Scientific notation is simply a method for expressing, and working with, very large or very small numbers. It is
a short hand method for writing numbers, and an easy method for calculations. Numbers in scientific notation
are made up of three parts: the coefficient, the base and the exponent. Observe the example below:
5.67 x 105
This is the scientific notation for the standard number, 567 000.
Now look at the number again, with the three parts labeled.
5.67 x 105
coefficient
base
exponent
In order for a number to be in correct scientific notation, the following conditions must be true:
1. The coefficient must be greater than or equal to 1 and less than 10.
2. The base must be 10.
3. The exponent must show the number of decimal places that the decimal needs to be moved to change
the number to standard notation. A negative exponent means that the decimal is moved to the left when
changing to standard notation.
SCIENTIFIC NOTATION
Write each number in scientific notation.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
0.07882
0.00000272338
118000
87200
0.00002786
0.000000664
450
74171.7
770
0.0000085
=
=
=
=
=
=
=
=
=
=
Write each number in standard format.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
3.443 × 10-7
7.75763 × 10-7
5.8 × 10-7
1.525 × 106
6.58157 × 107
5.1821 × 10-4
1.21 × 10-7
5.2314 × 10-7
7.141 × 10-5
5.256 × 106
=
=
=
=
=
=
=
=
=
=
DATE
Answer Key
Write each number in scientific notation.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
0.07882
0.00000272338
118000
87200
0.00002786
0.000000664
450
74171.7
770
0.0000085
=
=
=
=
=
=
=
=
=
=
7.882 × 10-2
2.72338 × 10-6
1.18000 × 105
8.7200 × 104
2.786 × 10-5
6.64 × 10-7
4.50 × 102
7.41717 × 104
7.70 × 102
8.5 × 10-6
Write each number in standard format.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
3.443 × 10-7
7.75763 × 10-7
5.8 × 10-7
1.525 × 106
6.58157 × 107
5.1821 x 10-4
1.21 × 10-7
5.2314 × 10-7
7.141 × 10-5
5.256 × 106
=
=
=
=
=
=
=
=
=
=
0.0000003443
0.000000775763
0.00000058
1525000
65815700
0.00051821
0.000000121
0.00000052314
0.00007141
5256000