Decimals

The decimal number system is a base-10 system, with digits from 0 through 9. A decimal fraction is a decimal number whose value is more than 0 but less than one. A mixed number is a combination of a whole number and a decimal fraction.

 The part of the number to the left of the decimal point is the whole number part, while the part of the number to the right of the decimal point is the fractional part.

The decimal point is a symbol that shows the boundary between the whole number part (integer) and the fractional number part (decimal fraction) of a number. 

For example: 0.789, 1.5, 3.33, 4.95, -12.6

The first number, 0.789, doesn’t have a whole number component. When that happens, the whole number part is understood to be 0.

Decimal places are the digits to the right of the decimal point. For example, the number 1.5 has one decimal place; the number 3.33 has two decimal places. The first number to the right of the decimal point is the first decimal place. The second number is the second decimal place, and so forth.

Precision

Decimal places can express precision. Most people use accurate and precise as synonyms, but they don't mean the exactly same thing. Accuracy is the degree of correctness of a quantity. Precision is the degree to which the correctness of a quantity is expressed.

Converting Fractions to Decimals

Turning a fraction into a decimal number is easy.  For example,

1/4 = 0.25; 1/2 = 0.5; 3/4 = 0.75

The rule for converting fractions to decimals is to simply divide the denominator into the numerator to get the answer. 

Converting Decimals to Fractions

The conversion rule is simple: Set the decimal up as a fraction and reduce it to its simplest terms. For example, to convert 0.75 to a fraction, set up the fraction as 75/100.

To reduce the fraction, divide both the top and bottom by a common factor.

75/100 = 3/4 

Rounding

Sometimes, the answer to a decimal calculation isn't useful because it has too many decimal places. In this situation, you need to do some rounding, replacing the answer with another value that is very close to the original. You round up and round down, depending on the original answer and the number of decimal places you want to round to.

  1. Figure out how many places you want to round to.
  2. Look at the numbers to the right of your chosen rounding place.
  3. Round up or down depending on the number to the immediate right of your chosen rounding place. If that digit is 5 or greater, round up to the next number.