Decimals, Fractions, and Percents

Rounding 

  • Sometimes after multiplying decimals or after converting a fraction to a decimal, the number of places after the decimal is too large to be manageable 

  • Extra numbers can contribute to calculation errors 

  • It is advisable to always round decimals 

Significant Figures/Digits 

  • A significant digit is one that is measurable 

  • The number is significant digits depends on the measuring device and capabilities 

  • Must always use the smallest number of significant digits 

Rules for Significant Figures 

  1. Digits other than 0 are significant 

  1. Final 0s after a decimal are significant 

  1. 0s between two other significant figures are significant 

  1. 0s used to place a decimal are not significant 

Whole/Arabic Numbers 

  • Based on the number 10 

  • Value of a number is determined by the place to the left of the decimal it holds 

Fractions 

  • Used to write numbers that are not whole 

  • Represent part of a whole unit 

  • The division of two whole numbers can also be represented by a fraction 

  • Numerator on top 

  • Denominator on bottom 

  • Denominator tells us how many parts the whole is divided into 

  • Numerator tells us how many of those parts exist 

  • Numerator can be 0 

  • 0 numerator means the fraction equals 0 

  • Denominator can never be 0 

  • Division by 0 is undefined 

Mixed Numbers 

  • Numbers that combine fractions and whole numbers 

  • Can be written as an improper fraction 

  • To change from a mixed number to an improper fraction, multiply the denominator and the whole number, then add the numerator 

  • An improper fraction should always be converted into a mixed number 

Decimals 

  • Decimal points express amounts less than one 

  • 1/10, 0.1 - tenths 

  • 1/100, 0.01 - hundredth 

  • 1/1000, 0.001 = thousandths 

  • To change a fraction to a decimal, divide