Question

The population of India based on 1981 census figure was 684 million. Express the results in scientific notation and calculate the number of significant figures.

Answer 1

The purpose of scientific notation is for scientists to write very large, or very small, numbers with ease.

Calculating scientific notation for a positive integer is simple, as it always follows this notation:

a x 10b

Follow the steps below to see how 684 is written in scientific notation.

Step 1

To find a, take the number and move a decimal place to the right one position.

Original Number: 684

New Number: 6.84

Step 2

Now, to find b, count how many places to the right of the decimal.

New Number: 6 . 8 4

Decimal Count: 1 2

There are 2 places to the right of the decimal place.

Step 3

Building upon what we know above, we can now reconstruct the number into scientific notation.

Remember, the notation is: a x 10b

a = 6.84

b = 2

Now the whole thing:

6.84 x 102

Step 4

Check your work:

102 = 100 x 6.84 = 684

Answer 2

The “significant figures” denotes the “number of important single digits” which is included from 0 to 9 in the “expression coefficient” in “scientific notation”. The “number” of “significant figures” in an expression shows the confidence or accuracy of a quantity.

The following three rules are used to determine the number of significant numbers in a number:  

· Non-zero numbers are always significant  

· Any zeros between two significant numbers are significant.

· A “final zero” or “trailing zeros” in the decimal portion are only important. For examples: 0.900 0r 0.928000 the zeros are significant.

                $1\quad million\quad =\quad { 10 }^{ 6 }$

Hence, $\quad 684\quad million\quad =\quad 684\quad \times \quad { 10 }^{ 6 }$

The value in terms of scientific notation may be expressed as $6.84\times \quad { 10 }^{ 8 }$. It has three significant figures.