MHB How can I convert degrees to grades using a conversion factor?

  • Thread starter Thread starter Drain Brain
  • Start date Start date
  • Tags Tags
    Degrees Grades
AI Thread Summary
To convert degrees to grades, use the conversion factor where $90^{\circ} = 100^g$, leading to $1^{\circ} = \frac{10^g}{9}$ and $1^g = \frac{9^{\circ}}{10}$. Start by rewriting the angle in degrees as a product, such as $45^\circ = 45 \cdot 1^\circ$. Replace $1^\circ$ with $\left(\frac{10}{9}\right)^g$, resulting in $45 \cdot \left(\frac{10}{9}\right)^g = 50^g$. For converting grades to degrees, represent $x^g$ as $x \cdot 1^g$ and substitute $1^g$ with $\left(\frac{9}{10}\right)^\circ$, yielding the conversion.
Drain Brain
Messages
143
Reaction score
0

please explain to me how can I utilize this conversion factor to convert degrees to grades

the book says,

$90^{\circ}=100^g$

$\therefore$ $1^{\circ}=\frac{10^g}{9}$ and $1^g=\frac{9^{\circ}}{10}$ - I don't know how to use this in actual convertion please help.

 
Mathematics news on Phys.org
Drain Brain said:
I don't know how to use this in actual convertion
Suppose you want to convert an angle measure from degrees to grades.

Step 1: Represent the number of degrees as a product by 1. For example, rewrite $45^\circ$ as $45\cdot1^\circ$.

Step 2: Replace $1^\circ$ by the quantity from your post, i.e., $\left(\frac{10}{9}\right)^g$. In this example,you get $45\cdot\left(\frac{10}{9}\right)^g=50^g$.

Similarly, to convert from grades to degrees, represent $x^g$ as $x\cdot1^g$ and then replace $1^g$ by $\left(\frac{9}{10}\right)^\circ$. For example,
\[
30^g=30\cdot1^g= 30\cdot\left(\frac{9}{10}\right)^\circ =27^\circ.
\]
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top