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8th Grade Math Flashcards: Perform Operations With Scientific Notation

Study Perform Operations With Scientific Notation in 8th Grade Math with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

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What this deck covers

This deck focuses on Perform Operations With Scientific Notation, giving you a quick way to review the definitions, rules, and examples that matter most for 8th Grade Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

8th Grade Math Flashcards: Perform Operations With Scientific Notation

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QUESTION

What is (3.4×105)−(1.9×105)(3.4\times10^5)-(1.9\times10^5)(3.4×105)−(1.9×105) in scientific notation?

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ANSWER

1.5×1051.5\times10^51.5×105. Subtract coefficients when exponents are same: (3.4−1.9)×105(3.4-1.9)×10^5(3.4−1.9)×105.

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Flashcard 1: What is (3.4×105)−(1.9×105)(3.4\times10^5)-(1.9\times10^5)(3.4×105)−(1.9×105) in scientific notation?

Answer: 1.5×1051.5\times10^51.5×105. Subtract coefficients when exponents are same: (3.4−1.9)×105(3.4-1.9)×10^5(3.4−1.9)×105.

Flashcard 2: Which unit is most appropriate for seafloor spreading at about 0.03 m/yr0.03\ \text{m/yr}0.03 m/yr?

Answer: 30 mm/yr30\ \text{mm/yr}30 mm/yr. 0.03 m=30 mm0.03\ \text{m} = 30\ \text{mm}0.03 m=30 mm, appropriate for small measurements.

Flashcard 3: What does a calculator display of 1.23E51.23\text{E}51.23E5 mean in scientific notation?

Answer: 1.23×1051.23\times 10^51.23×105. E notation means "times 10 to the power of" the following number.

Flashcard 4: What is (7.2×105)−(3.2×105)(7.2\times 10^5)-(3.2\times 10^5)(7.2×105)−(3.2×105) in scientific notation?

Answer: 4.0×1054.0\times 10^54.0×105. Same powers, so subtract coefficients: 7.2−3.2=4.07.2-3.2=4.07.2−3.2=4.0.

Flashcard 5: What is (4.5×106)+(2.0×106)(4.5\times 10^6)+(2.0\times 10^6)(4.5×106)+(2.0×106) in scientific notation?

Answer: 6.5×1066.5\times 10^66.5×106. Same powers, so add coefficients: 4.5+2.0=6.54.5+2.0=6.54.5+2.0=6.5.

Flashcard 6: What is (8×107)÷(2×103)(8\times 10^7)\div(2\times 10^3)(8×107)÷(2×103) in scientific notation?

Answer: 4×1044\times 10^44×104. Divide coefficients (8÷2=4)(8÷2=4)(8÷2=4) and subtract exponents (7−3=4)(7-3=4)(7−3=4).

Flashcard 7: What is 6.0×103+2.5×1026.0\times 10^3+2.5\times 10^26.0×103+2.5×102 written in scientific notation?

Answer: 6.25×1036.25\times 10^36.25×103. 2.5×102=0.25×1032.5×10^2 = 0.25×10^32.5×102=0.25×103, then 6.0+0.25=6.256.0+0.25=6.256.0+0.25=6.25.

Flashcard 8: What is (2×104)(3×102)(2\times 10^4)(3\times 10^2)(2×104)(3×102) in scientific notation?

Answer: 6×1066\times 10^66×106. Multiply coefficients (2×3=6)(2×3=6)(2×3=6) and add exponents (4+2=6)(4+2=6)(4+2=6).

Flashcard 9: What is 6.1×10−36.1\times 10^{-3}6.1×10−3 written in standard decimal form?

Answer: 0.00610.00610.0061. Move decimal 3 places left: 6.1→0.00616.1 \rightarrow 0.00616.1→0.0061.

Flashcard 10: What is 3.4×1053.4\times 10^53.4×105 written in standard decimal form?

Answer: 340,000340{,}000340,000. Move decimal 5 places right: 3.4→340,0003.4 \rightarrow 340{,}0003.4→340,000.

Flashcard 11: What is 0.000720.000720.00072 written in scientific notation?

Answer: 7.2×10−47.2\times 10^{-4}7.2×10−4. Move decimal 4 places right to get 7.2, so multiply by 10−410^{-4}10−4.

Flashcard 12: What is 5,600,0005{,}600{,}0005,600,000 written in scientific notation?

Answer: 5.6×1065.6\times 10^65.6×106. Move decimal 6 places left to get 5.6, so multiply by 10610^6106.

Flashcard 13: What power of 101010 is used when you move a decimal point right kkk places?

Answer: Multiply by 10−k10^{-k}10−k. Moving right decreases the exponent by the number of places moved.

Flashcard 14: What power of 101010 is used when you move a decimal point left kkk places?

Answer: Multiply by 10k10^k10k. Moving left increases the exponent by the number of places moved.

Flashcard 15: What is the definition of scientific notation in standard form?

Answer: a×10na\times 10^na×10n where 1≤∣a∣<101\le |a|<101≤∣a∣<10 and nnn is an integer. The coefficient must be between 1 and 10, with an integer exponent.

