Reason About Scale - Middle School Earth and Space Science

1. Which object is larger in diameter: Earth at $1.27\times 10^4\text{ km}$ or the Moon at $3.47\times 10^3\text{ km}$?

   Earth. $1.27 \times 10^4 > 3.47 \times 10^3$ (compare exponents first).

2. What is the scale factor from a model to the real object for a scale of $1:200$?

   Scale factor (model to real) is $\frac{1}{200}$. The model is $\frac{1}{200}$ the size of the real object.

3. What is the correct unit-canceling setup to find real distance from map distance and RF $1:n$?

   $\text{real}=(\text{map})\times n$ (same units). Multiply map distance by the denominator of the RF.

4. What is the formula for real distance using scale $1\text{ cm}:k\text{ km}$ and map length $m\text{ cm}$?

   $d=mk\text{ km}$. Multiply map length by scale factor to get real distance.

5. What is the formula to find real distance from map distance using scale factor $S$?

   $d_{real} = d_{map}\times S$. Multiply map distance by scale to get real distance.

6. What is the ratio of Earths diameter to the Moons diameter using $12{,}742\text{ km}$ and $3{,}474\text{ km}$?

   About $3.7:1$. Divide Earth's diameter by Moon's: $12{,}742 \div 3{,}474 \approx 3.7$.

7. What real distance does $1\text{ cm}$ represent on a map with scale $1:50{,}000$?

   $50{,}000\text{ cm}$. In a $1:50{,}000$ scale, each map unit represents $50{,}000$ real units.

8. Identify the real distance if $3\text{ cm}$ on a map uses scale $1\text{ cm}:5\text{ km}$.

   $15\text{ km}$. Multiply map distance by scale: $3 \times 5 = 15$.

9. What is the real distance in kilometers if $2\text{ cm}$ on a map equals $1\text{ km}$?

   $1\text{ km}$. Given directly: $2$ cm represents $1$ km.

10. Find the real distance for $7\text{ cm}$ on a map with RF $1:25{,}000$ in meters.

    $1{,}750\text{ m}$. $7\text{ cm} \times 25{,}000 = 175{,}000\text{ cm} = 1{,}750\text{ m}$.

11. Identify the correct conversion: how many centimeters are in $2\text{ km}$?

    $200{,}000\text{ cm}$. $2$ km $\times 1000$ m/km $\times 100$ cm/m = $200{,}000$ cm.

12. What is the real distance if the map distance is $3\text{ cm}$ at a scale of $1:50{,}000$?

    $150{,}000\text{ cm}$. Real distance = $3 \times 50{,}000 = 150{,}000$ cm.

13. Identify the larger scale: $1:25{,}000$ or $1:250{,}000$.

    $1:25{,}000$. Smaller denominator means larger scale (more detail).

14. What is the representative fraction (RF) for a bar scale where $1\text{ cm}$ equals $2\text{ km}$?

    $1:200{,}000$. Convert: $1\text{ cm} = 2\text{ km} = 200{,}000\text{ cm}$, so RF is $1:200{,}000$.

15. What is the map distance if the real distance is $12\text{ km}$ and the scale is $1\text{ cm}=3\text{ km}$?

    $4\text{ cm}$. Divide: $12\text{ km} \div 3\text{ km/cm} = 4\text{ cm}$.

16. What does a map scale of $1:50{,}000$ mean about map distance versus real distance?

    $1$ unit on the map represents $50{,}000$ of the same units in reality. The ratio shows map units to real-world units.

17. What is the real distance if $1\text{ cm}$ on a diagram represents $2\times 10^6\text{ km}$ and the measured distance is $4\text{ cm}$?

    $8\times 10^6\text{ km}$. $4\text{ cm} \times 2 \times 10^6\text{ km/cm} = 8 \times 10^6\text{ km}$.

