Add and Subtract with Significant Figures (1.6)

Main ideas / lessons

• Addition and subtraction with significant figures use different (and simpler) rules than multiplication/division.
• The key rule is about decimal places, not the number of significant figures.
• For the final rounded answer:
  • You may not keep more decimal places than the input number that has the fewest decimal places.
• After calculating exactly (unrounded), you round at the cutoff determined by that minimum decimal-place number.
• This applies whether you add:
  • Two numbers or many numbers
  • Numbers written horizontally or vertically (stacking can help align decimals)

Method / step-by-step rules (addition & subtraction)

1. Step 1: Do the arithmetic first
   • Add or subtract without worrying about rounding yet.

2. Step 2: Count decimal places in each given number

   • Include trailing zeros to the right of a decimal point as significant (e.g., 15. has a specific decimal-place meaning; 1.2 has 1 decimal place).

   • A whole number with no decimal point has 0 decimal places. 3. Step 3: Find the minimum decimal places among the numbers. 4. Step 4: Mark the cutoff

   • Draw a “rounding line” just to the side of the digit corresponding to that minimum decimal-place position.
   • That digit is the last decimal place allowed in the final answer. 5. Step 5: Round using the digit immediately to the right of the cutoff
   • If it’s 5 or more, round the last kept digit up.
   • Otherwise, keep it the same. 6. Step 6: Ensure the final answer has exactly the minimum decimal-place count

Examples conveyed in the subtitles

• Example 1 (two numbers)

  • The number with the fewest decimal places determines the rounding precision (final kept to 1 decimal place).
  • Result: 14.2 (kept because the rounding digit was 1, so it doesn’t increase the 2).

• Example 2 (adding three / many numbers)

  • Decimal-place counts include:
    • Some numbers having 2 decimal places
    • Others having 0
    • Others having 3
  • The minimum is 0 decimal places, so the result is rounded to the ones place.
  • Result: 291.

• Example 3 (subtraction)

  • Identify minimum decimal places among the operands.
  • Round accordingly (keeping 2 decimal places based on the example’s “line” position).
  • Result shown: 40.34.

• Example 4 (stacking vertically)

  • Writing numbers one above another helps line up decimal places visually.
  • Minimum decimal places is 1, so round to 1 decimal place.
  • Result shown: 18.9 (from the stacked values).

Speakers / sources

• No specific speaker name is provided in the subtitles (source appears to be the course/video instructor).