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Physics

Measurements

Significant Digits

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⚡ Quick Summary
Significant digits tell you how precisely a measurement was made. They include all the digits you're sure about, plus one estimated (doubtful) digit. More significant digits mean a more precise measurement!
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  • Significant digits indicate the reliability of a measurement.
  • All non-zero digits are significant.
  • Zeros between non-zero digits are significant.
  • Trailing zeros in a number with a decimal point are significant.
  • Trailing zeros in a whole number without a decimal point may or may not be significant. Use scientific notation to remove ambiguity. For example, 600 mm can be written as 6 x 10^2 mm (one significant digit), 6.0 x 10^2 mm (two significant digits), or 6.00 x 10^2 mm (three significant digits).
  • Leading zeros after a decimal point are not significant (e.g., 0.0023 has two significant digits, 2 and 3).

Rounding Off

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⚡ Quick Summary
When you have too many digits, rounding helps you keep only the important ones. If the next digit is 5 or more, round up. If it's less than 5, round down. If rounding a digit followed by a 5, round the digit to the nearest EVEN number.
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  • Rule 1: If the digit next to the one being rounded is greater than 5, increase the digit being rounded by 1.
  • Rule 2: If the digit next to the one being rounded is less than 5, leave the digit being rounded as it is.
  • Rule 3: If the digit next to the one being rounded is 5:
    • If the digit to be rounded is odd, increase it by 1.
    • If the digit to be rounded is even, leave it unchanged.

Significant Digits in Calculations (Multiplication and Division)

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⚡ Quick Summary
When multiplying or dividing, the answer should have the SAME number of significant digits as the number in the calculation with the FEWEST significant digits.
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  • The result of multiplication or division should be reported with the same number of significant digits as the quantity with the fewest significant digits used in the calculation.

Significant Digits in Calculations (Addition and Subtraction)

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⚡ Quick Summary
When adding or subtracting, line up the decimal points. The answer should be rounded to the same number of decimal places as the number with the FEWEST decimal places.
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  • Write the numbers one below the other, aligning the decimal points.
  • Locate the leftmost column that contains a doubtful digit (least significant digit).
  • Drop all digits to the right of this column from all the numbers.
  • Round the remaining digits to this column.
  • Perform the addition or subtraction with the rounded numbers.