Multiplication: (2×10³)×(4×10⁵)=(2×4)×10³⁺⁵=8×10⁸ (multiply coefficients, add exponents). Division: (6×10⁸)÷(2×10⁵)=(6÷2)×10⁸⁻⁵=3×10³ (divide coefficients, subtract exponents). Addition: requires same exponent—(3×10⁵)+(2×10⁴)=3×10⁵+0.2×10⁵=3.2×10⁵ (convert 2×10⁴ to 0.2×10⁵, then add); subtraction follows similarly. For this problem, subtract $9.1×10^8$ - $3.4×10^7$; convert $3.4×10^7$ to $0.34×10^8$, then 9.1 - 0.34 = $8.76×10^8$ bytes. This correct application adjusts for subtraction by aligning exponents. A common error is subtracting exponents instead of adjusting, like $10^{8-7}$$=10^1$, leading to wrong results. Steps: (1) identify operation as subtraction, (2) for ×/÷: not applicable, (3) for +/-: adjust to same exponent first (shift decimal), (4) verify proper form (1≤a<10, 8.76 is fine), (5) include units as bytes. Common errors: mixing operation rules (subtracting exponents for subtraction like division), forgetting adjustment (coefficients outside 1-10 range), wrong exponent arithmetic.

This question tests operations with scientific notation: multiply/divide (apply to coefficients and exponents separately), add/subtract (adjust to same exponent first). Multiplication: (2×10³)×(4×10⁵)=(2×4)×10³⁺⁵=8×10⁸ (multiply coefficients, add exponents). Division: (6×10⁸)÷(2×10⁵)=(6÷2)×10⁸⁻⁵=3×10³ (divide coefficients, subtract exponents). Addition: requires same exponent—(3×10⁵)+(2×10⁴)=3×10⁵+0.2×10⁵=3.2×10⁵ (convert 2×10⁴ to 0.2×10⁵, then add). Here, add $6.0×10^6$ and $4.0×10^5$: convert $4.0×10^5$ to $0.4×10^6$, then 6.0 + 0.4 = $6.4×10^6$. This correct application adjusts the smaller exponent by moving the decimal left and increasing the exponent. A common error is adding without adjustment, like 6.0 + 4.0 = $10.0×10^{11}$ or similar mismatch. Steps: (1) identify addition, (2) for +/-: adjust to same exponent first (shift decimal), (3) verify proper form (6.4 is between 1-10), (4) units are meters but not needed in answer. Common errors: forgetting adjustment, leading to wrong exponent, or wrong arithmetic on coefficients.

This question tests operations with scientific notation: multiply/divide (apply to coefficients and exponents separately), add/subtract (adjust to same exponent first). Multiplication: (2×10³)×(4×10⁵)=(2×4)×10³⁺⁵=8×10⁸ (multiply coefficients, add exponents). Division: (6×10⁸)÷(2×10⁵)=(6÷2)×10⁸⁻⁵=3×10³ (divide coefficients, subtract exponents). Addition: requires same exponent—(3×10⁵)+(2×10⁴)=3×10⁵+0.2×10⁵=3.2×10⁵ (convert 2×10⁴ to 0.2×10⁵, then add). For this problem, first convert 0.0045 to $4.5×10^{-3}$, then add to $3.2×10^{-3}$, so (4.5 + 3.2) × $10^{-3}$ = 7.7 × $10^{-3}$. This correct application gives the total length in scientific notation as $7.7×10^{-3}$ meters. A common error is adding without converting to scientific notation first. Steps: (1) identify operation as addition, (2) for +/-: adjust to same exponent first (already same), (3) add coefficients, (4) verify proper form (1≤a<10, adjust if needed), (5) include units like meters. Common errors: mixing operation rules (adding exponents for addition), forgetting adjustment (coefficients outside 1-10 range), wrong exponent arithmetic.

