Question

State how many significant figures are proper in the results of the following calculations: (a) (106.7)(98.2)/(46.210)(1.01) (b) (18.7)2 (c) (1.60×10−19)(3712).

Answer 1

Answer:

(a) The result is 3 significant figures

(b) The result is 3 significant figures

(c) The result is 3 significant figures

Step-by-step explanation:

* Lets explain how to solve the problem

- Significant figures are the number of digits in a value

- There are 3 rules to find how many significant figures are in a number

1. All non-zero digits are significant.

- Ex: 1234.56 is six significant figures

2. Any zeros between two significant digits are significant

- Ex: 2.03 is three significant figures

- A final zero or zeros between two significant digits in the decimal

 numbers ONLY are significant

- Ex: 0.056 is two significant figures , 12.04 is four significant figures ,

  5.60 is three significant figures

* Lets solve the problem

(a) (106.7)(98.2)/(46.210)(1.01)

∵ 106.7 is 4 significant figures

∵ 98.2 is 3 significant figures

∵ 46.210 is 5 significant figures

∵ 1.01 is 3 significant figures

∵ The smallest number of the significant figures is 3

∴ The result is limited by 3 significant figures

∴ The result is 3 significant figures

(b) (18.7)²

∵ 18.7 is 3 significant figures

∴ The result is limited by 3 significant figures

∴ The result is 3 significant figures#

(c) (1.60 × 10^-19)(3712)

- Remember: When a number is written in scientific notation, only

 significant figures are the numerical part only

∵ 1.60 × 10^-19 is 3 significant figures

∵ 3712 is 4 significant figures

∵ The smallest number of the significant figures is 3

∴ The result is limited by 3 significant figures

∴ The result is 3 significant figures