Historical Counting Systems: Background You’ll Need 1

  • Understand where and how to round numbers

Identify the Place Value of a Digit

Identifying the place value of a digit is a foundational step in mastering number rounding techniques. By using a place value chart, we can effectively categorize digits into groups of three, or periods, such as ones, thousands, millions, and beyond. This organization is not just for clarity—it directly informs where to round numbers for simplification, as rounding typically occurs at these period boundaries. In written form, we use commas to separate these periods, providing visual cues for where rounding can take place in larger numbers.

The chart below shows how the number [latex]5,278,194[/latex] is written in a place value chart.

A chart titled 'Place Value' with fifteen columns and 4 rows, with the columns broken down into five groups of three. The header row shows Trillions, Billions, Millions, Thousands, and Ones. The next row has the values 'Hundred trillions', 'Ten trillions', 'trillions', 'hundred billions', 'ten billions', 'billions', 'hundred millions', 'ten millions', 'millions', 'hundred thousands', 'ten thousands', 'thousands', 'hundreds', 'tens', and 'ones'. The first 8 values in the next row are blank. Starting with the ninth column, the values are '5', '2', '7', '8', '1', '9', and '4'.

 

  • The digit [latex]5[/latex] is in the millions place. Its value is [latex]5,000,000[/latex].
  • The digit [latex]2[/latex] is in the hundred thousands place. Its value is [latex]200,000[/latex].
  • The digit [latex]7[/latex] is in the ten thousands place. Its value is [latex]70,000[/latex].
  • The digit [latex]8[/latex] is in the thousands place. Its value is [latex]8,000[/latex].
  • The digit [latex]1[/latex] is in the hundreds place. Its value is [latex]100[/latex].
  • The digit [latex]9[/latex] is in the tens place. Its value is [latex]90[/latex].
  • The digit [latex]4[/latex] is in the ones place. Its value is [latex]4[/latex].
    In the number [latex]63,407,218[/latex]; find the place value of each of the following digits:

    1. [latex]7[/latex]
    2. [latex]0[/latex]
    3. [latex]1[/latex]
    4. [latex]6[/latex]
    5. [latex]3[/latex]

    Rounding Numbers

    Rounding numbers is a process used to simplify figures to make them easier to work with or understand. It involves adjusting a number to the nearest place value, which can be especially useful in estimating results or making numbers more readable. Here’s a step-by-step guide to help you round whole numbers accurately to any specific place value.

    How To: Round a Whole Number to a Specific Place Value

    1. Locate the given place value. All digits to the left of that place value do not change.
    2. Underline the digit to the right of the given place value.
    3. Determine if this digit is greater than or equal to [latex]5[/latex].
      • Yes—add [latex]1[/latex] to the digit in the given place value.
      • No—do not change the digit in the given place value.
    4. Replace all digits to the right of the given place value with zeros.
    Round [latex]843[/latex] to the nearest ten.