Question

sig fig multiplication and division
(1) complete the following multiplication questions (be careful with units):
(a) 2.89 cm x 4.01 cm
(b) 17.3 cm x 6.2 cm
(c) 5.08 m x 1.2 m
(d) 5.00 mm x 7.3216 mm
(e) 20.8 dm x 123.1 dm
(f) 5 cm x 5 cm
(g) 5.0 cm x 5 cm
(h) 5.0 cm x 5.0 cm
(2) complete the following division questions (be careful with units):
(a) $\frac{8.071\text{ cm}}{4.216\text{ cm}}$
(b) $\frac{24789.4\text{ km}}{43.5\text{ km}}$
(c) $\frac{4.819\text{ cm}}{9.852\text{ cm}}$
(d) $\frac{2.23\text{ m}}{18.941\text{ m}}$
(e) $\frac{8.423\times10^{14}\text{ mm}}{5.813\times10^{12}\text{ mm}}$
(f) $\frac{109.3758\text{ m}}{5.813\text{ m}}$

Explanation:

Step1: Multiply the numbers

(1)(a)

$2.89\times4.01 = 11.6889$. Rounding to 3 significant - figures (since 2.89 has 3 significant figures), the result is $11.7$ and the unit is $cm\times cm=cm^{2}$, so the answer is $11.7\ cm^{2}$.

(1)(b)

$17.3\times6.2 = 107.26$. Rounding to 2 significant - figures (since 6.2 has 2 significant figures), the result is $110$ and the unit is $cm^{2}$.

(1)(c)

$5.08\times1.2 = 6.096$. Rounding to 2 significant - figures (since 1.2 has 2 significant figures), the result is $6.1$ and the unit is $m^{2}$.

(1)(d)

$5.00\times7.3216 = 36.608$. Rounding to 3 significant - figures (since 5.00 has 3 significant figures), the result is $36.6$ and the unit is $mm^{2}$.

(1)(e)

$20.8\times123.1 = 2560.48$. Rounding to 3 significant - figures (since 20.8 has 3 significant figures), the result is $2560$ and the unit is $dm^{2}$.

(1)(f)

$5\times5 = 25$. Rounding to 1 significant - figure (since 5 has 1 significant figure), the result is $30$ and the unit is $cm^{2}$.

(1)(g)

$5.0\times5 = 25$. Rounding to 2 significant - figures (since 5.0 has 2 significant figures), the result is $25$ and the unit is $cm^{2}$.

(1)(h)

$5.0\times5.0 = 25.0$. Rounding to 2 significant - figures (since 5.0 has 2 significant figures), the result is $25$ and the unit is $cm^{2}$.

Step2: Divide the numbers

(2)(a)

$\frac{8.071}{4.216}=1.91437$. Rounding to 4 significant - figures (since 8.071 has 4 significant figures), the result is $1.914$. The unit $cm/cm = 1$ (dimensionless).

(2)(b)

$\frac{24789.4}{43.5}=569.871$. Rounding to 3 significant - figures (since 43.5 has 3 significant figures), the result is $570$. The unit $km/km = 1$ (dimensionless).

(2)(c)

$\frac{4.819}{9.852}=0.489139$. Rounding to 4 significant - figures (since 4.819 has 4 significant figures), the result is $0.4891$. The unit $cm/cm = 1$ (dimensionless).

(2)(d)

$\frac{2.23}{18.941}=0.117734$. Rounding to 3 significant - figures (since 2.23 has 3 significant figures), the result is $0.118$. The unit $m/m = 1$ (dimensionless).

(2)(e)

$\frac{8.423\times10^{14}}{5.813\times10^{12}}=\frac{8.423}{5.813}\times10^{14 - 12}\approx1.45\times10^{2}$. The unit $mm/mm = 1$ (dimensionless).

(2)(f)

$\frac{109.3758}{5.813}=18.8157$. Rounding to 4 significant - figures (since 5.813 has 4 significant figures), the result is $18.82$. The unit $m/m = 1$ (dimensionless).

Answer:

(1)(a) $11.7\ cm^{2}$
(1)(b) $110\ cm^{2}$
(1)(c) $6.1\ m^{2}$
(1)(d) $36.6\ mm^{2}$
(1)(e) $2560\ dm^{2}$
(1)(f) $30\ cm^{2}$
(1)(g) $25\ cm^{2}$
(1)(h) $25\ cm^{2}$
(2)(a) $1.914$
(2)(b) $570$
(2)(c) $0.4891$
(2)(d) $0.118$
(2)(e) $1.45\times10^{2}$
(2)(f) $18.82$