Scientific Notation ( Standard form)
Scientific notation is useful for writing very large or very small numbers.
a × 10n where 1 ≤ a ≤ 10
1. a must be greater than or equal to 1 and less than 10.
2. n is given by the number of places the decimal point has moved. (remember if
you can’t see a decimal point it is always at the right hand end of the number)
Changing large numbers into scientific notation
Ex 1
35600000
the point needs to move 7 places to the left.
3.56 × 107
Ex 2 Change 756800 and round to 1 decimal place.
756800
the point needs to move 5 places to the left.
7.56800 × 105
7.6 × 105
Ex 3 Change 3644000 and round to 2 decimal places.
3644000
the point needs to move 6 places to the left.
3.644000 × 106
3.64 × 106
Changing back from scientific notation to a large number
Ex 1
8.461 × 102 the power means move the point 2 places to the right.
846.1
Ex 2 1.95 × 103
move the decimal point 3 places to the right.
1950
Ex 3 3.87 × 107
38700000
move the decimal point 7 places to the right.
Changing small numbers into scientific notation
Ex 1
0.000215
the point needs to move 4 places to the right.
2.15 × 10-4
Ex 2 Change 0.00000678 and round to 1 decimal place.
0.00000678 the point needs to move 6 places to the right.
6.78 × 10-6
6.8 × 10-6
Ex 3 Change 0.000000001348 and round to 2 decimal places.
0.000000001348
the point needs to move 9 places to the right.
1.348 × 10-9
1.35 × 10-9
Changing from scientific notation back to a small number
Ex 1
5.37 × 10
-2
the power means move the point 2 places to the left.
0.0537
Ex 2 1.86 × 10-5
move the decimal point 5 places to the left.
0.0000186
Ex 3 9.24 × 10-7
move the decimal point 7 places to the left.
0.000000924