Convert 215.8745 to degrees, minutes, and seconds.

Question:

Convert 215.8745{eq}^{\circ} {/eq} to degrees, minutes, and seconds.

Degrees, Minutes, and Seconds:

A value in units of degrees can be converted into units of minutes by multiplying the value by {eq}60 {/eq}, there are {eq}60 {/eq} parts that make up one degree and each part is a minute. Similarly, a number in units of minutes can be converted into units of seconds by multiplying the value by {eq}60 {/eq}.

Answer and Explanation:

Given: {eq}215.8745^{\circ} {/eq}


To convert the given amount in degrees into an amount in units of degrees, minutes, and seconds, the strategy is to multiply the digits after the decimal ({eq}0.8745 {/eq}) by {eq}60 {/eq} to get the numerical answer in minutes.


Right now, there are {eq}215^{\circ} {/eq} in the amount {eq}215.8745^{\circ} {/eq}


Finding units in minutes:

{eq}\begin{align*} \text{ Amount in Minutes } &= .8745^{\circ}\cdot 60 \frac{'}{\circ} \\ &= 52.47' \\ &\approx 52' \end{align*} {/eq}


To convert the given amount in minutes into an amount in units of seconds ({eq}52.47' {/eq}), the strategy is to multiply the digits after the decimal ({eq}0.47 {/eq}) by {eq}60 {/eq} to get the numerical answer in seconds.


Finding units in minutes:

{eq}\begin{align*} \text{ Amount in Seconds } &= 0.47'\cdot 60 \frac{"}{'} \\ &= 28.2" \\ &\approx 28" \end{align*} {/eq}


Therefore, the given amount in degrees can be converted into the value {eq}215^{\circ} 52' 28" {/eq}


Learn more about this topic:

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Converting Between Radians and Degrees

from

Chapter 11 / Lesson 10
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Discover the meaning of degrees and radians, their relationship, converting degrees to radians, radians to degrees formula, and some worked out examples.


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