Whole Number Place Value Notes

• Etymology and Definition: The term mathematics is derived from a Greek word that means "__________".

• Biblical Integration: The study of mathematics is grounded in biblical principles, specifically referencing Proverbs 1:7a: "The fear of the LORD is the beginning of __________."

• Essential Question: How does the place value system show that math is a __________?

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The Place Value System

• Periods: Whole numbers are organized into groups of three digits called __________. The periods discussed include:

  • __________

  • __________

  • __________

  • __________

• Place Values within Periods: Each period contains three place value positions:

  • H: __________

  • T: __________

  • O: __________

Representing Whole Numbers: Forms

Using the example number $503,017,246$, numbers can be expressed in four distinct ways:

• Standard Form: The number written using digits and commas to separate periods.

  • Example: $\_\_\_\_\_\_\_\_\_\_$

• Word Form: Expressing the value of each period in words.

  • Millions period: "__________"

  • Thousands period: "__________"

  • Ones period: "__________"

• Expanded Form: Writing the number as a sum of the values of its digits.

  • Example: $500,000,000 + 3,000,000 + 10,000 + 7,000 + 200 + 40 + 6$

• Expanded Form using Multiplication: Writing the number as the sum of each non-zero digit multiplied by its place value.

  • Example: $(5 \times 100,000,000) + (3 \times 1,000,000) + (1 \times 10,000) + (7 \times 1,000) + (2 \times 100) + (4 \times 10) + (6 \times 1)$

Practice Numbers for Conversion

The following numbers are provided to be written in all four forms:

• $34,056,230,800$

• $9,720,480,056$

• $34,500,872$

Comparing Whole Numbers

Mathematical symbols used for comparison include:

• >: __________

• <: __________

• C5: __________

Examples of Comparison:

• 84,769,320 > 84,768,320

• 103,278,600 > 99,846,759 (A 9-digit number is __________ than an 8-digit number).

• 20,040,570 < 20,000,000 + 400,000 + 500 + 70 (The latter equals $20,400,570$).

Rounding Whole Numbers

Rounding is visualized using number lines to determine which benchmark number the target value is closer to.

• Example 1: Rounding $354,829$ to the nearest hundred thousand:

  • Lower Benchmark: $\_\_\_\_\_\_\_\_\_\_$

  • Upper Benchmark: $\_\_\_\_\_\_\_\_\_\_$

  • Midpoint: $\_\_\_\_\_\_\_\_\_\_$

  • Determination: Since 354,829 > 350,000, it rounds to $\_\_\_\_\_\_\_\_\_\_$.

• Example 2: Rounding $1,465,309$ to the nearest thousand:

  • Lower Benchmark: $\_\_\_\_\_\_\_\_\_\_$

  • Upper Benchmark: $\_\_\_\_\_\_\_\_\_\_$

  • Midpoint: $\_\_\_\_\_\_\_\_\_\_$

  • Determination: Since $\_\_\_\_\_\_\_\_\_\_$, it rounds to $\_\_\_\_\_\_\_\_\_\_$.

• Example 3: Rounding $378,720,526,482$ to the nearest ten billion:

  • Lower Benchmark: $\_\_\_\_\_\_\_\_\_\_$

  • Upper Benchmark: $\_\_\_\_\_\_\_\_\_\_$

  • Midpoint: $\_\_\_\_\_\_\_\_\_\_$

  • Determination: Since $\_\_\_\_\_\_\_\_\_\_$, it rounds to $\_\_\_\_\_\_\_\_\_\_$.