18. Find the real distance if a model uses $1\ \text{cm}=10\ \text{km}$ and the map shows $7\ \text{cm}$.

    $70\ \text{km}$. $7 \times 10 = 70$ km using the given scale.

19. What is the unit conversion for $1\text{ AU}$ into kilometers (approximate)?

    $1\text{ AU} \approx 1.5\times 10^8\text{ km}$. AU is the average Earth-Sun distance.

20. A model Earth has diameter $12\ \text{cm}$ and represents $12{,}700\ \text{km}$. What is $1\ \text{cm}$ in km?

    $\approx 1058\ \text{km}$. $12{,}700 \div 12 \approx 1058$ km per cm.

21. What is the scale factor from a map to reality for a scale of $1:50{,}000$?

    Multiply map distances by $50{,}000$. Each map unit represents $50{,}000$ real units.

22. What is the formula for real distance using a scale ratio $1:n$ and a map distance $d$?

    Real distance $= d\times n$. Multiply map distance by the scale denominator to get real distance.

23. Which option correctly converts $1\text{ km}$ to centimeters for scale calculations?

    $1\text{ km}=100{,}000\text{ cm}$. Conversion: $1\text{ km} = 1{,}000\text{ m} = 100{,}000\text{ cm}$.

24. Which option correctly converts m to cm for scale work: $1\text{ m}$ equals what in centimeters?

    $1\text{ m} = 100\text{ cm}$. Standard metric conversion for distance calculations.

25. Choose the larger value: $4.0\times 10^6$ or $3.5\times 10^7$.

    $3.5\times 10^7$. Compare exponents: $10^7 > 10^6$, so $3.5 \times 10^7$ is larger.

26. What is the correct unit-canceling setup to find map distance from real distance and RF $1:n$?

    $\text{map}=\frac{\text{real}}{n}$ (same units). Divide real distance by the denominator of the RF.

27. Identify the real distance in km: scale $1:100{,}000$, map distance $2\text{ cm}$, and $100{,}000\text{ cm}=1\text{ km}$.

    $2\text{ km}$. Convert $200{,}000\text{ cm}$ to km: $\div 100{,}000$.

28. Identify the correct scientific notation: $450{,}000{,}000\text{ km}$ written in scientific notation.

    $4.5\times 10^8\text{ km}$. Move decimal 8 places: $450{,}000{,}000 = 4.5 \times 10^8$.

29. What is the scale factor from a model to the real object if the scale is $1:200$?

    Scale factor (model to real) is $200$. To go from model to real, multiply by the denominator.

30. What is the scale ratio $1:n$ if $1\text{ cm}$ on the map represents $5\text{ km}$ in reality?

    $1:500{,}000$. $5$ km = $500{,}000$ cm, so scale is $1:500{,}000$.

31. If a model length is scaled up by $k=3$, by what factor does the area increase?

    Area increases by a factor of $9$. Area scales by $k^2 = 3^2 = 9$.

32. Find the model distance if $1\text{ AU}$ is represented by $5\text{ cm}$; what is $2\text{ AU}$ on the model?

    $10\text{ cm}$. Double the real distance means double the model distance.

33. What does a map scale of $1:50{,}000$ mean about map distance and real distance?

    1 unit on the map represents 50,000 of the same units in reality. Each map unit equals 50,000 real-world units of the same type.

34. What is the scale factor from a model to the real object if the model is $1:200$?

    Scale factor (model to real) is $200$. The denominator in $1:n$ gives the scale factor from model to real.

35. Find the real distance if a map distance is $3\text{ cm}$ at a scale of $1:50{,}000$.

    $150{,}000\text{ cm}$. $3 \times 50{,}000 = 150{,}000$ using the scale ratio.

36. Which option best describes why a scale model of the Solar System cannot fit in a classroom at one scale?

    Planet sizes and distances differ by extreme ratios. Planets are tiny compared to distances between them.

