Everyday calculations

3.1Chain and AOS calculation methods#

The calculator starts in Chain mode: each operator finishes the previous operation first, so 2 + 3 × 4 gives 20. In AOS mode (algebraic operating system) multiplication and powers come before addition, so the same entry gives 14. Change it in FORMAT; see Modes and settings.

Example 3.1

Chain method (start setting)

1. 2 + 3 × 4 is worked left to right.

   2+3×4=

Example 3.2

AOS method

1. Switch to AOS in FORMAT, leave, then enter the same sum.

   2NDFORMAT.↓↓↓↓2NDSETENTER2NDQUITCPT2+3×4=

Example 3.3

Brackets work in both methods

1. Brackets always make the inner sum first.

   2×(3+4)=

See also Use brackets to control the order

3.2Percent#

On its own, % divides the number by 100. After a plus or minus, it takes that percent of the number before it, so you can add a sales tax or take off a discount.

Example 3.4

Add 5% to 100

1. Type 100 + 5 %, then press equals.

   100+5%=

Example 3.5

Take 10% off 100

1. Type 100 − 10 %, then equals.

   100−10%=

Example 3.6

5% of 200

1. After a multiply, % just divides by 100.

   200×5%=

See also Find a percentage of a number

3.3Squares, roots, powers and reciprocals#

Press x² to square, √x for a square root and 1/x for the reciprocal. For other powers type the base, press yˣ, then the exponent. For the x-th root press 2NDx√yyˣ: type the number, the root key, then the root number.

Example 3.7

Square

1. 12 squared.

   12x²

Example 3.8

Power

1. 2 to the power 10.

   2yˣ10=

Example 3.9

Cube root

1. 27, then the root key, then 3.

   272NDx√yyˣ3=

Example 3.10

Square root

1. The square root of 2, rounded to two decimals.

   2√x

Example 3.11

Reciprocal

1. 1/8 shows as 0.13 with two decimals.

   81/x

See also Powers and exponentsFind a square rootCube roots and other roots

3.4Natural logarithm and e to a power#

LN gives the natural logarithm. 2NDeˣLN gives e to the power of the displayed number. Pressing INV first with LN also gives e to a power.

Example 3.12

ln of 10

1. Show nine decimals first, then take ln of 10.

   2NDFORMAT.9ENTER2NDQUITCPT10LN

Example 3.13

e to the power 1

1. The number e.

   2NDFORMAT.9ENTER2NDQUITCPT12NDeˣLN

See also Natural logs and the number e

3.5Factorials, permutations and combinations#

Factorial is 2NDx!). For permutations and combinations type n, press 2NDnPr− (nPr) or 2NDnCr× (nCr), type r and press equals. Factorials work for whole numbers up to 69.

Example 3.14

Factorial

1. 5 factorial.

   52NDx!)

Example 3.15

Permutations

1. Arrange 2 of 5.

   52NDnPr−2=

Example 3.16

Combinations

1. Choose 5 of 52 cards.

   522NDnCr×5=

See also Count arrangements and selections (nPr and nCr)Calculate a factorial

3.6Trigonometry and angle units#

Type the angle, then press the shifted trig key: 2NDSINx² is SIN, 2NDCOS1/x COS, 2NDTAN÷ TAN. Press INV first for the inverse. Press 2NDHYP√x (HYP) first for the hyperbolic versions. The angle unit is set in FORMAT (degrees at the start).

Example 3.17

Sine of 30 degrees

1. Type 30 and press SIN.

   302NDSINx²

Example 3.18

Inverse sine

1. INV then SIN of 0.5 gives 30 degrees.

   .5INV2NDSINx²

Example 3.19

Inverse tangent

1. INV then TAN of 1 gives 45.

   1INV2NDTAN÷

Example 3.20

Sine in radians

1. Switch FORMAT to RAD, show nine decimals, then sin 1.

   2NDFORMAT.↓2NDSETENTER2NDQUITCPT2NDFORMAT.9ENTER2NDQUITCPT12NDSINx²

Example 3.21

Hyperbolic sine

1. Press HYP, then SIN.

   2NDFORMAT.9ENTER2NDQUITCPT12NDHYP√x2NDSINx²

See also Find sine, cosine and tangentSet degrees or radians

3.7Round, random numbers and the last answer#

2NDROUNDINV (ROUND) rounds the displayed number to the number of decimals in FORMAT, and keeps the rounded value. 2NDRAND( (RAND) shows a random number between 0 and 1. 2NDANS= (ANS) recalls the last answer. 2NDK% (K) repeats the last operation and number every time you press equals.

Example 3.22

Recall the last answer

1. Work out 2 + 3, then use ANS in a new sum.

   2+3=×2NDANS==

Example 3.23

K constant

1. After 2 + 3 = 5, press × 4, then 2ND % (K), then = again.

   2+3=×42NDK%=