Notes for Lesson 7-2: Powers of 10 and Scientific Notation
7-2.1 – Evaluating Powers of 10
You can use powers of ten to read and write very large and very small numbers.
Each time you divide by 10 (or move the decimal to the left) the exponent on 10 decreases by 1
Each time you multiply by 10 (or move the decimal to the right) the exponent on 10 increases by 1
To write a power of 10 in standard form (as a number), start with 1 and move the decimal 1 place to the right, if
the exponent is positive, or the left, if the exponent is negative.
Examples: Find the value of each power of 10
10 3
.001
10 2
100
10 10
0.0000000001
7-2.2 – Writing Powers of 10
To write a number as a power of ten count the number of places needed to move the decimal to return to 1. Use
a positive exponent for large number and a negative exponent for small numbers.
Examples: Write each number as a power of 10
10,000,000 10 7
0.00001  10 5
10,000  10 4
7-2.3 – Multiplying by Powers of 10
To multiply a number by a power of ten, move the decimal the same way as above, right for positive exponents
and left for negative exponents. Instead of starting with 1, just start with the number given.
Examples: Find the value of each expression.
97.86 x10 6  97,860,000
19.5 x10 4  0.00195
163 x10 2  1.63
7-2.4 – Scientific notation
Vocabulary:
Scientific notation – A method of writing very large or very small numbers, by using powers of 10, in
the form m  10 n where 1  m  10 and n is an integer.
Scientific notion is a way of writing a number as the product of a smaller number and a power of 10. To write a
number in scientific notation move the decimal so there is one nonzero digit in front of the decimal point. Then
write the power of 10.
Examples: Write each number on scientific notation
235,000  2.35  10 5
0.0000077  7.7  10 6
0.0412  4.12  10 2
7-2.4 – Application
Jupiter has a diameter of about 143,000 kilometers. Its shortest distance from the Earth is about 5.91 108 km,
and its average distance from the Sun is about 778,400,000 km. Jupiter’s orbital speed is approximately
1.3  10 4 m / s .
A) Write Jupiter’s shortest distance from the Earth in standard form.
5.91 108  591,000,000km
B) Write Jupiter’s average distance from the Sun in scientific notation
778,400,000  7.784  108 km
7-2.5 – Comparing and Ordering Numbers in Scientific Notation
It can also be easier to put numbers in order if they are all written in scientific notation. To do this:
First place them in order by the power of ten, then place in order the number that have the same power
of 10
Example: Order the numbers from least to greatest
5.2  10 3 ; 3  1014 ; 4  10 3 ; 2  10 12 ; 4.5  10 30 ; 4.5  1014
Practice B as needed