To convert degrees into grades, you need to know the conversion factor. The grade scale is such that 90 degrees is equivalent to 100 grades. Therefore, to convert degrees to grades, you can use the formula:
[tex]\[ \text{grades} = \text{degrees} \times \left(\frac{100}{90}\right) \][/tex]
Let's apply this formula to each of the given degrees:
1. (a) 45°:
[tex]\[ 45 \times \left(\frac{100}{90}\right) = 45 \times \left(\frac{10}{9}\right) = 50 \text{ grades} \][/tex]
2. (b) 36°:
[tex]\[ 36 \times \left(\frac{100}{90}\right) = 36 \times \left(\frac{10}{9}\right) = 40 \text{ grades} \][/tex]
3. (c) 54°:
[tex]\[ 54 \times \left(\frac{100}{90}\right) = 54 \times \left(\frac{10}{9}\right) = 60 \text{ grades} \][/tex]
4. (d) 9°:
[tex]\[ 9 \times \left(\frac{100}{90}\right) = 9 \times \left(\frac{10}{9}\right) = 10 \text{ grades} \][/tex]
5. (e) 72°:
[tex]\[ 72 \times \left(\frac{100}{90}\right) = 72 \times \left(\frac{10}{9}\right) = 80 \text{ grades} \][/tex]
6. (f) 81°:
[tex]\[ 81 \times \left(\frac{100}{90}\right) = 81 \times \left(\frac{10}{9}\right) = 90 \text{ grades} \][/tex]
So, the converted grades are:
- 45° converts to 50 grades
- 36° converts to 40 grades
- 54° converts to 60 grades
- 9° converts to 10 grades
- 72° converts to 80 grades
- 81° converts to 90 grades