37. What is the real distance if $3\text{ cm}$ on a map uses a scale of $1\text{ cm}=5\text{ km}$?

    $15\text{ km}$. Multiply: $3\text{ cm} \times 5\text{ km/cm} = 15\text{ km}$.

38. What is the scale model distance if $1\text{ AU}$ is represented by $10\text{ cm}$ and Earth to Sun is $1\text{ AU}$?

    $10\text{ cm}$. Earth is $1\text{ AU}$ from Sun, so $1 \times 10\text{ cm} = 10\text{ cm}$.

39. What is the model distance if the real distance is $400\text{ m}$ at a scale of $1:2{,}000$?

    $0.2\text{ m}$. Model distance = $400 \div 2{,}000 = 0.2$ m.

40. What does "to scale" mean for a drawing or model of an Earth system?

    All lengths are in the same constant ratio to real lengths. Every dimension maintains the same proportional relationship.

41. What does a map scale of $1\text{ cm}:5\text{ km}$ mean about real distance per centimeter?

    $1\text{ cm}$ on the map represents $5\text{ km}$ in reality. The scale shows how map measurements relate to actual distances.

42. What is the formula for map distance using a scale ratio $1:n$ and a real distance $D$?

    Map distance $= \frac{D}{n}$. Divide real distance by the scale denominator to get map distance.

43. What is the conversion relationship between centimeters and millimeters?

    $1\ \text{cm}=10\ \text{mm}$. Standard metric conversion for distance.

44. What is the real distance if $5\text{ cm}$ on a map uses a scale of $1\text{ cm}:20\text{ km}$?

    $100\text{ km}$. Real distance = $5 \times 20 = 100$ km.

45. What is the scale factor from reality to a map for a scale of $1:50{,}000$?

    Divide real distances by $50{,}000$. Convert real to map by dividing by the scale denominator.

46. What is the formula for map length using scale $1\text{ cm}:k\text{ km}$ and real distance $d\text{ km}$?

    $m=\frac{d}{k}\text{ cm}$. Divide real distance by scale factor to get map length.

47. What is the unit conversion for $1\text{ cm}$ into millimeters?

    $1\text{ cm} = 10\text{ mm}$. The metric prefix 'milli' means 1/1000.

48. What is the rule for how area changes when linear scale factor is $s$?

    Area scales by $s^2$. Area is 2D, so it scales by the square of linear scale.

49. What is the ratio of Earth's diameter to the Moon's diameter using $12{,}742\text{ km}$ and $3{,}474\text{ km}$?

    About $3.7:1$. Divide: $12{,}742 \div 3{,}474 \approx 3.7$.

50. What is the scale ratio $1:n$ if $2\text{ cm}$ on a map represents $1\text{ km}$ in reality?

    $1:50{,}000$. $1$ km = $100{,}000$ cm; $2$ cm : $100{,}000$ cm = $1:50{,}000$.

51. Find the real distance if a map distance is $3\ \text{cm}$ at a scale of $1:50{,}000$.

    $150{,}000\ \text{cm}$. $3 \times 50{,}000 = 150{,}000$ cm in reality.

52. Which option describes a larger-scale map: $1:50{,}000$ or $1:500{,}000$?

    $1:50{,}000$. Smaller denominator means larger scale (more detail).

53. Identify the ratio of real distances if two map segments are $2\text{ cm}$ and $5\text{ cm}$ on the same scale.

    $2:5$. Same scale preserves ratios between distances.

54. Find the new area if a shape is enlarged by linear scale factor $3$ and original area is $4\text{ cm}^2$.

    $36\text{ cm}^2$. Area scales by $3^2 = 9$, so $4 \times 9 = 36\text{ cm}^2$.

55. What is the correct conversion needed to turn $2.5\text{ km}$ into centimeters?

    $2.5\text{ km}=250{,}000\text{ cm}$. Multiply by $100{,}000$ to convert km to cm.

56. What is the ratio of the Sun's diameter to Earth's diameter using $1{,}392{,}000\text{ km}$ and $12{,}742\text{ km}$?

