Reason About Scale - Middle School Earth and Space Science
Card 1 of 25
Identify the larger scale: $1:25{,}000$ or $1:250{,}000$.
Identify the larger scale: $1:25{,}000$ or $1:250{,}000$.
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$1:25{,}000$. Smaller denominators mean larger scales (more detail shown).
$1:25{,}000$. Smaller denominators mean larger scales (more detail shown).
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Identify the correct conversion: how many centimeters are in $2\text{ km}$?
Identify the correct conversion: how many centimeters are in $2\text{ km}$?
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$200{,}000\text{ cm}$. $2$ km $\times 1000$ m/km $\times 100$ cm/m = $200{,}000$ cm.
$200{,}000\text{ cm}$. $2$ km $\times 1000$ m/km $\times 100$ cm/m = $200{,}000$ cm.
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What is the scale ratio $1:n$ if $1\text{ cm}$ on the map represents $5\text{ km}$ in reality?
What is the scale ratio $1:n$ if $1\text{ cm}$ on the map represents $5\text{ km}$ in reality?
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$1:500{,}000$. $5$ km = $500{,}000$ cm, so scale is $1:500{,}000$.
$1:500{,}000$. $5$ km = $500{,}000$ cm, so scale is $1:500{,}000$.
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Which option best describes a scale factor greater than $1$ applied to a drawing?
Which option best describes a scale factor greater than $1$ applied to a drawing?
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An enlargement (the drawing is larger than the original). Scale factor >1 means the image is larger than the original object.
An enlargement (the drawing is larger than the original). Scale factor >1 means the image is larger than the original object.
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What is the unit conversion for $1\text{ light-year}$ into kilometers (approximate)?
What is the unit conversion for $1\text{ light-year}$ into kilometers (approximate)?
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$1\text{ ly} \approx 9.46\times 10^{12}\text{ km}$. Light travels this distance in one year.
$1\text{ ly} \approx 9.46\times 10^{12}\text{ km}$. Light travels this distance in one year.
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What is the scale model distance if $1\text{ AU}$ is represented by $10\text{ cm}$ and Earth to Sun is $1\text{ AU}$?
What is the scale model distance if $1\text{ AU}$ is represented by $10\text{ cm}$ and Earth to Sun is $1\text{ AU}$?
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$10\text{ cm}$. Earth is $1\text{ AU}$ from Sun, so $1 \times 10\text{ cm} = 10\text{ cm}$.
$10\text{ cm}$. Earth is $1\text{ AU}$ from Sun, so $1 \times 10\text{ cm} = 10\text{ cm}$.
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Identify the correct scientific notation: $450{,}000{,}000\text{ km}$ written in scientific notation.
Identify the correct scientific notation: $450{,}000{,}000\text{ km}$ written in scientific notation.
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$4.5\times 10^8\text{ km}$. Move decimal 8 places: $450{,}000{,}000 = 4.5 \times 10^8$.
$4.5\times 10^8\text{ km}$. Move decimal 8 places: $450{,}000{,}000 = 4.5 \times 10^8$.
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What is the scale model distance if $1\text{ AU}$ is $10\text{ cm}$ and Jupiter is $5.2\text{ AU}$ from the Sun?
What is the scale model distance if $1\text{ AU}$ is $10\text{ cm}$ and Jupiter is $5.2\text{ AU}$ from the Sun?
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$52\text{ cm}$. $5.2\text{ AU} \times 10\text{ cm/AU} = 52\text{ cm}$.
$52\text{ cm}$. $5.2\text{ AU} \times 10\text{ cm/AU} = 52\text{ cm}$.
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Which object is larger in diameter: Earth at $1.27\times 10^4\text{ km}$ or the Moon at $3.47\times 10^3\text{ km}$?
Which object is larger in diameter: Earth at $1.27\times 10^4\text{ km}$ or the Moon at $3.47\times 10^3\text{ km}$?
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Earth. $1.27 \times 10^4 > 3.47 \times 10^3$ (compare exponents first).
Earth. $1.27 \times 10^4 > 3.47 \times 10^3$ (compare exponents first).
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What is the formula to find map distance from real distance using scale factor $S$?
What is the formula to find map distance from real distance using scale factor $S$?
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$d_{map} = \frac{d_{real}}{S}$. Divide real distance by scale to get map distance.
$d_{map} = \frac{d_{real}}{S}$. Divide real distance by scale to get map distance.
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What is the scale factor from a map to reality for a scale of $1:50{,}000$?
What is the scale factor from a map to reality for a scale of $1:50{,}000$?
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Multiply map distances by $50{,}000$. Each map unit represents $50{,}000$ real units.
Multiply map distances by $50{,}000$. Each map unit represents $50{,}000$ real units.
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What is the real distance in meters if the model distance is $15\text{ cm}$ at a scale of $1:500$?
What is the real distance in meters if the model distance is $15\text{ cm}$ at a scale of $1:500$?
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$75\text{ m}$. $15$ cm $\times 500 = 7{,}500$ cm = $75$ m.
$75\text{ m}$. $15$ cm $\times 500 = 7{,}500$ cm = $75$ m.
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What does a map scale of $1:50{,}000$ mean for map distance versus real distance?
