SUBJECT: ROUNDING NUMBERS AND PERCENTAGES FOR REPORTING IN TEXT AND DISPLAYING IN SUMMARY TABLES AND FIGURES

NCES STANDARD: 5-3

PURPOSE: To ensure consistent practices for rounding and displaying numbers and percentages in text and tables/figures.

KEY TERMS: precision, and universe.

STANDARD 5-3-1: Calculations performed to produce summary data, and computations performed to estimate standard errors must be done on numbers and percentages that are carried out to at least four decimal places (i.e., not on proportions). The final rounded value must be obtained from the original figure available, not from a series of roundings (e.g., 7.1748 can be 7.175 or 7.17 or 7.2 or 7 but not 7.18). This situation typically arises when researchers round percentages from tables in tenths of a percent to full percents to be used in text.

STANDARD 5-3-2: Sums of column or row counts in a table must be derived using unrounded numbers, with appropriate rounding of the total after its derivation. Except in the case of unrounded counts from universe data, all tables that should logically sum to either 100 percent, or to a numeric total, must include a note that states: NOTE: Detail may not sum to totals because of rounding.

STANDARD 5-3-3: Because of software limitations, for presentation purposes the following specific rules for rounding must be used:

If the first digit to be dropped is less than 5, the last retained digit is not changed.
 
      6.1273 is rounded to 6.127

If the first digit to be dropped is greater than or equal to 5, the last digit retained is increased by 1.
 
      6.6888 is rounded to 6.69
 
      5.451 is rounded to 5.5
 
      5.452

STANDARD 5-3-4: In multiplying or dividing numbers using data from secondary sources, the resulting precision cannot be more precise than that of any of the component numbers. (For example, if 4.5 and 5.75 are rounded numbers, the product can be stated only as 26, with 4.5 having two significant digits and 5.75 having three.)

STANDARD 5-3-5: Before rounding numbers for publication, a decision must be made about the appropriate number of decimal places to be reported using the following rules:

1. Percentages appearing in text must be rounded to whole numbers unless small differences require finer breakdowns. Summary tables must be rounded to no more than one decimal place.
    
2. Percentages appearing in reference and methodological tables must be rounded to no more than two decimal places except in certain methodological tables where finer breakdowns may be necessary.
    
3. Standard errors must be rounded to one decimal place more than the estimates for which they are computed.
    
4. Universe data may be reported unrounded. Sample survey data must be rounded.
    
5. A measured zero in a universe survey (i.e., none of something) must always appear in a table or a figure as 0. If rounding is used in a sample survey, numbers that round to zero must be represented in tables and figures by the symbol #.
    
6. When dealing with small values in sample surveys, zero and numbers that round to zero must be represented in tables and figures by the symbol #.
    
7. When it is logically impossible to have a response in a cell (i.e., not applicable) that must be denoted by the symbol †.

GUIDELINE 5-3-5A: Numbers appearing in text and summary tables should adhere to the following conventions:

1. Round four- and five-digit numbers to hundreds (e.g., 1,255 is rounded to 1,300; 56,789 is rounded to 56,800);
    
2. Round six-digit numbers to thousands (e.g., 156,789 is rounded to 157,000); and
    
3. Round millions and larger numbers to no more than two decimal places (e.g., 1,234,567 is rounded to 1.2 or 1.23 million; 1,912,345,678 is rounded to 1.9 or 1.91 billion).