    About $109:1$. Divide: $1{,}392{,}000 \div 12{,}742 \approx 109$.

57. Identify the real distance: scale $1\text{ in}:10\text{ mi}$ and map distance $2.5\text{ in}$.

    $25\text{ mi}$. Multiply map distance by scale: $2.5 \times 10 = 25$.

58. Choose the correct map distance if the scale is $1\text{ cm}=2\text{ km}$ and the real distance is $10\text{ km}$.

    $5\text{ cm}$. Divide real distance by scale: $10\text{ km} \div 2\text{ km/cm} = 5\text{ cm}$.

59. Which option is the correct proportion for scale $1\text{ cm}:5\text{ km}$ and map distance $x\text{ cm}$ for $30\text{ km}$ real?

    $\frac{x}{30} = \frac{1}{5}$. Set up proportion: map/real = scale ratio.

60. What is the unit conversion for $1\text{ light-year}$ into kilometers (approximate)?

    $1\text{ ly} \approx 9.46\times 10^{12}\text{ km}$. Light travels this distance in one year.

61. What is the unit conversion for $1\text{ m}$ into centimeters?

    $1\text{ m} = 100\text{ cm}$. The metric prefix 'centi' means 1/100.

62. What is the real distance in meters if the model distance is $15\text{ cm}$ at a scale of $1:500$?

    $75\text{ m}$. $15$ cm $\times 500 = 7{,}500$ cm = $75$ m.

63. What happens to map detail when the scale changes from $1:50{,}000$ to $1:500{,}000$?

    Less detail; a larger area is shown. Smaller scale shows more area but with less detail.

64. What is the scale model distance if Earth–Moon real distance is $384{,}400\text{ km}$ at $1\text{ cm}=10{,}000\text{ km}$?

    $38.44\text{ cm}$. Divide: $384{,}400\text{ km} \div 10{,}000\text{ km/cm} = 38.44\text{ cm}$.

65. What is the rule for how volume changes when linear scale factor is $s$?

    Volume scales by $s^3$. Volume is 3D, so it scales by the cube of linear scale.

66. Find the real distance in $\text{km}$ if $4\text{ cm}$ on a map equals $200{,}000\text{ cm}$ in reality.

    $2\text{ km}$. Convert $200{,}000\text{ cm}$ to kilometers: $200{,}000 \div 100{,}000 = 2$.

67. Which option is the correct unit conversion: $1\text{ km}=?\text{ cm}$?

    $1\text{ km}=100{,}000\text{ cm}$. Kilo means 1000, and 100 cm = 1 m, so $1000 \times 100 = 100{,}000$.

68. What is the formula for map distance using a representative fraction scale $1:n$?

    Map distance $=$ real distance $\div n$. Divide real distance by the scale denominator.

69. What does a map scale of $1:50{,}000$ mean about map distance versus real distance?

    1 unit on map represents $50{,}000$ of the same units in reality. The ratio shows how many real-world units equal one map unit.

70. Find the missing value: If $1\text{ cm}$ on a map equals $2\text{ km}$, what real distance is $7\text{ cm}$?

    $14\text{ km}$. $7 \times 2 = 14$ using the given scale.

71. What is the unit conversion for $1\text{ km}$ into meters?

    $1\text{ km} = 1000\text{ m}$. The metric prefix 'kilo' means 1000.

72. What is the scale model distance if $1\text{ AU}$ is $10\text{ cm}$ and Jupiter is $5.2\text{ AU}$ from the Sun?

    $52\text{ cm}$. $5.2\text{ AU} \times 10\text{ cm/AU} = 52\text{ cm}$.

73. Identify the scale factor from a model to real life if $1\text{ cm}$ on the model equals $2\text{ m}$ in reality.

    Scale factor (model:real) is $1:200$. Convert to same units: $1\text{ cm}:200\text{ cm}$.

