Learning Outcome 1: Number and Number Relationships

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Learning Outcome 1 Number and Number
Relationships
Grade 10

• 10.1.1

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Rational Numbers

• What is a rational number?
• Rational comes from Ratio
• A ratio is a division sum or a fraction.
• for example Numerator
• Denominator
• A rational number is a ratio between two
  integers,

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• A rational number is a number of the form
• the denominator cannot be 0
  (division by 0 is undefined).
• Formally The set of rational numbers, denoted by
  Q is defined as

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Different forms of Rational Numbers

• Integers example 3, -2, 1, 0
• Proper fractions example
• Improper fractions/Mixed numbers for example
• Terminating decimals (with a limited number of
  decimal places) for example

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• Recurring decimals (where a digit or group of
  digits repeat indefinitely in a decimal number)
  for example
• written as
• written as or
• written as or
• written as
• Note a number such as
• which does not terminate/repeat is an
• irrational number.

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Any rational number can be represented as a
fraction

• You must be able to convert all of the FORMS to a
  fraction

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How do we convert the different forms to
fractions?

• 1. Integers Example
• (simply write an integer as a fraction with a
• denominator 1)

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• 2. Improper fractions/Mixed numbers Example
• (For the numerator
• Denominator x Whole part numerator).
• 7 x 3 4
• 21 4
• 25
• Denominator remains the same

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• 3. Terminating decimals Example
• .
• 5 units, 3 tenths, 2 hundredths, 8
  thousandths
• thousandths
• Simplified

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• 4. Recurring decimals Example1
• Let

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• Example 2
• Let
• Use those with the same decimal part

Use powers of 10 etc.
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To convert from fractions to decimals

• Example 1
• (Try to make the
• denominator a
• power of 10).

• Example 2
• (Try to make the
• denominator a
• power of 10).

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• Example 3

Cannot find a power of 10 as a multiple of
3. (Since neither 2 nor 5 is a factor of 3).
Do long division