Significant Figures Math Example 3

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Example 3

easy
Round each to 33 significant figures: (a) 0.00468720.0046872, (b) 12,35012{,}350, (c) 999.6999.6.

Solution

  1. 1
    (a) 0.00468720.0046872: significant digits are 4,6,8,7,24, 6, 8, 7, 2. Keep first 33: 4,6,84, 6, 8; next digit 7โ‰ฅ57 \geq 5, round up: 0.004690.00469.
  2. 2
    (b) 12,35012{,}350: significant digits 1,2,3,5,01, 2, 3, 5, 0. Keep 1,2,31, 2, 3; next digit 55, round up: 12,40012{,}400.
  3. 3
    (c) 999.6999.6: digits 9,9,9,69, 9, 9, 6. Keep first 33 (9,9,99, 9, 9); next digit 6โ‰ฅ56 \geq 5, round up: 999+1=1000999 + 1 = 1000, expressed as 1.00ร—1031.00 \times 10^3 to show 33 sig figs.

Answer

(a) 0.004690.00469; (b) 12,40012{,}400; (c) 1.00ร—1031.00 \times 10^3.
Rounding cascades when a digit rounds up to 1010: the carry propagates left, potentially changing the order of magnitude as in (c). Using scientific notation for (c) preserves the intended precision of 33 significant figures.

About Significant Figures

Significant figures are the meaningful digits in a measured quantity, reflecting its precision.

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