Perform Operations With Scientific Notation - 8th Grade Math
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What is $(3.4\times10^5)-(1.9\times10^5)$ in scientific notation?
What is $(3.4\times10^5)-(1.9\times10^5)$ in scientific notation?
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$1.5\times10^5$. Subtract coefficients when exponents are same: $(3.4-1.9)×10^5$.
$1.5\times10^5$. Subtract coefficients when exponents are same: $(3.4-1.9)×10^5$.
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Which unit is most appropriate for seafloor spreading at about $0.03\ \text{m/yr}$?
Which unit is most appropriate for seafloor spreading at about $0.03\ \text{m/yr}$?
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$30\ \text{mm/yr}$. $0.03\ \text{m} = 30\ \text{mm}$, appropriate for small measurements.
$30\ \text{mm/yr}$. $0.03\ \text{m} = 30\ \text{mm}$, appropriate for small measurements.
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What does a calculator display of $1.23\text{E}5$ mean in scientific notation?
What does a calculator display of $1.23\text{E}5$ mean in scientific notation?
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$1.23\times 10^5$. E notation means "times 10 to the power of" the following number.
$1.23\times 10^5$. E notation means "times 10 to the power of" the following number.
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What is $(7.2\times 10^5)-(3.2\times 10^5)$ in scientific notation?
What is $(7.2\times 10^5)-(3.2\times 10^5)$ in scientific notation?
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$4.0\times 10^5$. Same powers, so subtract coefficients: $7.2-3.2=4.0$.
$4.0\times 10^5$. Same powers, so subtract coefficients: $7.2-3.2=4.0$.
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What is $(4.5\times 10^6)+(2.0\times 10^6)$ in scientific notation?
What is $(4.5\times 10^6)+(2.0\times 10^6)$ in scientific notation?
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$6.5\times 10^6$. Same powers, so add coefficients: $4.5+2.0=6.5$.
$6.5\times 10^6$. Same powers, so add coefficients: $4.5+2.0=6.5$.
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What is $(8\times 10^7)\div(2\times 10^3)$ in scientific notation?
What is $(8\times 10^7)\div(2\times 10^3)$ in scientific notation?
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$4\times 10^4$. Divide coefficients $(8÷2=4)$ and subtract exponents $(7-3=4)$.
$4\times 10^4$. Divide coefficients $(8÷2=4)$ and subtract exponents $(7-3=4)$.
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What is $6.0\times 10^3+2.5\times 10^2$ written in scientific notation?
What is $6.0\times 10^3+2.5\times 10^2$ written in scientific notation?
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$6.25\times 10^3$. $2.5×10^2 = 0.25×10^3$, then $6.0+0.25=6.25$.
$6.25\times 10^3$. $2.5×10^2 = 0.25×10^3$, then $6.0+0.25=6.25$.
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What is $(2\times 10^4)(3\times 10^2)$ in scientific notation?
What is $(2\times 10^4)(3\times 10^2)$ in scientific notation?
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$6\times 10^6$. Multiply coefficients $(2×3=6)$ and add exponents $(4+2=6)$.
$6\times 10^6$. Multiply coefficients $(2×3=6)$ and add exponents $(4+2=6)$.
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What is $6.1\times 10^{-3}$ written in standard decimal form?
What is $6.1\times 10^{-3}$ written in standard decimal form?
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$0.0061$. Move decimal 3 places left: $6.1 \rightarrow 0.0061$.
$0.0061$. Move decimal 3 places left: $6.1 \rightarrow 0.0061$.
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What is $3.4\times 10^5$ written in standard decimal form?
What is $3.4\times 10^5$ written in standard decimal form?
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$340{,}000$. Move decimal 5 places right: $3.4 \rightarrow 340{,}000$.
$340{,}000$. Move decimal 5 places right: $3.4 \rightarrow 340{,}000$.
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What is $0.00072$ written in scientific notation?
What is $0.00072$ written in scientific notation?
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$7.2\times 10^{-4}$. Move decimal 4 places right to get 7.2, so multiply by $10^{-4}$.
$7.2\times 10^{-4}$. Move decimal 4 places right to get 7.2, so multiply by $10^{-4}$.
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What is $5{,}600{,}000$ written in scientific notation?
What is $5{,}600{,}000$ written in scientific notation?
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$5.6\times 10^6$. Move decimal 6 places left to get 5.6, so multiply by $10^6$.
$5.6\times 10^6$. Move decimal 6 places left to get 5.6, so multiply by $10^6$.
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What power of $10$ is used when you move a decimal point right $k$ places?
What power of $10$ is used when you move a decimal point right $k$ places?
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Multiply by $10^{-k}$. Moving right decreases the exponent by the number of places moved.
Multiply by $10^{-k}$. Moving right decreases the exponent by the number of places moved.
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What power of $10$ is used when you move a decimal point left $k$ places?
What power of $10$ is used when you move a decimal point left $k$ places?
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Multiply by $10^k$. Moving left increases the exponent by the number of places moved.
Multiply by $10^k$. Moving left increases the exponent by the number of places moved.
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What is the definition of scientific notation in standard form?
What is the definition of scientific notation in standard form?
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$a\times 10^n$ where $1\le |a|<10$ and $n$ is an integer. The coefficient must be between 1 and 10, with an integer exponent.
$a\times 10^n$ where $1\le |a|<10$ and $n$ is an integer. The coefficient must be between 1 and 10, with an integer exponent.
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What is $0.004\times 10^6$ written in scientific notation?
What is $0.004\times 10^6$ written in scientific notation?
