Math Problem Statement

Solve problems

Solve problems

Solution

Here are the solutions to the given problems in the uploaded image. The answers are calculated and rounded as per the instructions provided in the questions.


F. Convert from smaller to larger weights. Round to the nearest tenth.

  1. 35. 473 cg = 47.3 dg
  2. 36. 171 hg = 17.1 kg
  3. 37. 1,100 dag = 110.0 hg
  4. 38. 200 dg = 20.0 g
  5. 39. 213 mg = 21.3 cg
  6. 40. 398 g = 39.8 dag

G. Convert from larger to smaller weights. Round to the nearest whole number.

  1. 41. 605 g = 60,500 dg
  2. 42. 61,216 dg = 612,160 cg
  3. 43. 141 cg = 1,410 mg
  4. 44. 741,000 dag = 7,410,000 g
  5. 45. 803 kg = 8,030 hg
  6. 46. 102 g = 10,200 dg

H. Convert English measures to metric measures for weight. Carry answers to 3 decimal places.

  1. 47. 757 lb = 343.226 kg
  2. 48. 88 oz = 2,494.757 g
  3. 49. 2,000 T = 1,814,369.480 t
  4. 50. 629 lb = 285.331 kg
  5. 51. 69 oz = 1,956.069 g
  6. 52. 55 T = 49,895.160 t

I. Convert from smaller to larger volumes. Round to the nearest tenth.

  1. 53. 504 mL = 50.4 cL
  2. 54. 5,120 dL = 512.0 L
  3. 55. 69,411 L = 6,941.1 daL
  4. 56. 45 daL = 4.5 hL

J. Convert English measures to metric measures for volume. Carry answers to 3 decimal places.

  1. 57. 12 yd³ = 9.174 m³
  2. 58. 18 cups = 4.257 L
  3. 59. 509 gal = 1,926.376 L
  4. 60. 3 qts = 2.839 L

K. Convert degrees Fahrenheit to degrees Celsius. Round your answers to the nearest degree.

  1. 61. 98°F = 37°C
  2. 62. 47°F = 8°C

Let me know if you'd like explanations for any of these solutions or further assistance!


Expanding Questions:

  1. How are conversions between units of weight and volume derived?
  2. Why is rounding important in measurements and conversions?
  3. Can you explain the relationship between metric and English measurement systems?
  4. What is the formula to convert Fahrenheit to Celsius and vice versa?
  5. How would you calculate more complex unit conversions like yards cubed to liters?

Tip: Always double-check the conversion factors for accuracy, especially when switching between metric and English systems!

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Math Problem Analysis

Mathematical Concepts

Unit conversions
Metric and English measurement systems
Rounding rules

Formulas

1 kg = 10 hg
1 g = 10 dg
1 T = 907.18474 t
Fahrenheit to Celsius formula: C = (F - 32) × 5/9

Theorems

Proportionality in unit conversion

Suitable Grade Level

Grades 6-8