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Convert the following angle measures: i) 198 degrees to minutes ii) 247 degrees, 30 minutes to seconds iii) 2367 minutes to seconds iv) 98.5 degrees to minutes v) 6656 seconds to degree minutes second

Mathematics

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Step-by-step solution

23 steps

Here are the conversions for question 1a:

Part i· 2 steps

198 degrees to minutes

  1. Use the conversion factor 1∘=60′1^\circ = 60'.

    198∘=198×60′198^\circ = 198 \times 60'

  2. Calculate the product.

    198×60=11880198 \times 60 = 11880

    The converted value is:

    11880 minutes\boxed{\text{11880 minutes}}

Part ii· 3 steps

247 degrees, 30 minutes to seconds

  1. Convert degrees to seconds using 1∘=3600′′1^\circ = 3600''.

    247∘=247×3600′′=889200′′247^\circ = 247 \times 3600'' = 889200''

  2. Convert minutes to seconds using 1′=60′′1' = 60''.

    30′=30×60′′=1800′′30' = 30 \times 60'' = 1800''

  3. Add the seconds together.

    889200′′+1800′′=891000′′889200'' + 1800'' = 891000''

    The converted value is:

    891000 seconds\boxed{\text{891000 seconds}}

Part iii· 2 steps

2367 minutes to seconds

  1. Use the conversion factor 1′=60′′1' = 60''.

    2367′=2367×60′′2367' = 2367 \times 60''

  2. Calculate the product.

    2367×60=1420202367 \times 60 = 142020

    The converted value is:

    142020 seconds\boxed{\text{142020 seconds}}

Part iv· 2 steps

98.5 degrees to minutes

  1. Use the conversion factor 1∘=60′1^\circ = 60'.

    98.5∘=98.5×60′98.5^\circ = 98.5 \times 60'

  2. Calculate the product.

    98.5×60=591098.5 \times 60 = 5910

    The converted value is:

    5910 minutes\boxed{\text{5910 minutes}}

Part v· 4 steps

6656 seconds to degree minutes seconds

  1. Convert seconds to degrees by dividing by 3600′′/degree3600''/\text{degree}.

    66563600=1 with a remainder\frac{6656}{3600} = 1 \text{ with a remainder} 1∘1^\circ

  2. Calculate the remaining seconds.

    6656−(1×3600)=3056′′6656 - (1 \times 3600) = 3056''

  3. Convert the remaining seconds to minutes by dividing by 60′′/minute60''/\text{minute}.

    305660=50 with a remainder\frac{3056}{60} = 50 \text{ with a remainder} 50′50'

  4. Calculate the remaining seconds.

    3056−(50×60)=3056−3000=56′′3056 - (50 \times 60) = 3056 - 3000 = 56''

    The converted value is:

    1 degree, 50 minutes, 56 seconds\boxed{\text{1 degree, 50 minutes, 56 seconds}}

Part vi· 2 steps

156 ft to meters

  1. Use the conversion factor 1 ft=0.3048 m1 \text{ ft} = 0.3048 \text{ m}.

    156 ft=156×0.3048 m156 \text{ ft} = 156 \times 0.3048 \text{ m}

  2. Calculate the product.

    156×0.3048=47.5488156 \times 0.3048 = 47.5488

    The converted value is:

    47.5488 m\boxed{\text{47.5488 m}}

Part vii· 2 steps

708 meters to feet

  1. Use the conversion factor 1 m=3.28084 ft1 \text{ m} = 3.28084 \text{ ft}.

    708 m=708×3.28084 ft708 \text{ m} = 708 \times 3.28084 \text{ ft}

  2. Calculate the product.

    708×3.28084=2322.83052708 \times 3.28084 = 2322.83052

    The converted value is:

    2322.83052 ft\boxed{\text{2322.83052 ft}}

Part viii· 2 steps

1.23 km to meters

  1. Use the conversion factor 1 km=1000 m1 \text{ km} = 1000 \text{ m}.

    1.23 km=1.23×1000 m1.23 \text{ km} = 1.23 \times 1000 \text{ m}

  2. Calculate the product.

    1.23×1000=12301.23 \times 1000 = 1230

    The converted value is:

    1230 m\boxed{\text{1230 m}}

Part ix· 2 steps

100 ft to meters

  1. Use the conversion factor 1 ft=0.3048 m1 \text{ ft} = 0.3048 \text{ m}.

    100 ft=100×0.3048 m100 \text{ ft} = 100 \times 0.3048 \text{ m}

  2. Calculate the product.

    100×0.3048=30.48100 \times 0.3048 = 30.48

    The converted value is:

    30.48 m\boxed{\text{30.48 m}}

Part x· 2 steps

0.55 km to meters

  1. Use the conversion factor 1 km=1000 m1 \text{ km} = 1000 \text{ m}.

    0.55 km=0.55×1000 m0.55 \text{ km} = 0.55 \times 1000 \text{ m}

  2. Calculate the product.

    0.55×1000=5500.55 \times 1000 = 550

    The converted value is:

    550 m\boxed{\text{550 m}}
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