Decimals in Standard Form

Decimals or decimal numbers can be written in standard form .Standard form or scientific notation consists of numbers that are written into two parts .The two parts are as follows,The digits by the decimal point positioned after the first digit, followed by ×10 to a power that would place the decimal point reverse where it supposed to be (that is it illustrates how many places to go the decimal point).

Decimals in Standard Form:

 

We can write the decimals in the standard form in the following way,

 

Standard form

  • In the above shown example, 5326.6 can be written as 5.3266 × 103, since 5326.6 = 5.3266 × 1000 = 5326.6 × 103.

  • If the number is 10 or >10 then the decimal place have to shift to the left, and the power(exponent) of 10 will be positive.    

  • Similarly if the number is <1 then the decimal place have to shift to the right , and the power(exponent) of 10 will be negative:

  • For example: 0.0043 can be written as 4.3 × 10-3, because 0.0043 = 4.3 × 0.001

                                                                                                 = 4.3 × 10-3

Examples –decimals in Standard Form:

 

The following examples make you understood to write decimals in standard form.

 

Example 1:

Write the decimal 56.78 in standard form.

Solution:

Given decimal number is 56.78

56.78 = 0.5678 x 100

          = 5.678 x 10

          = 56.78 x 1

          =567.8 x 0.1

          = 5678 x 0.01.

Therefore in standard form 56.78 can be written as 0.5678 x 102 or

                                                                                   5.678 x 101 or

                                                                                   56.78 x 100 or

                                                                                   567.8 x 10-1 or

                                                                                   5678 x 10-2 and so on.

Example 2:

Write the decimal 5876766.29 in standard form.

Solution:

Given decimal number is 5876766.29

5876766.29= 0.587676629 x 10000000

                  = 5.87676629 x 1000000

                  = 58.7676629 x 100000

                  = 587.676629 x 10000

                  = 5876.76629 x 1000

                  = 58767.6629 x 100

                  = 587676.629 x 10

                  = 5876766.29 x 1

                  = 58767662.9 x 0.1

                  = 587676629 x 0.01

Therefore in standard form 5876766.29 can be written as 0.587676629 x 107 or

                                                                                    5.87676629 x 10or

                                                                                    58.7676629 x 105 or

                                                                                    587.676629 x 104 or

                                                                                    5876.76629 x 103 or

                                                                                    58767.6629 x 102 or                                                                                            587676.629 x 101 or

                                                                                    5876766.29 x 100 or

                                                                                    58767662.9 x 10-1 or

                                                                                587676629 x 10-2 and so on

 

Practice problem- Decimals in standard form:

 

Write the following decimal numbers in standard form.

1)      -5050

2)      56.5

Answers:

1)      The answers are -5050 x 100, -505.0 x 101, -50.50 x 102, -5.050 x 103, -0.5050 x 104 and so on.

2)      The answers are 56.5 x 100, 5.65x 101, 0.565 x 102, 0.00565 x 103 , 565 x 10-1 and so on.