Math / Numbers & Operations

Question9. Convert the decimal degree, $19.35^\circ$ to DMS

Studdy Solution

STEP 1

What is this asking? We need to rewrite the angle $19.35^\circ$ in degrees, minutes, and seconds! Watch out! There are 60 minutes in a degree and 60 seconds in a minute.
Don't mix these up!

STEP 2

1. Separate the whole degrees
2. Convert the decimal part to minutes
3. Convert the remaining decimal to seconds
4. Combine degrees, minutes, and seconds

STEP 3

The whole number part of $19.35^\circ$ represents the degrees.
So, we have 19 degrees to start with.
We'll keep that aside for now and focus on the decimal part.

STEP 4

We have $0.35$ of a degree left.
Since there are 60 minutes in one degree, we multiply this decimal by 60 to find out how many minutes we have: $0.35 \cdot 60 = \textbf{21}$ This gives us 21 minutes!

STEP 5

In this case, the result of our calculation in the previous step was a whole number (21), so there's no decimal part left to convert to seconds.
This means we have zero seconds.
Sometimes you'll have a decimal left over, and you'll multiply that by 60 to get the seconds.

STEP 6

Putting it all together, we have 19 degrees, 21 minutes, and 0 seconds.
We write this as $19^\circ 21' 0''$ .

STEP 7

The final answer is $19^\circ 21' 0''$ .

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Question9. Convert the decimal degree, $19.35^\circ$ to DMS

Studdy Solution

STEP 1

What is this asking? We need to rewrite the angle $19.35^\circ$ in degrees, minutes, and seconds! Watch out! There are 60 minutes in a degree and 60 seconds in a minute.
Don't mix these up!

STEP 2

1. Separate the whole degrees
2. Convert the decimal part to minutes
3. Convert the remaining decimal to seconds
4. Combine degrees, minutes, and seconds

STEP 3

The whole number part of $19.35^\circ$ represents the degrees.
So, we have 19 degrees to start with.
We'll keep that aside for now and focus on the decimal part.

STEP 4

We have $0.35$ of a degree left.
Since there are 60 minutes in one degree, we multiply this decimal by 60 to find out how many minutes we have: $0.35 \cdot 60 = \textbf{21}$ This gives us 21 minutes!

STEP 5

In this case, the result of our calculation in the previous step was a whole number (21), so there's no decimal part left to convert to seconds.
This means we have zero seconds.
Sometimes you'll have a decimal left over, and you'll multiply that by 60 to get the seconds.

STEP 6

Putting it all together, we have 19 degrees, 21 minutes, and 0 seconds.
We write this as $19^\circ 21' 0''$ .

STEP 7

The final answer is $19^\circ 21' 0''$ .

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Question9. Convert the decimal degree, 19.35∘19.35^\circ19.35∘ to DMS

Studdy Solution

STEP 1

What is this asking? We need to rewrite the angle 19.35∘19.35^\circ19.35∘ in degrees, minutes, and seconds! Watch out! There are 60 minutes in a degree and 60 seconds in a minute.Don't mix these up!

STEP 2

1. Separate the whole degrees2. Convert the decimal part to minutes3. Convert the remaining decimal to seconds4. Combine degrees, minutes, and seconds

STEP 3

The whole number part of 19.35∘19.35^\circ19.35∘ represents the **degrees**.So, we have **19 degrees** to start with.We'll keep that aside for now and focus on the decimal part.

STEP 4

We have 0.350.350.35 of a degree left.Since there are **60 minutes** in one degree, we multiply this decimal by 60 to find out how many minutes we have: 0.35⋅60=210.35 \cdot 60 = \textbf{21}0.35⋅60=21 This gives us **21 minutes**!

STEP 5

In this case, the result of our calculation in the previous step was a whole number (**21**), so there's no decimal part left to convert to seconds.This means we have **zero seconds**.Sometimes you'll have a decimal left over, and you'll multiply that by **60** to get the **seconds**.

STEP 6

Putting it all together, we have **19 degrees**, **21 minutes**, and **0 seconds**.We write this as 19∘21′0′′19^\circ 21' 0''19∘21′0′′.

STEP 7

The final answer is 19∘21′0′′19^\circ 21' 0''19∘21′0′′.

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Question9. Convert the decimal degree, $19.35^\circ$ to DMS

What is this asking? We need to rewrite the angle $19.35^\circ$ in degrees, minutes, and seconds! Watch out! There are 60 minutes in a degree and 60 seconds in a minute.
Don't mix these up!

1. Separate the whole degrees
2. Convert the decimal part to minutes
3. Convert the remaining decimal to seconds
4. Combine degrees, minutes, and seconds

The whole number part of $19.35^\circ$ represents the degrees.
So, we have 19 degrees to start with.
We'll keep that aside for now and focus on the decimal part.

We have $0.35$ of a degree left.
Since there are 60 minutes in one degree, we multiply this decimal by 60 to find out how many minutes we have: $0.35 \cdot 60 = \textbf{21}$ This gives us 21 minutes!

In this case, the result of our calculation in the previous step was a whole number (21), so there's no decimal part left to convert to seconds.
This means we have zero seconds.
Sometimes you'll have a decimal left over, and you'll multiply that by 60 to get the seconds.

Putting it all together, we have 19 degrees, 21 minutes, and 0 seconds.
We write this as $19^\circ 21' 0''$ .

The final answer is $19^\circ 21' 0''$ .