Question

1. How many significant figures are there in each of the following numbers?

45.6.......

0.041.......

343.2.......

0.361362.......

2. When 42.9 is divided by 83.581, the answer should be reported to how many significant digits?

What is the result of this calculation (when reported to the correct number of significant figures)? 42.9 / 83.581 =

When 83.581 is subtracted from 42.9, the result should be reported with how many digits after the decimal point?

What is the result of this calculation (when reported to the correct number of significant places)? 42.9 - 83.581 =

3. Write each of the following numbers to 3 significant figures in exponential or scientific notation Write each number with only one non-zero digit before the decimal point.

Example: Use  not  or .

(Do not include the plus sign for positive exponents.)

0.0222
124000
16300
0.0000775

Answer 1

1. The significant figures in the given numbers can be expressed on the basis of some rules. We will discuss them for each number.

45.6 has 3 significant figures because non-zero digits are always significant.

0.041 has 2 significant figures because zeros at the starting of a number are not significant as the number is less than 1.

Similarly, 343.2 has 4 significant figures and 0.361362 has 6 significant figures.

2. In multiplication and division, the significant figures must not exceed the least number of significant figures used in the multiplication or division.

When 42.9 is divided by 83.581, the answer must have 3 significant figures because 42.9 has least significant number of figures, i.e, 3.

  

Also, in addition and subtraction the answer must not be expressed in the smaller place (decimal, tens, hundreds,etc.) than the number with smaller place. While subtracting 83.581 from 42.9, we have to check the number with the smallest place which is 42.9 having tenth decimal place as the smallest place. So, the answer will have 3 significant figures.

  

3. The numbers can be written in 3 significant figures and only one non-zero digit before decimal place in the following way:

Number	Scientific or exponential notation
0.0222
124000
16300
0.0000775