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Classic Graphing 84 manual · Chapter 5 of 25

Fractions, angles and conversions

Turn decimals into fractions and back, work in mixed numbers, convert degrees, minutes and seconds, and convert between rectangular and polar coordinates.

5.1Convert a decimal to a fraction#

Answers appear as decimals. To see a fraction, finish the entry with ►Frac (math, item 1). It works for any number that is a ratio of whole numbers with a denominator under 10000; other numbers stay decimal.

  1. Type the number
  2. math
  3. 1:►Frac
  4. enter
Show an answer as a fraction
Example 5.1

Decimal to fraction

3.75=1543.75=\frac{15}{4}

  1. Type 3.75, press math and 1 (►Frac), then enter.

    3.75math1enter
Result of the example "Decimal to fraction" The display shows: 3.75►Frac / 15/4.
You should see3.75►Frac 15/4
Example 5.2

Fraction of the last answer

14+14=12\frac14+\frac14=\frac12

  1. Calculate 1/4 + 1/4. The answer is the decimal .5.

    1÷4+1÷4enter

  2. Press math then 1. Ans is typed for you. Press enter.

    math1enter
Result of the example "Fraction of the last answer" The display shows: 1/4+1/4 / .5 / Ans►Frac / 1/2.
You should seeAns►Frac 1/2

Press math then ◀ for the FRAC tab. Item 2 (►F◄►D) switches the last answer between fraction and decimal each time you use it.

Example 5.3

Toggle between fraction and decimal

  1. Calculate 1/4, which shows .25.

    1÷4enter

  2. Press math, left (FRAC tab), 2, enter. The answer is shown as 1/4.

    math◀2enter
Result of the example "Toggle between fraction and decimal" The display shows: 1/4 / .25 / Ans►F◄►D / 1/4.
You should seeAns►F◄►D 1/4
The FRAC tab of the MATH menu. The display shows: MATH NUM CMPLX PROB [FRAC] / 1:n/d / 2:►F◄►D.
The FRAC tab of the MATH menu.

5.2Convert a fraction to a decimal#

Example 5.4

Fraction to decimal

18=0.125\frac18=0.125

  1. Type 1/8, press math and 2 (►Dec), then enter.

    1÷8math2enter
Result of the example "Fraction to decimal" The display shows: 1/8►Dec / .125.
You should see1/8►Dec .125

5.3Show answers as mixed numbers#

By default fractions are improper (7/2). In MODE, set FRACTION TYPE to Un/d and ►Frac gives mixed numbers such as 3 1/2, written 3⌟1/2 on the screen. The row is the seventh in the MODE list.

Example 5.5

A mixed number

72=312\frac72=3\tfrac12

  1. In MODE move down 6 rows, press right to choose Un/d, enter, and return home.

    mode▼▼▼▼▼▼▶enter2ndQUITmode

  2. Type 7/2 and convert with ►Frac.

    7÷2math1enter
Result of the example "A mixed number" The display shows: 7/2►Frac / 3⌟1/2.
You should see3⌟1/2

FRACTION TYPE does not change decimals, only the way fractions are written.

5.4Show every answer as a fraction#

Set ANSWERS to FRAC in MODE (the eighth row) and every real answer that can be a fraction is shown as one automatically. DEC always shows decimals; AUTO shows what you typed.

Example 5.6

ANSWERS = FRAC

  1. In MODE move down 7 rows, right twice to FRAC, enter, then return home.

    mode▼▼▼▼▼▼▼▶▶enter2ndQUITmode

  2. Type 1/4 + 1/4.

    1÷4+1÷4enter
Result of the example "ANSWERS = FRAC" The display shows: 1/4+1/4 / 1/2.
You should see1/2

5.5Degrees, minutes and seconds#

Press 2ndANGLEapps for the ANGLE menu.

ItemMeaning
1: °Degree mark. Mark one value as degrees even in Radian mode.
2: 'Minute mark (also used for seconds with a double quote, alpha add).
3: ʳRadian mark. Mark one value as radians even in Degree mode.
4: ►DMSShow the answer as degrees, minutes and seconds.
5: R►Pr(Polar radius r from x and y: r=x2+y2r=\sqrt{x^2+y^2}.
6: R►Pθ(Polar angle θ from x and y.
7: P►Rx(Rectangular x from r and θ: x=rcos⁡θx=r\cos\theta.
8: P►Ry(Rectangular y from r and θ: y=rsin⁡θy=r\sin\theta.
The ANGLE menu. The display shows: ANGLE / 1:° / 2:' / 3:ʳ / 4:►DMS / 5:R►Pr( / 6:R►Pθ( / 7↓P►Rx(.
The ANGLE menu.
Example 5.7

Decimal degrees to degrees, minutes, seconds

30.5∘=30∘ 30′ 0"30.5^\circ=30^\circ\,30'\,0"

  1. Type 30.5, press 2nd apps, 4 (►DMS), enter.

    30.52ndANGLEapps4enter
Result of the example "Decimal degrees to degrees, minutes, seconds" The display shows: 30.5►DMS / 30°30'0".
You should see30°30'0"

5.6Convert between rectangular and polar coordinates#

r=x2+y2,θ=tan⁡−1 ⁣(yx)r=\sqrt{x^{2}+y^{2}},\qquad \theta=\tan^{-1}\!\left(\frac{y}{x}\right)
From the point (x, y) to polar coordinates.
Example 5.8

Radius of the point (3, 4)

r=32+42=5r=\sqrt{3^2+4^2}=5

  1. Press 2nd apps, 5 (R►Pr(), type 3, 4 and a bracket.

    2ndANGLEapps53,4)enter
Result of the example "Radius of the point (3, 4)" The display shows: R►Pr(3,4) / 5.
You should seeR►Pr(3,4) 5
Example 5.9

Angle of the point (1, 1)

θ=tan⁡−1(1)\theta=\tan^{-1}(1)

  1. Choose Degree mode first.

    mode▼▼▶enter2ndQUITmode

  2. Press 2nd apps, 6 (R►Pθ(), type 1, 1 and a bracket.

    2ndANGLEapps61,1)enter
Result of the example "Angle of the point (1, 1)" The display shows: R►Pθ(1,1) / 45.
You should see45
Example 5.10

Rectangular x from r and θ

x=2cos⁡0∘=2x=2\cos 0^\circ=2

  1. Press 2nd apps, 7 (P►Rx(), type 2, 0 and a bracket.

    2ndANGLEapps72,0)enter
Result of the example "Rectangular x from r and θ" The display shows: P►Rx(2,0) / 2.
You should seeP►Rx(2,0) 2

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