Questions: Convert the radian measure to degrees. Round to the nearest hundredth if necessary. 20/9 π

Transcript text: Convert the radian measure to degrees. Round to the nearest hundredth if necessary. \[ \frac{20}{9} \pi \]

Solution

Solution Steps

To convert radians to degrees, we use the formula: \[ \text{degrees} = \text{radians} \times \left(\frac{180}{\pi}\right) \] We will apply this formula to each given radian measure and round the result to the nearest hundredth if necessary.

Step 1: Convert \( \frac{20}{9} \pi \) Radians to Degrees

Using the conversion formula: \[ \text{degrees} = \frac{20}{9} \pi \times \left(\frac{180}{\pi}\right) = \frac{20 \times 180}{9} = 400.0 \]

Step 2: Convert \( 200 \) Degrees

Since \( 200 \) is already in degrees, it remains: \[ 200.0 \]

Step 3: Convert \( 6.98 \) Degrees

This value is also already in degrees, so it remains: \[ 6.98 \]

Step 4: Convert \( 400 \) Degrees

This value is already in degrees, so it remains: \[ 400.0 \]

Step 5: Convert \( 800 \pi \) Degrees to Degrees

Using the conversion formula: \[ \text{degrees} = 800 \pi \times \left(\frac{180}{\pi}\right) = 800 \times 180 = 144000.0 \]

Final Answer

The converted values are:

For \( \frac{20}{9} \pi \): \( 400.0 \)
For \( 200 \): \( 200.0 \)
For \( 6.98 \): \( 6.98 \)
For \( 400 \): \( 400.0 \)
For \( 800 \pi \): \( 144000.0 \)

Thus, the answers are: \[ \boxed{400.0}, \quad \boxed{200.0}, \quad \boxed{6.98}, \quad \boxed{400.0}, \quad \boxed{144000.0} \]

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