74. What does a map scale of $1:50{,}000$ mean in terms of map distance to real distance?

    1 unit on the map equals $50{,}000$ of the same units in reality. The ratio shows how many real-world units correspond to one map unit.

75. What is the real distance if a model shows $8\text{ cm}$ and the scale is $1\text{ cm}=50{,}000\text{ km}$?

    $400{,}000\text{ km}$. Multiply: $8\text{ cm} \times 50{,}000\text{ km/cm} = 400{,}000\text{ km}$.

76. What is the conversion relationship between meters and centimeters?

    $1\ \text{m}=100\ \text{cm}$. Standard metric conversion for distance.

77. Find the real distance if $3\text{ cm}$ on a map uses scale $1\text{ cm}:4\text{ km}$.

    $12\text{ km}$. Multiply: $3\text{ cm} \times 4\text{ km/cm} = 12\text{ km}$.

78. What does a map scale of $1:50{,}000$ mean for map distance versus real distance?

    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.

79. Which option best describes a scale model in science: proportional representation or exact full size?

    A proportional representation of an object or distance. Scale models maintain proportions but change size.

80. What is the diameter ratio Earth:Moon using $1.27\times 10^4\text{ km}$ and $3.47\times 10^3\text{ km}$ (approx.)?

    $\approx 3.7:1$. $\frac{1.27 \times 10^4}{3.47 \times 10^3} \approx \frac{12.7}{3.47} \approx 3.7$.

81. What is the formula for real distance using a representative fraction scale $1:n$?

    Real distance $=$ map distance $\times n$. Multiply map distance by the scale denominator.

82. Two planets are shown with diameters $2\text{ cm}$ and $5\text{ cm}$ on a scale diagram. What is the diameter ratio (small:large)?

    $2:5$. Direct ratio of the given measurements.

83. Which option is closer to true: Earth–Sun distance is about $1\text{ AU}$ or about $1\text{ ly}$?

    About $1\text{ AU}$. $1\text{ AU} \approx 150$ million km; $1\text{ ly}$ is much farther.

84. Identify the area scale factor if a model is enlarged by a linear factor of $3$.

    $9$. Area scale factor = $(\text{linear scale factor})^2 = 3^2 = 9$.

85. Identify the volume scale factor if a model is reduced by a linear factor of $\frac{1}{2}$.

    $\frac{1}{8}$. Volume scale factor = $(\text{linear scale factor})^3 = (\frac{1}{2})^3$.

86. What is the approximate value of $1\text{ AU}$ in kilometers?

    About $1.5\times10^8\text{ km}$. AU is Earth-Sun distance, about 150 million km.

87. Identify the larger scale: $1:25{,}000$ or $1:250{,}000$.

    $1:25{,}000$. Smaller denominators mean larger scales (more detail shown).

88. Convert $150{,}000\ \text{cm}$ to kilometers using $100{,}000\ \text{cm}=1\ \text{km}$.

    $1.5\ \text{km}$. $150{,}000 \div 100{,}000 = 1.5$ km.

89. Choose the correct real distance for $2\ \text{cm}$ on a map with scale $1\ \text{cm}=5\ \text{km}$.

    $10\ \text{km}$. $2 \times 5 = 10$ km using the given scale.

90. What is the formula for scale factor using lengths: model length $\div$ real length?

    $\text{scale factor} = \frac{\text{model}}{\text{real}}$. Scale factor is the ratio of model to actual size.

91. Find the map distance for a real distance of $4\ \text{km}$ at a scale of $1:100{,}000$.

    $4\ \text{cm}$. $4$ km $= 400{,}000$ cm; $400{,}000 \div 100{,}000 = 4$ cm.

92. What is the map distance if the real distance is $12\text{ km}$ at a scale of $1\text{ cm}:4\text{ km}$?

    $3\text{ cm}$. Map distance = $12 \div 4 = 3$ cm.

