Place Value in Numbers

Place Value

• Definition: The value of a digit in a number based on its position or place in the number.
• Places: Units (ones), Tens, Hundreds, Thousands, etc.
• Key Concepts:
  • Each place has a value 10 times the value of the place to its right.
  • The value of a digit depends on its place in the number.

Examples:

• In the number 456, the 4 is in the Hundreds place, the 5 is in the Tens place, and the 6 is in the Units place.
• The value of the digit 4 in the number 456 is 400 (4 x 100).

Fractions

• Definition: A way to represent part of a whole as a ratio of two numbers.
• Key Concepts:
  • Numerator (top number): Tells how many equal parts are being referred to.
  • Denominator (bottom number): Tells how many parts the whole is divided into.
  • Equivalent Fractions: Fractions that have the same value, but different numbers.
• Operations:
  • Adding Fractions: Require a common denominator.
  • Multiplying Fractions: Multiply numerators and denominators separately.

Examples:

• The fraction 3/4 represents 3 equal parts out of a total of 4 equal parts.
• Equivalent fractions: 1/2 = 2/4 = 3/6

Percentages

• Definition: A way to express a value as a fraction of 100.
• Key Concepts:
  • Percentage Increase/Decrease: Calculated as a percentage of the original value.
  • Percentage of a Value: Calculated as a percentage of the original value.
• Conversions:
  • Fraction to Percentage: Divide by the denominator and multiply by 100.
  • Percentage to Fraction: Divide by 100 and simplify.

Examples:

• 25% of 120 is 30 (25/100 x 120).
• The fraction 3/4 is equal to 75% (3 ÷ 4 = 0.75 x 100).

Place Value

• The value of a digit in a number depends on its position or place in the number.
• The places in a number, from right to left, are Units, Tens, Hundreds, Thousands, and so on.
• Each place has a value 10 times the value of the place to its right.
• The value of a digit is determined by its place in the number.

Fractions

• A fraction is a way to represent part of a whole as a ratio of two numbers.
• The numerator (top number) tells how many equal parts are being referred to.
• The denominator (bottom number) tells how many parts the whole is divided into.
• Equivalent fractions are fractions that have the same value but different numbers.
• To add fractions, you need a common denominator.
• To multiply fractions, you multiply the numerators and denominators separately.

Percentages

• A percentage is a way to express a value as a fraction of 100.
• Percentage increase or decrease is calculated as a percentage of the original value.
• Percentage of a value is calculated as a percentage of the original value.
• To convert a fraction to a percentage, you divide by the denominator and multiply by 100.
• To convert a percentage to a fraction, you divide by 100 and simplify.