This question tests operations with scientific notation: multiply/divide (apply to coefficients and exponents separately), add/subtract (adjust to same exponent first). Multiplication: (2×10³)×(4×10⁵)=(2×4)×10³⁺⁵=8×10⁸ (multiply coefficients, add exponents). Division: (6×10⁸)÷(2×10⁵)=(6÷2)×10⁸⁻⁵=3×10³ (divide coefficients, subtract exponents). Addition: requires same exponent—(3×10⁵)+(2×10⁴)=3×10⁵+0.2×10⁵=3.2×10⁵ (convert 2×10⁴ to 0.2×10⁵, then add). Here, add 0.0045 $(4.5×10^{-3}$) and $3.2×10^{-3}$: exponents match, 4.5 + 3.2 = $7.7×10^{-3}$. This correct application converts decimal to scientific notation first. A common error is adding without converting, treating as regular decimals incorrectly. Steps: (1) identify addition, (2) for +/-: adjust to same exponent (done by converting), (3) verify proper form (7.7 is fine), (4) units in meters. Common errors: not handling negative exponents properly, or coefficient sum outside 1-10 without adjustment.

This question tests operations with scientific notation: multiply/divide (apply to coefficients and exponents separately), add/subtract (adjust to same exponent first). Multiplication: (2×10³)×(4×10⁵)=(2×4)×10³⁺⁵=8×10⁸ (multiply coefficients, add exponents). Division: (6×10⁸)÷(2×10⁵)=(6÷2)×10⁸⁻⁵=3×10³ (divide coefficients, subtract exponents). Addition: requires same exponent—(3×10⁵)+(2×10⁴)=3×10⁵+0.2×10⁵=3.2×10⁵ (convert 2×10⁴ to 0.2×10⁵, then add). For this problem, multiply $1.5×10^3$ by $3×10^{-2}$, so (1.5 × 3) × 10^(3-2) = 4.5 × $10^1$. This correct application gives the product in scientific notation as $4.5×10^1$. A common error is adding exponents instead of subtracting the negative one. Steps: (1) identify operation as multiplication, (2) for ×/÷: coefficients and exponents separately, (3) multiply coefficients and add exponents (including negatives), (4) verify proper form (1≤a<10, here it's fine), (5) no units here. Common errors: mixing operation rules (adding exponents for addition), forgetting adjustment (coefficients outside 1-10 range), wrong exponent arithmetic.

This question tests operations with scientific notation: multiply/divide (apply to coefficients and exponents separately), add/subtract (adjust to same exponent first). Multiplication: (2×10³)×(4×10⁵)=(2×4)×10³⁺⁵=8×10⁸ (multiply coefficients, add exponents). Division: (6×10⁸)÷(2×10⁵)=(6÷2)×10⁸⁻⁵=3×10³ (divide coefficients, subtract exponents). Addition: requires same exponent—(3×10⁵)+(2×10⁴)=3×10⁵+0.2×10⁵=3.2×10⁵ (convert 2×10⁴ to 0.2×10⁵, then add). Here, add $3.6×10^5$ and $4.9×10^5$: since exponents match, sum coefficients 3.6 + 4.9 = 8.5, so $8.5×10^5$. This correct application gives the total bacteria count directly without adjustment. A common error is adding exponents like in multiplication, yielding $8.5×10^{10}$. Steps: (1) identify addition, (2) for +/-: adjust to same exponent first (not needed here), (3) verify proper form (1≤a<10, 8.5 is fine), (4) no units given. Common errors: mixing rules by adding exponents, or not converting if exponents differed.

This question tests operations with scientific notation: multiply/divide (apply to coefficients and exponents separately), add/subtract (adjust to same exponent first). Multiplication: $(2\times10^3)\times(4\times10^5)=(2\times4)\times10^{3+5}=8\times10^8$ (multiply coefficients, add exponents). Division: $(6\times10^8)\div(2\times10^5)=(6\div2)\times10^{8-5}=3\times10^3$ (divide coefficients, subtract exponents). Addition: requires same exponent—$(3\times10^5)+(2\times10^4)=3\times10^5+0.2\times10^5=3.2\times10^5$ (convert $2\times10^4$ to $0.2\times10^5$, then add). For this problem, compute numerator $(4.8\times10^7)(2.5\times10^{-3}) = 1.2\times10^5$, then divide by $6\times10^2$ to get $2.0\times10^2$. This correct application simplifies the expression in scientific notation as $2.0\times10^2$. A common error is mishandling the exponents in combined operations. Steps: (1) identify operations as multiplication then division, (2) for $\times$/÷: coefficients and exponents separately, (3) handle numerator first, then divide, (4) verify proper form ($1\leq a<10$, adjust if needed), (5) no units here. Common errors: mixing operation rules (adding exponents for addition), forgetting adjustment (coefficients outside 1-10 range), wrong exponent arithmetic.