What does a map scale of $1:50{,}000$ mean for map distance versus real distance?
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1 unit on the map represents $50{,}000$ of the same units in reality. The ratio shows how many real-world units equal one map unit.
1 unit on the map represents $50{,}000$ of the same units in reality. The ratio shows how many real-world units equal one map unit.
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What is the scale factor from a model to the real object if the model is $1:200$?
What is the scale factor from a model to the real object if the model is $1:200$?
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Scale factor (model to real) is $200$. The denominator in $1:n$ gives the scale factor from model to real.
Scale factor (model to real) is $200$. The denominator in $1:n$ gives the scale factor from model to real.
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Find the missing value: If $1\text{ cm}$ on a map equals $2\text{ km}$, what real distance is $7\text{ cm}$?
Find the missing value: If $1\text{ cm}$ on a map equals $2\text{ km}$, what real distance is $7\text{ cm}$?
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$14\text{ km}$. $7 \times 2 = 14$ using the given scale.
$14\text{ km}$. $7 \times 2 = 14$ using the given scale.
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Identify the correct comparison: If Object A is $2$ times as far as Object B, what is the ratio $A:B$?
Identify the correct comparison: If Object A is $2$ times as far as Object B, what is the ratio $A:B$?
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$2:1$. A is twice B's distance, so ratio is 2 to 1.
$2:1$. A is twice B's distance, so ratio is 2 to 1.
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What is the ratio of Earth’s diameter to the Moon’s diameter using $12{,}742\text{ km}$ and $3{,}474\text{ km}$?
What is the ratio of Earth’s diameter to the Moon’s diameter using $12{,}742\text{ km}$ and $3{,}474\text{ km}$?
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About $3.7:1$. Divide: $12{,}742 \div 3{,}474 \approx 3.7$.
About $3.7:1$. Divide: $12{,}742 \div 3{,}474 \approx 3.7$.
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What does a map scale of $1:50{,}000$ mean about map distance versus real distance?
What does a map scale of $1:50{,}000$ mean about map distance versus real distance?
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$1$ unit on the map represents $50{,}000$ of the same units in reality. The ratio shows map units to real-world units.
$1$ unit on the map represents $50{,}000$ of the same units in reality. The ratio shows map units to real-world units.
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What is the representative fraction (RF) for a bar scale where $1\text{ cm}$ equals $2\text{ km}$?
What is the representative fraction (RF) for a bar scale where $1\text{ cm}$ equals $2\text{ km}$?
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$1:200{,}000$. Convert: $1\text{ cm} = 2\text{ km} = 200{,}000\text{ cm}$, so RF is $1:200{,}000$.
$1:200{,}000$. Convert: $1\text{ cm} = 2\text{ km} = 200{,}000\text{ cm}$, so RF is $1:200{,}000$.
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Which option is a larger scale: $1:10{,}000$ or $1:250{,}000$?
Which option is a larger scale: $1:10{,}000$ or $1:250{,}000$?
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$1:10{,}000$. Smaller denominator means larger scale and more detail.
$1:10{,}000$. Smaller denominator means larger scale and more detail.
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What is the real distance if $3\text{ cm}$ on a map uses a scale of $1\text{ cm}=5\text{ km}$?
What is the real distance if $3\text{ cm}$ on a map uses a scale of $1\text{ cm}=5\text{ km}$?
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$15\text{ km}$. Multiply: $3\text{ cm} \times 5\text{ km/cm} = 15\text{ km}$.
$15\text{ km}$. Multiply: $3\text{ cm} \times 5\text{ km/cm} = 15\text{ km}$.
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What is the map distance if the real distance is $12\text{ km}$ and the scale is $1\text{ cm}=3\text{ km}$?
What is the map distance if the real distance is $12\text{ km}$ and the scale is $1\text{ cm}=3\text{ km}$?
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$4\text{ cm}$. Divide: $12\text{ km} \div 3\text{ km/cm} = 4\text{ cm}$.
$4\text{ cm}$. Divide: $12\text{ km} \div 3\text{ km/cm} = 4\text{ cm}$.
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What is the correct conversion needed to turn $2.5\text{ km}$ into centimeters?
What is the correct conversion needed to turn $2.5\text{ km}$ into centimeters?
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$2.5\text{ km}=250{,}000\text{ cm}$. Multiply by $100{,}000$ to convert km to cm.
$2.5\text{ km}=250{,}000\text{ cm}$. Multiply by $100{,}000$ to convert km to cm.
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What is the scale factor from a model to the real object for a scale of $1:200$?
What is the scale factor from a model to the real object for a scale of $1:200$?
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Scale factor (model to real) is $\frac{1}{200}$. The model is $\frac{1}{200}$ the size of the real object.
Scale factor (model to real) is $\frac{1}{200}$. The model is $\frac{1}{200}$ the size of the real object.
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What happens to area when linear scale is reduced by a factor of $\frac{1}{10}$?
What happens to area when linear scale is reduced by a factor of $\frac{1}{10}$?
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Area becomes $\left(\frac{1}{10}\right)^2=\frac{1}{100}$. Area scales with the square of linear scale.
Area becomes $\left(\frac{1}{10}\right)^2=\frac{1}{100}$. Area scales with the square of linear scale.
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