Calculate to the correct number of significant figures.a.

Chapter 1, Problem 84E

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QUESTION:

Calculate to the correct number of significant figures.

 

a. 89.3 x 77.0 x 0.08

b. (5.01 x 105 ) ÷ (7.8 x 102 )

c. 4.005 x 74 x 0.007

d. 453 ÷ 2.031

Questions & Answers

QUESTION:

Calculate to the correct number of significant figures.

 

a. 89.3 x 77.0 x 0.08

b. (5.01 x 105 ) ÷ (7.8 x 102 )

c. 4.005 x 74 x 0.007

d. 453 ÷ 2.031

ANSWER:

Problem 84E

Calculate to the correct number of significant figures.

     a. 89.3 x 77.0 x 0.08

     b. (5.01 x 105) / (7.8x102)

     c. 4.005x74x0.007

     d. 453 / 2.031

                                                     

                                                               Step by step solution

Step 1 of 4

Significant figure rules:

Rule - 1

All nonzero digits are significant.

Example - 28.03

Rule - 2

Zeros between two non zero digits are significant.

Example -408

Rule - 3

Leading zeros are not significant. They only serve to locate the decimal point.

Example -0.0032

Rule - 4

Zeros at the end of a number are categorized as follows.

Trailing zeros after a decimal point are always significant

Example - 45.000

Trailing zeros before a decimal point are always significant

Example - 140.00

Trailing zeros before an implied decimal point are ambiguous and should be avoided by scientific notation.

During all mathematical calculations, all the answers should be reported in the same number of significant figures with the term having least significant figures.

When the numbers are being dropped off, there are three conditions as shown below.

       * When the last digit of a number is greater than 5 and it is being dropped off then the digi to the right of it is increased by 1.

       * When the last digit is less than 5 and it is being dropped off then the number on the right shall not be increased.

       * When the last digit is 5, then the number is rounded off or not whichever makes the even number.

a)

The given value -

In the case of multiplication, we round off  the final answer to the same number of significant figures as in the factor with the fewest signifigures. So, we round off one significant figure.

                                   

                                   
                                 

Therefore, the correct number of significant figure is .

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