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Natural Scientific 991 manual · Chapter 3 of 18

Calculations

Arithmetic, order of operations, exact fractions and roots, decimals, percent, scientific and engineering notation, and Ans.

3.1Order of operations#

Powers and roots come first, then multiplication and division, then addition and subtraction. Use brackets to change the order. Implied multiplication such as 2π binds tighter than a division sign, so 1÷2π means 1 divided by (2π).

Example 3.1

Brackets change the order

  1. Type (2 + 3) × 4.

    (2+3)×4

  2. Equals.

    =
Result of the example "Brackets change the order" The display shows: (2+3)×4 / 20.
You should see20
Example 3.2

Implied multiplication

  1. Type 1 ÷ 2π.

    1÷2SHIFTπ×10ˣ

  2. Equals, then press S⇔D for the decimal.

    =S⇔D
Result of the example "Implied multiplication" The display shows: 1÷2π / 0.1591549431.
You should see0.1591549431
a+b×c=a+(b×c)a+b\times c = a+(b\times c)
Multiplication is done before addition

3.2Negative numbers versus subtraction#

Use the (−) key for the sign of a number, as in -5, and − for subtraction. They are different keys.

Example 3.3

Add a negative number

  1. Type -5 + 8.

    (−)5+8

  2. Equals.

    =
Result of the example "Add a negative number" The display shows: -5+8 / 3.
You should see3

3.3Add and multiply fractions#

Press / to open a fraction template. Type the numerator, press ▼ to move to the denominator, type it, then press ▶ to step out of the fraction. If you typed a number first, that number becomes the numerator.

Example 3.4

Add two fractions

12+13\frac12+\frac13

  1. Type 1/2.

    /1▼2▶

  2. Plus 1/3.

    +/1▼3▶

  3. Equals.

    =
Result of the example "Add two fractions" The display shows: 1/2+1/3 / 5/6.
You should see5/6
Example 3.5

Multiply fractions

  1. Type 2/3 × 3/4. Typing the number first makes it the numerator.

    2/3▶×3/4▶

  2. Equals. The answer is reduced.

    =
Result of the example "Multiply fractions" The display shows: 2/3×3/4 / 1/2.
You should see1/2
12+13=56\frac{1}{2}+\frac{1}{3}=\frac{5}{6}
The fraction template keeps exact answers

3.4Mixed numbers and improper fractions#

Press SHIFT// to type a mixed number: whole part, then numerator, then denominator. Use ▶ to move from box to box. Press SHIFTa b/c⇔d/cS⇔D on an answer to switch between mixed and improper form.

Example 3.6

Type a mixed number

  1. Open the mixed template and type 1, 1, 2.

    SHIFT//1▶1▶2▶

  2. Add 1/2 and press equals.

    +/1▼2▶=
Result of the example "Type a mixed number" The display shows: 1⌟1/2+1/2 / 2.
You should see2
Example 3.7

Show an answer as a mixed number

  1. Calculate 7/2.

    7/2▶=

  2. Press SHIFT then S⇔D.

    SHIFTa b/c⇔d/cS⇔D
Result of the example "Show an answer as a mixed number" The display shows: 7/2 / 3 1/2.
You should seeThe answer changes from 7/2 to 3 1/2. Press SHIFT S⇔D again to go back.

3.5Convert a decimal to a fraction#

Type the decimal and press =. The answer is shown as a fraction when one fits exactly.

Example 3.8

0.1 + 0.2 as a fraction

  1. Type 0.1 + 0.2 and press equals.

    0.1+0.2=
Result of the example "0.1 + 0.2 as a fraction" The display shows: 0.1+0.2 / 3/10.
You should see3/10
Example 3.9

1.5 as a fraction

  1. Type 1.5 and press equals.

    1.5=
Result of the example "1.5 as a fraction" The display shows: 1.5 / 3/2.
You should see3/2

3.6Convert a fraction or root to a decimal#

Press S⇔D after an answer to switch between the exact form and the decimal form. Press SHIFT≈= instead of = to get the decimal straight away.