This question tests operations with scientific notation: multiply/divide (apply to coefficients and exponents separately), add/subtract (adjust to same exponent first). Multiplication: (2×10³)×(4×10⁵)=(2×4)×10³⁺⁵=8×10⁸ (multiply coefficients, add exponents). Division: (6×10⁸)÷(2×10⁵)=(6÷2)×10⁸⁻⁵=3×10³ (divide coefficients, subtract exponents). Addition: requires same exponent—(3×10⁵)+(2×10⁴)=3×10⁵+0.2×10⁵=3.2×10⁵ (convert 2×10⁴ to 0.2×10⁵, then add). For this problem, add $6.0×10^6$ and $4.0×10^5$; convert $4.0×10^5$ to $0.4×10^6$, then sum: 6.0 + 0.4 = $6.4×10^6$ cm. This correct application involves adjusting the smaller exponent by moving the decimal left and increasing the exponent. A common error is adding without adjustment, like 6.0 + 4.0 = $10.0×10^{something}$, but that ignores exponents. Steps: (1) identify operation as addition, (2) for ×/÷: not applicable, (3) for +/-: adjust to same exponent first (shift decimal), (4) verify proper form (1≤a<10, 6.4 is fine), (5) include units if given, here cm but not in final answer. Common errors: mixing operation rules (adding exponents for addition), forgetting adjustment (coefficients outside 1-10 range), wrong exponent arithmetic.

This question tests operations with scientific notation: multiply/divide (apply to coefficients and exponents separately), add/subtract (adjust to same exponent first). Multiplication: (2×10³)×(4×10⁵)=(2×4)×10³⁺⁵=8×10⁸ (multiply coefficients, add exponents). Division: (6×10⁸)÷(2×10⁵)=(6÷2)×10⁸⁻⁵=3×10³ (divide coefficients, subtract exponents). Addition: requires same exponent—(3×10⁵)+(2×10⁴)=3×10⁵+0.2×10⁵=3.2×10⁵ (convert 2×10⁴ to 0.2×10⁵, then add). For this problem, divide $6×10^8$ by $2×10^5$, so (6 ÷ 2) × 10^(8-5) = 3 × $10^3$. This correct application estimates cells per square in scientific notation as $3×10^3$. A common error is adding exponents instead of subtracting for division. Steps: (1) identify operation as division, (2) for ×/÷: coefficients and exponents separately, (3) divide coefficients and subtract exponents, (4) verify proper form (1≤a<10, here it's fine), (5) no units specified. Common errors: mixing operation rules (adding exponents for addition), forgetting adjustment (coefficients outside 1-10 range), wrong exponent arithmetic.

This question tests operations with scientific notation: multiply/divide (apply to coefficients and exponents separately), add/subtract (adjust to same exponent first). Multiplication: (2×10³)×(4×10⁵)=(2×4)×10³⁺⁵=8×10⁸ (multiply coefficients, add exponents). Division: (6×10⁸)÷(2×10⁵)=(6÷2)×10⁸⁻⁵=3×10³ (divide coefficients, subtract exponents). Addition: requires same exponent—(3×10⁵)+(2×10⁴)=3×10⁵+0.2×10⁵=3.2×10⁵ (convert 2×10⁴ to 0.2×10⁵, then add). For this problem, multiply $1.2×10^2$ by $3.5×10^1$, so (1.2 × 3.5) × 10^(2+1) = 4.2 × $10^3$. This correct application gives the total distance in scientific notation as $4.2×10^3$ meters. A common error is subtracting exponents instead of adding for multiplication. Steps: (1) identify operation as multiplication, (2) for ×/÷: coefficients and exponents separately, (3) multiply coefficients and add exponents, (4) verify proper form (1≤a<10, here it's fine), (5) include units like meters. Common errors: mixing operation rules (adding exponents for addition), forgetting adjustment (coefficients outside 1-10 range), wrong exponent arithmetic.