SEQUENCE OF MATHEMATICAL OPERATIONS


Remember

Please Excuse My Dear Aunt Sally

Parentheses (P)

Exponents (E)

Multiply (M)

Divide (D)

Add (A)

Subtract (S)

 

SIGNIFICANT FIGURES / SIGNIFICANT DIGITS


Figures arrived at by counting are often exact. On the other hand, figures arrived at by measuring are approximate. Significant figures express the accuracy of the measurement.

When counting significant figures, all digits (including zeros) are counted EXCEPT those zeros that are to the left of the number.

Example: 4.3 contains 2 significant figures/digits

0.0234 contains 3 significant figures/digits

0.1100 contains 4 significant figures/digits

 

ROUNDING OFF NUMBERS


Rule 1:
If the first digit to the right of the last significant digit is a 6, 7, 8, or 9 round up by increasing the last significant digit by one and dropping all the following digits. (Example rounded off to three significant digits to the right of the decimal)
45.784624 becomes 45.785

Rule 2: If the first digit to the right of the last significant digit is a 0, 1, 2, 3, or 4, round down by leaving the last significant digit unchanged, and dropping all the following digits. (Example rounded off to two significant digits to the right of the decimal) 45.784624 becomes 45.78

Rule 3: If the first digit to the right of the last significant digit is a 5, and there are additional digits other than 0, round up by increasing the last significant digit by one, and dropping all the following digits. (Example rounded off to two significant digits to the right of the decimal) 7.1450004 becomes 7.15

Rule 4: If the first digit to the right of the last significant digit is a 5, and there are no additional digits other than 0, round to the nearest even digit. This rule is also known as the odd-even rule for rounding off numbers. (Example rounded off to two significant digits to the right of the decimal) 7.1450000 becomes 7.14

 

EXPONENTS


Zero exponent 

Negative exponent 

Multiplication 

Division 

Power of a product 

Power of a power 

Root of a power 

Fractional exponents     

Radicals     

 

INTERPOLATION

To interpolate a value for any number in a given table  X =+

X = unknown

Am = measured amount

A1 = lower of the two amounts bracketing the measured amount

A2 = higher of the two amounts bracketing the measured amount

B1 = value (from table) for A1

B2 = value (from table) for A2

 

SCIENTIFIC NOTATION


A whole number between 1 and 10 times the proper power of ten, also called standard form.

Example: 4.30 x 104

 

NUMERICAL CONSTANTS (extended)


p = 3.14159 26535 89793 23846 26433 83279 50288 41971

= 2.71828 18284 59045 23536 02874 71352 66249 77572

 

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