## Fractions to Decimals

Suppose we had a fraction like $\frac12,$ and we wanted to convert it to decimaldecimal notation. All we have to do is divide 2 into 1 like this:

## Binary Numeral System

A numeral system is a way of representing numbers, not to be confused with number systems which classify numbers based on properties.

## Converting Fractions

Suppose we had a fraction like $\frac12,$ and we wanted to convert it to decimaldecimal notation. All we have to do is divide 2 into 1 like this:

## Decimal to Binary

Suppose we wanted to convert the decimal number 27 to binary. To get started we have to find out what place the first digit is going to be in. 27 is between $2^4=16$ and $2^5=32$. Our number is less than 32 so we can put a 0 in the "thirty-twos" place. We put a 0 in the thirty-twos place because if we put a 1 that would immediately turn the value of our binary number to at least 32. However, sixteen will fit inside 27 so we can put a 1 in the "sixteens" place.

## Fraction Operations I

The most basic fraction operations are addition and multiplication. So let's start there. There are two simple rules to follow when we add or multiply fractions.

## Fraction Terminology

factor a factor is an integer that divides another integer with no remainder leftover

Hexadecimal is different from binary and decimal notation (base 10) in that there are sixteen unique digits whereas in decimal we have ten. Since we have sixteen digits we have to designate six new digits which are the letters A, B, C, D, E, and F. 'A' stands for 10, 'B' is 11, 'C' 12, 'D' 13, 'E' 14, and 'F' is 15.

## Mathematics Symbols

The most common symbols found in mathematics are listed below. The table is not exhaustive but covers numerals, trigonometry and geometry. If you would like to see a mathematics symbol added you can contact North Penn Networks. Likewise if there are errors please also reach out. The math symbols below are rendered with MathJax. $+$plus or additon sign $-$minus or subtraction sign $\times$times or multiplication sign $\div$division sign $=$equal sign $\neq$inequality $\gt$greater than $\geq$greater than or equal to $\lt$less than $\leq$less than or equal to $\%$percent $\sqrt{n}$square root of n $\left|n\right|$absolute value of n $\infty$infinity $\parallel$parallel $\perp$perpendicular $\angle$angle $!$factorial $!!$double...

## Subtraction and Division

The most common terms found in subtraction and division arithmetic are listed below. If you find any math errors, you may reach out to North Penn Networks using the contact form. $a-b=c$ minuend the first number in a subtraction operation; the subtrahend is taking away from this number; the minuend is $a$ subtrahend the second number in a subtraction operation; the amount taken away from the minuend; the subtrahend is $b$ difference the result of taking the subtrahend from the minuend; the difference is $c$ $a \div b = c$ dividend the number being divided, $a$...

## The Decimal System

The decimal system is a way of representing a number using powers of ten. The first digit before the decimal is the ones place. Suppose we have a digit, $d$, that is in the ones place. Since $d$ is in the ones place the value of $d = d \times 10^0.$ We use 10 since we are in the decimal system (base 10). We use 0 for the exponent because we are 1 digit to the left of the decimal. Why 0? In Computer Science and Mathematics, counting is often started at 0. Also...