93. What is the formula to find map distance from real distance using scale factor $S$?

    $d_{map} = \frac{d_{real}}{S}$. Divide real distance by scale to get map distance.

94. Which option correctly converts $1\text{ m}$ to centimeters for scale calculations?

    $1\text{ m}=100\text{ cm}$. Basic metric conversion for scale calculations.

95. Which option describes a smaller scale map: $1:25{,}000$ or $1:250{,}000$?

    $1:250{,}000$. Larger denominator means smaller scale and less detail.

96. Identify the map distance if the scale is $1:25{,}000$ and the real distance is $500{,}000\text{ cm}$.

    $20\text{ cm}$. Divide: $500{,}000\text{ cm} \div 25{,}000 = 20\text{ cm}$.

97. What happens to area when linear scale is reduced by a factor of $\frac{1}{10}$?

    Area becomes $\left(\frac{1}{10}\right)^2=\frac{1}{100}$. Area scales with the square of linear scale.

98. Which option correctly converts km to m for scale work: $1\text{ km}$ equals what in meters?

    $1\text{ km} = 1000\text{ m}$. Standard metric conversion for distance calculations.

99. What does a map scale of $1:50{,}000$ mean for real distance compared to map distance?

    1 unit on the map represents $50{,}000$ of the same units in reality. Each map unit equals 50,000 real-world units.

100. What is the conversion relationship between kilometers and meters?

     $1\ \text{km}=1000\ \text{m}$. Standard metric conversion for distance.

101. A model Earth has radius $6\text{ cm}$. If real Earth radius is $6.4\times 10^3\text{ km}$, what is the scale (model:real)?

     $6\text{ cm} : 6.4\times 10^3\text{ km}$. Write the actual measurements with their units.

102. Find the new volume if an object is enlarged by linear scale factor $2$ and original volume is $5\text{ cm}^3$.

     $40\text{ cm}^3$. Volume scales by $2^3 = 8$, so $5 \times 8 = 40\text{ cm}^3$.

103. What is the map distance if the scale is $1:50{,}000$ and the real distance is $2\text{ km}$?

     $4\text{ cm}$. $2\text{ km} = 200{,}000\text{ cm}$; $200{,}000 \div 50{,}000 = 4$.

104. Which option correctly states how to compare two scales $1:50{,}000$ and $1:100{,}000$ for detail?

     $1:50{,}000$ shows more detail (less reduction). Smaller denominator means larger scale and more detail shown.

105. Identify the correct statement: If the RF denominator increases, map detail increases or decreases?

     Decreases. Larger denominator means smaller scale, less detail.

106. What does a map scale of $1\text{ cm}:5\text{ km}$ mean?

     $1\text{ cm}$ on the map represents $5\text{ km}$ in real distance. Each centimeter on the map corresponds to 5 kilometers in reality.

107. Find and correct the unit error: "Scale is $1\text{ cm}:5$" (distance unit missing on the real side).

     Correct: $1\text{ cm}:5\text{ km}$ (or another stated distance unit). Scale must specify units on both sides of the ratio.

108. What is the map distance for $18\text{ km}$ in reality at a scale of $1\text{ cm}:3\text{ km}$?

     $6\text{ cm}$. Divide real distance by scale: $18 \div 3 = 6$.

109. Identify the map distance if the real distance is $20\text{ km}$ and scale is $1\text{ cm}:5\text{ km}$.

     $4\text{ cm}$. Divide real distance by scale: $20 \div 5 = 4$.

110. Which option gives the correct rule for how volume changes with linear scale factor $k$?

     Volume scales by $k^3$. When linear dimensions scale by $k$, volume scales by $k^3$.

111. Which option best describes a scale factor between $0$ and $1$ applied to a model?

     A reduction (the model is smaller than the real object). Scale factor <1 means the image is smaller than the original object.

112. Which option states how areas scale when all lengths are scaled by a factor of $k$?

     Area scales by a factor of $k^2$. Area is 2D, so scale factor is squared.

