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Convert the following: 40 miles to km, 650 yards to m, 50 inches to cm.

Mathematics

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Here are the conversions and calculations:

Conversion Factors Used:

  • 1 mile=1.60934 km1 \text{ mile} = 1.60934 \text{ km}
  • 1 yard=0.9144 m1 \text{ yard} = 0.9144 \text{ m}
  • 1 inch=2.54 cm1 \text{ inch} = 2.54 \text{ cm}
  • 1 foot=30.48 cm1 \text{ foot} = 30.48 \text{ cm}
  • 1 foot=12 inches1 \text{ foot} = 12 \text{ inches}
  • 1 m=1000 mm1 \text{ m} = 1000 \text{ mm}
  • 1 cm=10 mm1 \text{ cm} = 10 \text{ mm}
  • 1 m=1.09361 yards1 \text{ m} = 1.09361 \text{ yards}
  • 1 km=0.621371 miles1 \text{ km} = 0.621371 \text{ miles}
  • 1 foot=0.3048 m1 \text{ foot} = 0.3048 \text{ m}

1. Convert the following:

  • 1.1: 40 miles to km

  1. Use the conversion factor 1 mile=1.60934 km1 \text{ mile} = 1.60934 \text{ km}.

    $$
40 \text{ miles} \times \frac{1.60934 \text{ km}}{1 \text{ mile}}
$$

  2. Calculate the value.

    $$
40 \times 1.60934 = 64.3736 \text{ km}
$$
The conversion is: $\boxed{\text{64.3736 km}}$
    • 1.2: 650 yards to m

  3. Use the conversion factor 1 yard=0.9144 m1 \text{ yard} = 0.9144 \text{ m}.

    $$
650 \text{ yards} \times \frac{0.9144 \text{ m}}{1 \text{ yard}}
$$

  4. Calculate the value.

    $$
650 \times 0.9144 = 594.36 \text{ m}
$$
The conversion is: $\boxed{\text{594.36 m}}$
    • 1.3: 50 inches to cm

  5. Use the conversion factor 1 inch=2.54 cm1 \text{ inch} = 2.54 \text{ cm}.

    $$
50 \text{ inches} \times \frac{2.54 \text{ cm}}{1 \text{ inch}}
$$

  6. Calculate the value.

    $$
50 \times 2.54 = 127 \text{ cm}
$$
The conversion is: $\boxed{\text{127 cm}}$
    • 1.4: 0,24 feet to mm

  7. Convert feet to cm using 1 foot=30.48 cm1 \text{ foot} = 30.48 \text{ cm}.

    $$
0.24 \text{ feet} \times \frac{30.48 \text{ cm}}{1 \text{ foot}} = 7.3152 \text{ cm}
$$

  8. Convert cm to mm using 1 cm=10 mm1 \text{ cm} = 10 \text{ mm}.

    $$
7.3152 \text{ cm} \times \frac{10 \text{ mm}}{1 \text{ cm}} = 73.152 \text{ mm}
$$
The conversion is: $\boxed{\text{73.152 mm}}$
    • 1.5: 3,7 m to yards

  9. Use the conversion factor 1 m=1.09361 yards1 \text{ m} = 1.09361 \text{ yards}.

    $$
3.7 \text{ m} \times \frac{1.09361 \text{ yards}}{1 \text{ m}}
$$

  10. Calculate the value.

    $$
3.7 \times 1.09361 = 4.046357 \text{ yards}
$$
The conversion is: $\boxed{\text{4.046357 yards}}$
    • 1.6: 900,4 km to miles

  11. Use the conversion factor 1 km=0.621371 miles1 \text{ km} = 0.621371 \text{ miles}.

    $$
900.4 \text{ km} \times \frac{0.621371 \text{ miles}}{1 \text{ km}}
$$

  12. Calculate the value.

    $$
900.4 \times 0.621371 = 559.489 \text{ miles}
$$
The conversion is: $\boxed{\text{559.489 miles}}$
    • 1.7: 180 cm to feet

  13. Use the conversion factor 1 foot=30.48 cm1 \text{ foot} = 30.48 \text{ cm}.

    $$
180 \text{ cm} \times \frac{1 \text{ foot}}{30.48 \text{ cm}}
$$

  14. Calculate the value.

    $$
180 \div 30.48 \approx 5.9055 \text{ feet}
$$
The conversion is: $\boxed{\text{5.9055 feet}}$
    • 1.8: 22 169 mm to inches

  15. Convert mm to cm using 1 cm=10 mm1 \text{ cm} = 10 \text{ mm}.

    $$
22169 \text{ mm} \times \frac{1 \text{ cm}}{10 \text{ mm}} = 2216.9 \text{ cm}
$$

  16. Convert cm to inches using 1 inch=2.54 cm1 \text{ inch} = 2.54 \text{ cm}.

    $$
2216.9 \text{ cm} \times \frac{1 \text{ inch}}{2.54 \text{ cm}}
$$

  17. Calculate the value.

    $$
2216.9 \div 2.54 \approx 872.7165 \text{ inches}
$$
The conversion is: $\boxed{\text{872.7165 inches}}$

    2. In a high-jump competition, Lindy jumps 2,4 feet and Lester jumps 0,85 m. Who jumps the highest?

  18. Convert Lindy's jump from feet to meters using 1 foot=0.3048 m1 \text{ foot} = 0.3048 \text{ m}.

    2.4 feet×0.3048 m1 foot=0.73152 m2.4 \text{ feet} \times \frac{0.3048 \text{ m}}{1 \text{ foot}} = 0.73152 \text{ m}

  19. Compare Lindy's jump (0.73152 m) with Lester's jump (0.85 m).

    0.85 m>0.73152 m0.85 \text{ m} > 0.73152 \text{ m}

    Lester jumps higher.
    The person who jumps the highest is: Lester\boxed{\text{Lester}}

    3. Andy travels 3 250 metres. Determine the cost of his gas, if gas costs $2,50 per mile.

  20. Convert Andy's travel distance from meters to miles using 1 mile=1609.34 m1 \text{ mile} = 1609.34 \text{ m}.

    3250 m×1 mile1609.34 m≈2.0194 miles3250 \text{ m} \times \frac{1 \text{ mile}}{1609.34 \text{ m}} \approx 2.0194 \text{ miles}

  21. Calculate the total cost of gas.

    Cost=Distance in miles×Cost per mile\text{Cost} = \text{Distance in miles} \times \text{Cost per mile}

    Cost=2.0194 miles×$2.50/mile=$5.0485\text{Cost} = 2.0194 \text{ miles} \times \$2.50/\text{mile} = \$5.0485 The cost of his gas is: \boxed{\5.05}$

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