Example 3.10

Fraction to decimal

  1. Calculate 1 ÷ 3.

    1÷3=

  2. Press S⇔D.

    S⇔D
Result of the example "Fraction to decimal" The display shows: 1÷3 / 0.3333333333.
You should see0.3333333333
Example 3.11

Decimal straight away

  1. Type 2/3, then press SHIFT equals (≈).

    2/3▶SHIFT≈=
Result of the example "Decimal straight away" The display shows: 2/3 / 0.6666666667.
You should see0.6666666667
Example 3.12

Square root to a decimal

  1. Calculate √8, then press S⇔D.

    √8=S⇔D
Result of the example "Square root to a decimal" The display shows: √8 / 2.828427125.
You should see2.828427125
  1. Answer 1/3
  2. S⇔D
  3. 0.3333333333
  4. S⇔D
  5. 1/3
Switch between exact and decimal

3.7Exact roots and π#

Square roots are simplified and kept exact. Multiples of π are kept exact too, until you ask for a decimal.

Example 3.13

Simplify a root

  1. Type √8 and press equals.

    √8=
Result of the example "Simplify a root" The display shows: √8 / 2√2.
You should see2√2
Example 3.14

Rationalize a denominator

  1. Type 1 divided by √2.

    1/√2▶

  2. Equals.

    =
Result of the example "Rationalize a denominator" The display shows: 1/(√2) / √2/2.
You should see√2/2
Example 3.15

Add roots

  1. Type √18 + √2. Press right to leave the first root.

    √18▶+√2=
Result of the example "Add roots" The display shows: √(18)+√2 / 4√2.
You should see4√2
Example 3.16

Keep π exact

  1. Type π × 2/3 and press equals.

    SHIFTπ×10ˣ×2/3▶=
Result of the example "Keep π exact" The display shows: π×2/3 / 2π/3.
You should see2π/3

3.8Find a percentage#

Type SHIFT%( after a number to make it a percent. 15%=15100=0.1515\% = \frac{15}{100} = 0.15.

Example 3.17

15% of 200

  1. Type 200 × 15 then the percent key.

    200×15SHIFT%(

  2. Equals.

    =
Result of the example "15% of 200" The display shows: 200×15% / 30.
You should see30

3.9Enter numbers in scientific notation#

Press ×10ˣ to type "times ten to the power". Type the exponent in the box that appears. Use (−) inside the box for a negative exponent.

Example 3.18

2 × 10³

  1. Type 2, the ×10ˣ key, and 3.

    2×10ˣ3

  2. Equals.

    =
Result of the example "2 × 10³" The display shows: 2ᴇ3 / 2000.
You should see2000
Example 3.19

A small number

  1. Type 2 × 10 to the minus 3.

    2×10ˣ(−)3=
Result of the example "A small number" The display shows: 2ᴇ-3 / 1/500.
You should see1/500

3.10Show an answer in engineering notation#

Press ENG after an answer to move to an exponent that is a multiple of three, as used with units such as kilo and milli. Press ENG again to go further down, and SHIFT←ENGENG to go back up.

Example 3.20

Move to ×10³

  1. Calculate 123456.

    123456=

  2. Press ENG.

    ENG
Result of the example "Move to ×10³" The display shows: 123456 / 123.456×10^3.
You should see123.456×10^3
Example 3.21

Step the other way

  1. Calculate 123456, then SHIFT ENG.

    123456=SHIFT←ENGENG
Result of the example "Step the other way" The display shows: 123456 / 0.123456×10^6.
You should see0.123456×10^6

3.11Use the last answer (Ans)#

Every answer is saved in Ans. Press Ans to type it into a new line. If you start a new line with an operator, Ans is inserted for you.

Example 3.22

Operator after an answer

  1. Calculate 2 + 3.

    2+3=

  2. Press × 2 and equals.

    ×2=
Result of the example "Operator after an answer" The display shows: Ans×2 / 10.
You should seeAns×2 10
Example 3.23

The Ans key

  1. Calculate 2 + 3, then type Ans + 1.

    2+3=Ans+1=
Result of the example "The Ans key" The display shows: Ans+1 / 6.
You should see6

3.12Degrees, minutes and seconds#

Press °'" while typing to place the degree mark, then the minute mark, then the second mark. After an answer, press °'" to see a decimal angle as degrees, minutes and seconds.

Example 3.24

Enter 3°30′

  1. Type 3, the DMS key, 30, the DMS key.

    3°'"30°'"

  2. Equals gives the angle as a decimal.

    =
Result of the example "Enter 3°30′" The display shows: 3°30° / 3.5.
You should see3.5
Example 3.25

Show 3.5 as DMS

  1. Calculate 3.5, then press the DMS key.

    3.5=°'"
Result of the example "Show 3.5 as DMS" The display shows: 3.5 / 3°30'0".
You should see3°30'0"

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