What is the meaning of the number of digits reported in a measured quantity?

Solution 26 E: The metric prefixes will be as following: (a) 2.3 x 10 -10L, -9 1.0 nL =1 x 10 L Conversion of Liter (L) to nanoliter(nL) Thus, Desired unit = given unit x (desired unit/ given unit) = 2.3 x 10 -10L x (1 nL/1 x 10 L) -1 = 2.3 x 10 nL = 0.23 nL -10 Thus Thus, the volume of 2.3 x 10 L without exponent is equal to 0.23 nL -6 (b) 4.7 x 10 g 1 g =1 x 10 g -6 Conversion of gram (g) to microgram(g) Thus, Desired unit = given unit x (desired unit/ given unit) -6 -6 = 4.7 x 10 g x( 1g /1 x 10 g ) = 4.7 g Thus, the mass of 4.7 x 10 g, without exponent is equal to 4.7g -12 (c)1.85 x 10 m -12 1 pico meter (pm) =1 x 10 m Conversion of meter (m) to picometer(pm) Thus, Desired unit = given unit x (desired unit/ given unit) -12 -12 m = 1.85 x 10 m x (1.0 pm/1 x 10 ) = 1.85 pm -12 Thus, the length of 1.85 x 10 m, without exponent is equal to 1.85 pm 6 d) 16.7 x 10 s 6 1 mega s (Ms) =1 x 10 s Conversion of sec (s) to Megasec(Ms) Thus, Desired unit = given unit x (desired unit/ given unit) = 16.7 x 10 s x( 1 Ms/1 x 10 s) = 1.67 Ms Thus, the time of 16.7 x 10 s, without exponent is equal to 1 .67 Ms 3 (e) 15.7 x 10 g, 3 1 kilogram (kg) =1 x 10 g Conversion of gram g) to Kilogram (kg) Thus, Desired unit = given unit x (desired unit/ given unit) 3 3 = 15.7 x 10 g x( 1 kg/ 1 x 10 g) = 15.7 kg Thus, the mass of 15.7 x 10 g, , without exponent is equal to 1 5.7 kg (f) 1.34 x 10-3 m, -3 1 millimeter(mm) =1 x 10 m Conversion of meter (m) to millimeter(mm)) Thus, Desired unit = given unit x (desired unit/ given unit) = 1.34 x 10 m x( 1mm/1 x 10 m) = 1.34 mm -3 Thus, the length of 1.34 x 10 m, , without exponent is equal to 1 .34 mm 2 (g) 1.84 x 10 cm. 1 m = 100 cm Conversion of centimeter (cm) to meter(m ) Thus, Desired unit = given unit x (desired unit/ given unit) 2 = 1.84 x 10 cm x( 1.m/ 1x 100 cm) = 1.84 m 2 Thus, the length of 1.84 x 10 cm., without exponent is equal to 1.84 m