Sig Figs Operations Add248

1. **Problem A: Give the number of significant figures in each of the following (Odd numbers only).** We count all digits except leading zeros as significant figures. - 1) $4,007,584$ has 7 significant figures. - 3) $4,570$ has 3 significant figures (trailing zero without decimal is not significant). - 5) $0.00087$ has 2 significant figures (leading zeros not counted). - 7) $3.5050$ has 5 significant figures (trailing zero after decimal is significant). - 9) $0.020304$ has 5 significant figures. 2. **Problem D: Carry out the following operations, and express the answers with the appropriate number of significant figures (Odd numbers only).** Rules: - For addition/subtraction, round to the least number of decimal places. - For multiplication/division, round to the least number of significant figures. Calculations: 1) $320.55 - \frac{6104.5}{23}$ Calculate division first: $$\frac{6104.5}{23} = 265.4130...$$ Now subtraction: $$320.55 - 265.4130 = 55.137$$ Rounding to least decimal places: $320.55$ has 2 decimal places, $265.4130$ has 4 decimal places, so round to 2 decimal places: $$\boxed{55.14}$$ 2) $1.24056 + 75.80$ Least decimal places is 2 (from $75.80$), so sum: $$1.24056 + 75.80 = 77.04056$$ Rounded to 2 decimal places: $$\boxed{77.04}$$ 3) $58.78 - 73$ $58.78$ has 2 decimal places, $73$ has 0 decimal places, so round to 0 decimal places: $$58.78 - 73 = -14.22$$ Rounded to 0 decimal places: $$\boxed{-14}$$ 4) $890.00 \times 224.3$ $890.00$ has 5 significant figures, $224.3$ has 4 significant figures. Multiply: $$890.00 \times 224.3 = 199627$$ Round to 4 significant figures: $$\boxed{199600}$$ 5) $78,132 / 2.50$ $78,132$ has 5 significant figures, $2.50$ has 3 significant figures. Divide: $$\frac{78132}{2.50} = 31252.8$$ Round to 3 significant figures: $$\boxed{31300}$$ 6) $45.230 - 0.02594$ $45.230$ has 3 decimal places, $0.02594$ has 5 decimal places. Subtract: $$45.230 - 0.02594 = 45.20406$$ Round to 3 decimal places: $$\boxed{45.204}$$ 7) $[(285.3 \times 10^5) - (1.200 \times 10^3)] \times 2.8954$ Calculate inside brackets: $$285.3 \times 10^5 = 28530000$$ (5 significant figures) $$1.200 \times 10^3 = 1200$$ (4 significant figures) Subtract: $$28530000 - 1200 = 28528800$$ Multiply by $2.8954$ (5 significant figures): $$28528800 \times 2.8954 = 82613455.52$$ Round to least significant figures (4 sig figs from subtraction result): $$\boxed{8.261 \times 10^7}$$ 8) $(0.0045 \times 20000) + (2813 \times 12)$ Calculate each: $$0.0045 \times 20000 = 90$$ (2 sig figs) $$2813 \times 12 = 33756$$ (4 sig figs) Sum: $$90 + 33756 = 33846$$ Round to least decimal places (0 decimal places): $$\boxed{33846}$$ 9) $863 \times [1255 - (3.45 \times 10^8)]$ Calculate inside brackets: $$3.45 \times 10^8 = 345000000$$ (3 sig figs) $$1255 - 345000000 = -344998745$$ Multiply: $$863 \times (-344998745) = -297726027435$$ Round to least sig figs (3 sig figs from $3.45 \times 10^8$): $$\boxed{-2.98 \times 10^{11}}$$ 10) $1.10 \times 10^4 - 1.92 \times 10^2$ Convert to same power: $$1.10 \times 10^4 = 11000$$ (3 sig figs) $$1.92 \times 10^2 = 192$$ (3 sig figs) Subtract: $$11000 - 192 = 10808$$ Round to least decimal places (0 decimal places): $$\boxed{10800}$$