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MAT 156 topics for UNIT #4
7-1, 7-3, 7-2, 8-2, 7-4, 8-1
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*Animated tutorials available are listed as blue web-page links
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7-1: Place Value:

• Place Value
• Write the name in words given a decimal
• Write the decimal number from the word name
  
  

7-1: Relationship between rational numbers in fraction and decimal form :

• Visual Manipulatives
  • Base ten blocks (1, 1/10, 1/100)
  • Money (dollar, dime and penny)
• Rational numbers can be written in 3 forms:
  • Fractional form (no decimals allowed in fraction form)
  • Decimal form (can terminate OR repeat - no fractions allowed in decimal form)
  • percents (no repentends - bar- allowed in percent form)
• Rational numbers =
  any number that CAN be written in its fraction form as
  • Terminates in decimal form if the denominator has no factors other than 2 or 5.
  • Repeats in decimal form if the denominator does have factors other than 2 or 5 (these are studied in 6-3)
• Decimal Fraction = -- ALWAYS TERMINATES in decimal form
  
• Be able to convert between fractions (to decimal fractions) to decimals that TERMINATE. Be able to tell ahead of time how many places it will terminate in.
  
• Be able to convert a terminating decimal back into a fraction in its most simplified form. Use the expanded notation form (by place value).
  
  

7-3: Repeating decimals:

• If the fraction cannot be written as a decimal fraction (if the denominator has factors other than 2 or 5) then it will REPEAT. Be able to write as a repeating decimal and label the REPETEND.

• Given a repeating decimal, use algebra to write the decimal as an exact fraction, in its simplest form.

• Be able to determine whether a rational number, given in its fractional form, will repeat or terminate as a decimal. If it will repeat, within how many places.
  
  

7-2: Decimal operations:

• Arithmetic (operations) on decimals- Be able to explain (or show proof for) all shortcuts on the four operations and be able to perform each with or without the shortcut (as decimal fractions).

• Addition -
• Be able to explain why you need to line up the decimals
• Subtraction -
• Be able to use equal addition and explain why it works
• Multiplication -
• Show why it works to just add up the number of decimal places and move it that many places for the final answer.
• Division -
  • Show why it works to move the decimal place of the divisor and the dividend by the same amount.

8-2: Percents:

• Definition : (per cent = per hundred)
• Be able to convert any rational number to its decimal, fraction and percent form
  • convert fractions to percents and percents(must go through definition form: n/100) to fractions
  • convert decimals to percents (must go through definition form: n/100) and percents to decimals
    (fractions to decimals and reverse are done in 6-1 and 6-3)
• Solve simple equations of the form 25% of 8 is 2
  
  

7-4: Real numbers:

• Simplify radicals
• Discuss irrational numbers (like )
• never repeats or terminates as a decimal
  (cannot be written as an exact decimal)
• cannot be written as a
• cannot be written as percents

8-1: Proportions:

• Ratios
• Solving proportions
• Solving applications involving proportions