113. What is the scale factor if $1\text{ cm}$ on a model represents $5\text{ cm}$ in real life?

     Scale factor $=\frac{1}{5}$. Scale factor equals model size divided by real size: $\frac{1}{5}$.

114. If a scale model uses $k=3$ for linear enlargement, by what factor does the volume increase?

     $27$. $k^3 = 3^3 = 27$ for volume scaling.

115. If a model length is scaled down by $k=\frac{1}{2}$, by what factor does the volume change?

     Volume becomes $\frac{1}{8}$ of the original. Volume scales by $k^3 = (\frac{1}{2})^3 = \frac{1}{8}$.

116. What is the real distance for $4\text{ mm}$ on a diagram with scale $1\text{ mm}=2\text{ m}$?

     $8\text{ m}$. Multiply: $4\text{ mm} \times 2\text{ m/mm} = 8\text{ m}$.

117. What is the real distance if a map uses $1:100{,}000$ and two towns are $3\text{ cm}$ apart?

     $3\text{ km}$. $3\text{ cm} \times 100{,}000 = 300{,}000\text{ cm} = 3\text{ km}$.

118. Which scale shows more detail on a map: $1:10{,}000$ or $1:100{,}000$?

     $1:10{,}000$. Smaller scale denominators show more detail per unit area.

119. Which comparison is correct for scales: $1:10{,}000$ or $1:100{,}000$ shows more detail?

     $1:10{,}000$ shows more detail (larger scale). Smaller denominator means larger scale and more detail.

120. Which option best describes a scale bar on a map?

     A line segment showing how map length corresponds to real distance. Visual reference showing map distances as real-world measurements.

121. What happens to volume when linear scale is increased by a factor of $3$?

     Volume becomes $3^3=27$ times larger. Volume scales with the cube of linear scale.

122. What is the real distance for $6\text{ cm}$ on a map with scale $1\text{ cm}:2\text{ km}$?

     $12\text{ km}$. Multiply map distance by scale: $6 \times 2 = 12$.

123. Which option correctly compares distances: $1\text{ AU}$ or $1\text{ ly}$ is larger?

     $1\text{ ly}$ is larger. Light-year is about 63,000 times larger than an AU.

124. Identify the scale factor from model to real object for a scale written as $1:200$.

     Scale factor (model to real) $=200$. The denominator shows how many times larger reality is.

125. Find the map distance if the real distance is $18\text{ km}$ and the scale is $1\text{ cm}:6\text{ km}$.

     $3\text{ cm}$. Divide: $18\text{ km} \div 6\text{ km/cm} = 3\text{ cm}$.

126. Which option is the correct proportion for a scale of $1:100{,}000$ with map $d$ and real $D$?

     $\frac{d}{D}=\frac{1}{100{,}000}$. Scale ratios can be written as proportions with map over real.

127. Which option best describes a scale factor greater than $1$ applied to a drawing?

     An enlargement (the drawing is larger than the original). Scale factor >1 means the image is larger than the original object.

128. Identify the real distance if the scale is $1:100{,}000$ and the map distance is $3\text{ cm}$.

     $300{,}000\text{ cm}$. Multiply: $3\text{ cm} \times 100{,}000 = 300{,}000\text{ cm}$.

129. Which option gives the correct rule for how area changes with linear scale factor $k$?

     Area scales by $k^2$. When linear dimensions scale by $k$, area scales by $k^2$.

130. What is the ratio of $150\text{ million km}$ to $1.5\text{ million km}$, representing two space distances?

     $100:1$. $150 \div 1.5 = 100$, so the ratio is $100:1$.

131. What happens to volume when all linear dimensions are scaled by a factor of $k$?

     Volume scales by $k^3$. Volume is 3D, so scale factor is cubed.

132. Identify the larger ratio: compare $1:10{,}000$ and $1:100{,}000$ for map detail (larger scale).

     $1:10{,}000$ is the larger scale (more detail). Smaller denominator means larger scale and more detail.