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$4\times 10^3$. $0.004 = 4×10^{-3}$, so $4×10^{-3}×10^6 = 4×10^3$.
$4\times 10^3$. $0.004 = 4×10^{-3}$, so $4×10^{-3}×10^6 = 4×10^3$.
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What is $(9\times 10^{-2})\div(3\times 10^4)$ in scientific notation?
What is $(9\times 10^{-2})\div(3\times 10^4)$ in scientific notation?
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$3\times 10^{-6}$. $(9÷3)×10^{-2-4} = 3×10^{-6}$.
$3\times 10^{-6}$. $(9÷3)×10^{-2-4} = 3×10^{-6}$.
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What is $(3\times 10^8)(4\times 10^{-3})$ in scientific notation?
What is $(3\times 10^8)(4\times 10^{-3})$ in scientific notation?
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$1.2\times 10^6$. $(3×4)×10^{8+(-3)} = 12×10^5 = 1.2×10^6$.
$1.2\times 10^6$. $(3×4)×10^{8+(-3)} = 12×10^5 = 1.2×10^6$.
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What is $3.6\times 10^7-9\times 10^6$ written in scientific notation?
What is $3.6\times 10^7-9\times 10^6$ written in scientific notation?
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$2.7\times 10^7$. $9×10^6 = 0.9×10^7$, then $3.6-0.9=2.7$.
$2.7\times 10^7$. $9×10^6 = 0.9×10^7$, then $3.6-0.9=2.7$.
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What is $(1.2\times 10^3)(5\times 10^2)$ in scientific notation?
What is $(1.2\times 10^3)(5\times 10^2)$ in scientific notation?
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$6\times 10^5$. $(1.2×5)×10^{3+2} = 6×10^5$.
$6\times 10^5$. $(1.2×5)×10^{3+2} = 6×10^5$.
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What is $(7.5\times 10^{-6})\div(2.5\times 10^{-2})$ in scientific notation?
What is $(7.5\times 10^{-6})\div(2.5\times 10^{-2})$ in scientific notation?
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$3\times 10^{-4}$. $(7.5÷2.5)×10^{-6-(-2)} = 3×10^{-4}$.
$3\times 10^{-4}$. $(7.5÷2.5)×10^{-6-(-2)} = 3×10^{-4}$.
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What is the number $0.09\times 10^6$ written in proper scientific notation?
What is the number $0.09\times 10^6$ written in proper scientific notation?
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$9\times 10^4$. Move decimal right: $0.09 = 9×10^{-2}$, so $0.09×10^6 = 9×10^4$.
$9\times 10^4$. Move decimal right: $0.09 = 9×10^{-2}$, so $0.09×10^6 = 9×10^4$.
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What is the number $12\times 10^3$ written in proper scientific notation?
What is the number $12\times 10^3$ written in proper scientific notation?
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$1.2\times 10^4$. Move decimal left: $12 = 1.2×10^1$, so $12×10^3 = 1.2×10^4$.
$1.2\times 10^4$. Move decimal left: $12 = 1.2×10^1$, so $12×10^3 = 1.2×10^4$.
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What is $(9\times 10^3)(7\times 10^{-2})$ in scientific notation?
What is $(9\times 10^3)(7\times 10^{-2})$ in scientific notation?
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$6.3\times 10^2$. $(9×7)×10^{3+(-2)} = 63×10^1 = 6.3×10^2$.
$6.3\times 10^2$. $(9×7)×10^{3+(-2)} = 63×10^1 = 6.3×10^2$.
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What is $(0.0009)\div(3\times 10^{-4})$ in scientific notation?
What is $(0.0009)\div(3\times 10^{-4})$ in scientific notation?
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$3\times 10^0$. $(9×10^{-4})÷(3×10^{-4}) = 3×10^0 = 3$.
$3\times 10^0$. $(9×10^{-4})÷(3×10^{-4}) = 3×10^0 = 3$.
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What is $(4\times 10^5)-(1.5\times 10^5)$ in scientific notation?
What is $(4\times 10^5)-(1.5\times 10^5)$ in scientific notation?
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$2.5\times 10^5$. Same powers, so subtract coefficients: $(4-1.5)×10^5$.
$2.5\times 10^5$. Same powers, so subtract coefficients: $(4-1.5)×10^5$.
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What is $(5\times 10^6)+(2\times 10^6)$ in scientific notation?
What is $(5\times 10^6)+(2\times 10^6)$ in scientific notation?
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$7\times 10^6$. Same powers, so add coefficients: $(5+2)×10^6$.
$7\times 10^6$. Same powers, so add coefficients: $(5+2)×10^6$.
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What is the definition of scientific notation for a number?
What is the definition of scientific notation for a number?
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$a\times 10^n$ where $1\le |a|<10$ and $n$ is an integer. The coefficient must be between 1 and 10, with an integer exponent.
$a\times 10^n$ where $1\le |a|<10$ and $n$ is an integer. The coefficient must be between 1 and 10, with an integer exponent.
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What is $4{,}500{,}000$ written in scientific notation?
What is $4{,}500{,}000$ written in scientific notation?
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$4.5\times 10^6$. Move decimal 6 places left, so exponent is positive 6.
$4.5\times 10^6$. Move decimal 6 places left, so exponent is positive 6.
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What is $6.3\times 10^4$ written in standard decimal form?
What is $6.3\times 10^4$ written in standard decimal form?
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$63{,}000$. Move decimal point 4 places right from 6.3.
$63{,}000$. Move decimal point 4 places right from 6.3.
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