6.19 1 < 5 Discard .19 ≈ 6 |
341.275 2 < 5 Discard .275 ≈ 341 |
12,333.5 5 = 5 Call it 1; add to 3 from behind 3 + 1 = 4 ≈ 12,334 |
−17.2805 2 < 5 Discard .2805 ≈ −17 |
196.35 5 = 5 Call it 1; add to 3 1 + 3 = 4 ≈ 196.4 |
412.143 4 < 5 Discard 43 ≈ 412.1 |
412.963 6 > 5 Call it 1 and add to 9 This gives 10. Call it 1 again and add to 2 ≈ 413.0 |
661.9 There is no second number after the decimal point Leave as is = 661.9 |
−59.714 1 < 5 Discard 14 ≈ −59.7 |
109.13 unit digit = 9 9 > 5 Call it 1; add to 0 1 + 0 = 1 Then, write 0 as the unit digit and discard .13 ≈ 110 |
412.963 unit digit = 2 2 < 5 Call it 0 and discard .963 ≈ 410 |
685.7 unit digit = 5 5 = 5 Call it 1; add to 8 1 + 8 = 9 Then, write 0 as the unit digit and discard .7 ≈ 690 |
−72.548 unit digit = 2 2 < 5 Call it 0 and discard .548 ≈ −70 |
(a.) 42(32.7) = 1373.4 1373.4 has 5 significant digits (Rule #1) To approximate it to 3 significant digits: Look at the 4th number The 4th number is 3 3 < 5 Call it 0 Discard .4 ≈ 1370 to 3 s.d |
(b.) 259.82 ÷ 0.092 = 2824.130435 2824.130435 has 10 s.d (Rules #1 and #2) To approximate it to 3 significant digits: Look at the 3rd number The 3rd number = 2 2 < 5 Call it 0. Call the 4th number 0. Discard .130435 ≈ 2800 to 2 s.d |
$
(c.) \\[3ex]
(1.68 * 10^3) * (6.6 * 10^{-2}) \\[3ex]
= 1.68 * 6.6 * 10^3 * 10^{-2} \\[3ex]
= 11.088 * 10^{3 + -2} \\[3ex]
= 11.088 * 10^{3 - 2} \\[3ex]
= 11.088 * 10^1 \\[3ex]
= 1.1088 * 10^1 * 10^1 \\[3ex]
= 1.1088 * 10^{1 + 1} \\[3ex]
= 1.1088 * 10^2 \\[3ex]
$
Let us focus on 1.1088 1.1088 has 5 significant digits (Rule #2) To approximate it to 3 significant digits: Look at the 4th number 8 > 5 Call it 1 and add to 0 1 + 0 = 1 Discard the rest This becomes: 1.11 ≈ 1.11 * 10^2 |