Question

2. & Indicate the precision and the. of significant digits of the following measurements in the space provided. Round off the measurements to the correct number of digits needed. 8 Express these rounded measurements in proper scientific notation in the last column. See example. OF SIG. DIG. MEASUREMENT PRECISION MEASUREMENT MEASUREMENT IN NOW NEEDED ROUNDED OFF SCI. NOT 63.479 m (example) 3 5 3 63.5 m 6.35 x 10 m uz A 0.004 659 m 2 B5 803 L C565 g 2 D 123 456.7 mm 3 E2.074 MW 3 33. Perform the following operations, expressing the answers to the correct accuracy/precision including units. 12 cm+ 0.031 cm + 7.969 cm

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Answer 1

1) See the solution below:

Measurement in Sci. Not. А 6 # of sig. dig. Measurement Measurement Precesion Rouned of Now Needed 0.004659 m 4 2 0.0047 m 5803 L 0 4 1 6000 L 565 g 2 570 g 123456.7 mm 1 7 3 123000 mm 2.074 MW 32.07 MW 3 O B с D E 4.7 x 10^-3 m 6 x 10^3 m 5.7 x 10^2 g 1.23 x 10^5 mm 2.07 x 10^0 MW 3 4

While writing in scientific notation, the number should be as expressed between 1 to 10 followed by the required powers of 10.

A) As there are 6 decimal places. 59 is rounded to 100 so, 0.0047.

B) As there is zero decimal place. 803 is rounded to 1000, so 6000.

C) As there is zero decimal place. 5 is rounded to 10, so 570.

D) As there is 1 decimal place. 456 is rounded to 000, so 123000.

E) As there is 3 decimal place. 4 is rounded to 0, so 2.07.

2) See the solution below:

A	12 cm + 0.031 cm + 7.969 cm	20 cm
B	(6.1m)(8.2m)(1.1m)	$55m^{3}$
C	$\mathbf{(14\times 10^{-8}cm^{2})\div (3.25*10^{-6}cm)}$
D	$\mathbf{\sqrt[3]{0.189m^{3}}}$
E	$\frac{(282g)(5.98\times 10^{8}mm)(4.0cm)}{(7.5\times 10^{7}cm)(2.62\times 10^{2}g)}$	34 mm

A) 12 cm + 0.031 cm + 7.969 cm = 20 cm [as the minimum no of decimal places is zero]

B) (6.1m)(8.2m)(1.1m) = 55.022 m^3 = 55 m^3 [as the minimum no of significant digits is 2]

C) $\mathbf{(14\times 10^{-8}cm^{2})\div (3.25*10^{-6}cm)}$ = 0.0431 cm = 0.43 cm[as the minimum no of significant digits is 2]

D) $\mathbf{\sqrt[3]{0.189m^{3}}}$ = 0.3274 m = 0.327 m [as the minimum no of significant digits is 2]

E) $\frac{(282g)(5.98\times 10^{8}mm)(4.0cm)}{(7.5\times 10^{7}cm)(2.62\times 10^{2}g)}$ = 34.32 mm = 34 mm [as the minimum no of significant digits is 2]