Decimals

1
Decimals

• Decimals are a type of fractional number
• The denominator is always a power of 10
• A decimal point is used to show that it is less
  than 1

The decimal 0.5 represents the fraction 5/10
The decimal 0.25 represents the fraction 25/100
What decimal is represented by the fraction
461/1000?
0.461
2
Significant Digits or Figures

• Significant digits are the most important parts
  of the number
• They tell you how precise a number or measurement
  is
• They are the digits after the decimal point and
  after any zeros
• Trailing zeros count as significant digits

0.000567
0
significant digits
3
4
3
Positions

• Positions tell us how much each digit is worth,
  like they do for whole numbers
• They are the number of spaces each digit is
  behind the decimal point

0 . 0 0 0 0
tenths
ten thousandths
hundredths
thousandths
4
Addition

• Line up the decimal points to make sure
  everything is in the correct column
• Add like you would integers

0.587 0.036
0.623
5
Subtraction

• Line up the decimal points to make sure
  everything is in the correct column
• Subtract like you would integers

0.587 - 0.036
0.551
6
Multiplication

• Move the decimal point of the first number to the
  left one space for each position behind the
  decimal point of the second number
• Multiply that new number by the whole number
  value of the second number (ignore decimal point)
• Make sure to fill in any missing zeros

0.07 x 0.3
x 3 0.021
0 07
0
One position behind decimal
7
Division

• Like multiplication, but move the decimal point
  of the first number to the right one place for
  each position behind the decimal point of the
  second number
• Divide that new number by the whole number value
  of the second number (ignore decimal point)

4 0.2
0 8
0
0.08 0.4
One position behind decimal
8
Review

• Decimals are fractional numbers where the
  denominators are powers of 10
• Significant digits tell you how precise the
  number is
• Decimals add and subtract like integers
• Multiplying two decimals makes a smaller decimal
• Dividing two decimals makes a larger number