Flashcard 16: What is 0.004×1060.004\times 10^60.004×106 written in scientific notation?

Answer: 4×1034\times 10^34×103. 0.004=4×10−30.004 = 4×10^{-3}0.004=4×10−3, so 4×10−3×106=4×1034×10^{-3}×10^6 = 4×10^34×10−3×106=4×103.

Flashcard 17: What is (9×10−2)÷(3×104)(9\times 10^{-2})\div(3\times 10^4)(9×10−2)÷(3×104) in scientific notation?

Answer: 3×10−63\times 10^{-6}3×10−6. (9÷3)×10−2−4=3×10−6(9÷3)×10^{-2-4} = 3×10^{-6}(9÷3)×10−2−4=3×10−6.

Flashcard 18: What is (3×108)(4×10−3)(3\times 10^8)(4\times 10^{-3})(3×108)(4×10−3) in scientific notation?

Answer: 1.2×1061.2\times 10^61.2×106. (3×4)×108+(−3)=12×105=1.2×106(3×4)×10^{8+(-3)} = 12×10^5 = 1.2×10^6(3×4)×108+(−3)=12×105=1.2×106.

Flashcard 19: What is 3.6×107−9×1063.6\times 10^7-9\times 10^63.6×107−9×106 written in scientific notation?

Answer: 2.7×1072.7\times 10^72.7×107. 9×106=0.9×1079×10^6 = 0.9×10^79×106=0.9×107, then 3.6−0.9=2.73.6-0.9=2.73.6−0.9=2.7.

Flashcard 20: What is (1.2×103)(5×102)(1.2\times 10^3)(5\times 10^2)(1.2×103)(5×102) in scientific notation?

Answer: 6×1056\times 10^56×105. (1.2×5)×103+2=6×105(1.2×5)×10^{3+2} = 6×10^5(1.2×5)×103+2=6×105.

Flashcard 21: What is (7.5×10−6)÷(2.5×10−2)(7.5\times 10^{-6})\div(2.5\times 10^{-2})(7.5×10−6)÷(2.5×10−2) in scientific notation?

Answer: 3×10−43\times 10^{-4}3×10−4. (7.5÷2.5)×10−6−(−2)=3×10−4(7.5÷2.5)×10^{-6-(-2)} = 3×10^{-4}(7.5÷2.5)×10−6−(−2)=3×10−4.

Flashcard 22: What is the number 0.09×1060.09\times 10^60.09×106 written in proper scientific notation?

Answer: 9×1049\times 10^49×104. Move decimal right: 0.09=9×10−20.09 = 9×10^{-2}0.09=9×10−2, so 0.09×106=9×1040.09×10^6 = 9×10^40.09×106=9×104.

Flashcard 23: What is the number 12×10312\times 10^312×103 written in proper scientific notation?

Answer: 1.2×1041.2\times 10^41.2×104. Move decimal left: 12=1.2×10112 = 1.2×10^112=1.2×101, so 12×103=1.2×10412×10^3 = 1.2×10^412×103=1.2×104.

Flashcard 24: What is (9×103)(7×10−2)(9\times 10^3)(7\times 10^{-2})(9×103)(7×10−2) in scientific notation?

Answer: 6.3×1026.3\times 10^26.3×102. (9×7)×103+(−2)=63×101=6.3×102(9×7)×10^{3+(-2)} = 63×10^1 = 6.3×10^2(9×7)×103+(−2)=63×101=6.3×102.

Flashcard 25: What is (0.0009)÷(3×10−4)(0.0009)\div(3\times 10^{-4})(0.0009)÷(3×10−4) in scientific notation?

Answer: 3×1003\times 10^03×100. (9×10−4)÷(3×10−4)=3×100=3(9×10^{-4})÷(3×10^{-4}) = 3×10^0 = 3(9×10−4)÷(3×10−4)=3×100=3.

Flashcard 26: What is (4×105)−(1.5×105)(4\times 10^5)-(1.5\times 10^5)(4×105)−(1.5×105) in scientific notation?

Answer: 2.5×1052.5\times 10^52.5×105. Same powers, so subtract coefficients: (4−1.5)×105(4-1.5)×10^5(4−1.5)×105.

Flashcard 27: What is (5×106)+(2×106)(5\times 10^6)+(2\times 10^6)(5×106)+(2×106) in scientific notation?

Answer: 7×1067\times 10^67×106. Same powers, so add coefficients: (5+2)×106(5+2)×10^6(5+2)×106.

Flashcard 28: What is the definition of scientific notation for a number?

Answer: a×10na\times 10^na×10n where 1≤∣a∣<101\le |a|<101≤∣a∣<10 and nnn is an integer. The coefficient must be between 1 and 10, with an integer exponent.

Flashcard 29: What is 4,500,0004{,}500{,}0004,500,000 written in scientific notation?

Answer: 4.5×1064.5\times 10^64.5×106. Move decimal 6 places left, so exponent is positive 6.

Flashcard 30: What is 6.3×1046.3\times 10^46.3×104 written in standard decimal form?

Answer: 63,00063{,}00063,000. Move decimal point 4 places right from 6.3.