Question

Carry out the following conversions. Enter your answers in scientific notation.

(a) 284 amu to grams x 10 g
(b) 106 amu to kilograms x 10 kg
(c) 2.96 A to meter's h x 10 m
(d) 2.84 A to nanometer's X 10 nm​

Answer 1

To convert amu to grams or kilograms, use the conversion factor 1 amu = 1.660539066×10-24 grams, and then, for kilograms, divide by 1,000. Convert Angstroms to meters or nanometers using factors of 1 A=1×10-10 meters and 1 nm=10 A, respectively.

Step-by-step explanation:

The correct answer is option (a) 23 mg to kg = 2.3 × 10-5 kg.

To convert milligrams (mg) to kilograms, we need to divide by 1000 since there are 1000 milligrams in 1 gram, and 1000 grams in 1 kilogram. So, 23 mg divided by 1000 is 0.023 grams. Then, to convert grams to kilograms, we divide by another 1000. Therefore, 0.023 grams is equal to 0.000023 kilograms, which can be written in scientific notation as 2.3 × 10-5 kg.

Similarly, option (b) 320 Tg to kg = 3.2 × 1020 kg, option (c) 42 ng to m = 4.2 × 10-11 m, and option (d) 7 g to nm = 7 × 1015 nm.The correct answer involves converting atomic mass units (amu) to grams or kilograms and Angstroms (A) to meters or nanometers. Here is how you can carry out these conversions:

1. Converting amu to grams: The conversion factor is that 1 amu equals 1.660539066×10-24 grams. Therefore, to convert 284 amu to grams, you multiply by this factor, resulting in 4.71353298×10-22 grams.
2. For converting amu to kilograms: Since 1 kilogram equals 1,000 grams, you first convert amu to grams and then divide by 1,000. Thus, 106 amu is 1.76057063×10-25 kilograms.
3. To convert Angstroms to meters: 1 Angstrom equals 1×10-10 meters. Therefore, 2.96 A is 2.96×10-10 meters.
4. Converting Angstroms to nanometers: 1 nanometer is 10 Angstroms, so 2.84 A is 0.284 nanometers, or 2.84×10-1 nanometers in scientific notation.