Fractions and exact answers

4.1When an answer is exact and when it is a decimal#

If your entry has no decimal point, the calculator gives an exact answer: a fraction, a simplified root or a multiple of pi. If you type a number with a decimal point, the answer is a decimal. You can change the form of the last answer at any time with ◄►.

Example 4.1

Division stays a fraction

1. 1 divided by 3 is an exact fraction, shown as 1/3.

   1÷3enter

Example 4.2

A decimal in the entry gives a decimal

1. Typing 0.5 makes the whole answer a decimal.

   0.5+0.25enter

See also Work with fractions

4.2Type and add fractions#

Press n/d to make a fraction. The cursor starts in the top box. Type the numerator, press ▼ to go to the bottom box (or just keep typing if a number is already in the top box), type the denominator, then press ▶ to leave the fraction. If you type a number first and then press n/d, that number becomes the numerator.

Example 4.3

Add two fractions

1. Type 1 over 3, step out of the fraction, add, then 1 over 6.

   1n/d3▶+1n/d6enter

Example 4.4

Multiply fractions

1. 2/3 times 3/4 simplifies.

   2n/d3▶×3n/d4enter

Example 4.5

A sum as numerator

1. Put a bracket group first. The fraction takes the whole group as its numerator.

   (1+2)n/d4enter

See also Work with fractions

4.3Enter and show mixed numbers#

Press 2ndUn/dn/d (Un/d) for a mixed number. Type the whole part, press ▶, type the numerator, press ▶, then type the denominator.

Example 4.6

Type 2 and one third

1. Whole part 2, numerator 1, denominator 3.

   2ndUn/dn/d2▶1▶3enter

Example 4.7

Show an improper fraction as a mixed number

1. Type 7/2, step out, then pick the first item of the MATH menu (►n/d◄►Un/d) and press enter.

   7n/d2▶math1enter

4.4Convert a decimal to a fraction (and back)#

The F◄►D key (2ndf◄►d◄►) flips an entry between fraction and decimal. Put it after the number you want to convert and press enter. To change the answer you already have, press ◄► instead. For a decimal answer to any entry, press 2nd≈enter (≈) instead of enter.

Example 4.8

Turn 0.75 into a fraction

1. Type 0.75, press 2nd and the toggle key (F◄►D), then enter.

   0.752ndf◄►d◄►enter

Example 4.9

Turn 3/8 into a decimal

1. Type 3/8, step out, press F◄►D, then enter.

   3n/d8▶2ndf◄►d◄►enter

Example 4.10

Switch the last answer to a decimal

1. Work out 1/3 + 1/6, then press the toggle key.

   1n/d3▶+1n/d6enter◄►

Example 4.11

Switch it back

1. Press the toggle key a second time to return to the fraction.

   1n/d3▶+1n/d6enter◄►◄►

Example 4.12

Ask for a decimal answer directly

1. 2nd then enter gives the approximate (decimal) answer.

   1n/d3▶2nd≈enter

See also Convert between fractions and decimals

4.5Square roots in simplest form#

Press 2nd√x² for a square root template, type the number and press enter. Roots that are not whole numbers are simplified: √8 becomes 2√2.

Example 4.13

Simplify a root

1. The square root of 8 is shown as 2√2.

   2nd√x²8enter

Example 4.14

See the root as a decimal

1. Press the toggle key to turn 2√2 into a decimal.

   2nd√x²8enter◄►

Example 4.15

A perfect square

1. The square root of 16 is just 4.

   2nd√x²16enter

Example 4.16

Multiply roots

1. Close the first root with right, then multiply by another root.

   2nd√x²2▶×2nd√x²3enter

See also Find a square root

4.6Answers in terms of pi#

The π key types pi. If your entry is a whole-number multiple of pi, the answer stays in terms of pi. Press ◄► for the decimal value.

Example 4.17

Two pi

1. Type 2 then pi. The answer is kept as 2π.

   2πenter

Example 4.18

Pi as a decimal

1. Press the toggle key to see the decimal.

   πenter◄►