133. Find the map distance for $12\text{ km}$ at a scale of $1\text{ cm}:4\text{ km}$.

     $3\text{ cm}$. $12 \div 4 = 3$ since each cm represents 4 km.

134. Which option is a correct unit rule when using a scale: keep units, or mix units freely?

     Keep units consistent; convert units before applying the scale. Scale ratios only work when both distances use the same units.

135. What is the ratio of Earth's diameter to the Moon's diameter using $12{,}742\text{ km}$ and $3{,}474\text{ km}$?

     About $3.7:1$. $12{,}742 \div 3{,}474 \approx 3.7$, so Earth is about $3.7$ times wider.

136. Which option best describes a larger-scale map: more detail or less detail?

     More detail. Larger scale maps show smaller areas with greater detail.

137. Identify the missing value: scale $1:100{,}000$, map distance $2\text{ cm}$; what is real distance in cm?

     $200{,}000\text{ cm}$. Multiply map distance by scale: $2 \times 100{,}000$.

138. What happens to area when all linear dimensions are scaled by a factor of $k$?

     Area scales by $k^2$. Area is 2D, so scale factor is squared.

139. Identify the representative fraction (RF) for a scale of $1\text{ cm}:10\text{ km}$.

     $1:1{,}000{,}000$. Convert both to same units: $1\text{ cm}:1{,}000{,}000\text{ cm}$.

140. What is the real distance if a map scale is $1\text{ cm}=5\text{ km}$ and the map distance is $6\text{ cm}$?

     $30\text{ km}$. Multiply: $6\text{ cm} \times 5\text{ km/cm} = 30\text{ km}$.

141. What does an exponent of $-3$ in scientific notation, such as $4.2\times 10^{-3}$, indicate?

     The decimal moves $3$ places to the left. Negative exponent means divide by $10^3 = 1000$.

142. Which option is a larger scale: $1:10{,}000$ or $1:250{,}000$?

     $1:10{,}000$. Smaller denominator means larger scale and more detail.

143. What unit rule must be followed when using a scale like $1:1000$ with distances?

     Use the same units on both sides before converting units. Both sides of the ratio must use matching units.

144. Which option best defines a scale model in Earth and space science?

     A smaller or larger representation that keeps proportional relationships. Scale models maintain the same ratios as the original.

145. If a scale model uses $k=3$ for linear enlargement, by what factor does the area increase?

     $9$. $k^2 = 3^2 = 9$ for area scaling.

146. Identify the correct comparison: If Object A is $2$ times as far as Object B, what is the ratio $A:B$?

     $2:1$. A is twice B's distance, so ratio is 2 to 1.

147. Identify the scale factor: a model Earth diameter is $12\text{ cm}$ and real diameter is $12{,}000\text{ km}$.

     $1\text{ cm}:1000\text{ km}$. Simplify ratio: $12:12{,}000 = 1:1000$.

148. What is the map distance if a map scale is $1\text{ cm}=20\text{ km}$ and the real distance is $100\text{ km}$?

     $5\text{ cm}$. Divide: $100\text{ km} \div 20\text{ km/cm} = 5\text{ cm}$.

149. What is the approximate value of $1\text{ ly}$ in kilometers?

     About $9.46\times10^{12}\text{ km}$. Light travels this distance in one year.

150. Identify the unit rule for scale calculations when using a ratio like $1:1000$.

     Use the same units on both sides before converting units. Both sides of the ratio must use identical units.

151. Convert the real distance $150{,}000\text{ cm}$ to kilometers using $1\text{ km}=100{,}000\text{ cm}$.

     $1.5\text{ km}$. $150{,}000 \div 100{,}000 = 1.5$ using the conversion factor.

152. Which option states how volumes scale when all lengths are scaled by a factor of $k$?

     Volume scales by a factor of $k^3$. Volume is 3D, so scale factor is cubed.

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