Scientific notation - NSW Department of Education

Scientific notation We can use scientific notation to write very large or very small numbers in a concise way. It is also called standard notation. For example: 

The population of the Earth in May 2010 was approximately 6 820 000 000. This can be written in scientific notation as:

6.82 x 109 

The mass of an electron is approximately 0·00000000000000000000000000000091 kg. This can be written in scientific notation as:

9.1 x 10 -31 kg Numbers written in scientific notation: 

have a number between 1 and 10 – the decimal point is after the first significant digit



that are multiplied by a power of 10 – the power is equal to the number of places the decimal point has changed.

If the original decimal number is bigger than 10, the power is a positive number. If the original decimal number is between 1 and 10, the power will be zero. If the original decimal is smaller than 1, the power is a negative number. The decimal point goes after the 6. The original number was bigger than 1 so the power is +14.

657 000 000 000 000 is written as:

6.57 x 1014 There are 14 digits between where the decimal point was and where it has been put.

For more homework help, tips and info sheets go to www.schoolatoz.com.au © Owned by State of NSW through the Department of Education and Communities 2011. This work may be freely reproduced and distributed for non-commercial educational purposes only. Permission must be received from the department for all other uses.

1/2

The decimal point goes after the 5. The original number was less than 1 so the power is -15.

0·000000000000005 is written as:

5 x 10 -15 There are 15 digits between where the decimal point was and where it has been put.

When changing from scientific notation to an ordinary decimal: 

if the power is positive, the decimal number will be bigger than 10



if the power is 0, the decimal number remains the same



if the power is negative, the decimal number will be less than 1



the power tells us how many digits there has to be between where the decimal point is and where it goes in the decimal number



we use zeros to fill in the missing numbers.

Power is +5 so the decimal number is bigger than 1.

Need to add three zeros so there are 5 digits between the positions of the decimal points.

2.61 x 105 = 261 000

Power is -3 so the decimal number is smaller than 1.

Need to add two zeros so there are three digits between the positions of the decimal points.

5.3 x 10 -3 = 0.0053

For more homework help, tips and info sheets go to www.myschoolkids.com.au © Owned by State of NSW through the Department of Education and Training 2010. This work may be freely reproduced and distributed for non-commercial educational purposes only. Permission must be received from NSW DET for all other uses.

2/2