SI Lesson: Scientific Notation
A number is written in scientific notation when it is expressed in the form
below, where a is greater than or equal to 1 and less than 10, and n is an
integer.
ax
n
10
From Standard Notation Into Scientific Notation
1. If the number is greater than or equal to 10, move the decimal n places to the left until the
new number (a) is greater than or equal to 1 and less than 10. Then, write the number in the
correct scientific notation shown above.
2. If the number is less than 1, move the decimal n places to the right until the new number (a)
is greater than or equal to 1 and less than 10. Then, write the number in the correct scientific
notation shown above.
From Scientific Notation Into Standard Notation
1. If the exponent is POSITIVE, move the decimal of a to the RIGHT n places.
2. If the exponent is NEGATIVE, move the decimal of a to the LEFT n places.
Example 1: Write 73,200 in scientific notation.
Solution: To write 73,200 as a number greater than or equal to 1 and less than 10, move the decimal
point 4 places to the left. Then, multiply by 104 to offset moving the decimal point.
73,200 = 7.32 × 104
Example 2: Write 0.0000732 in scientific notation.
Solution: To write 0.0000732 as a number greater than or equal to 1 and less than 10, move the decimal
point 5 places to the right. Then, multiply by 10-5 to offset moving the decimal point.
0.0000732 = 7.32 × 10-5
Example 3: Write 5.126 × 103 in standard form.
Solution: To write the number in standard form, multiply 5.126 by 103. This is the same as moving the
decimal point to the right 3 spaces.
5.126 × 103 = 5,126
Compute with Scientific Notation
Add / Subtract in Scientific Notation
First convert one of the numbers so that both numbers are multiplied by the same power of ten.
Next, add or subtract the numbers multiplied by the powers of 10 and keep the power of 10 the same. If
necessary, move the decimal point and change the exponent of 10 so that the answer is in scientific
notation.
Example 1: Simplify the following expression.
Solution:
First, write 1.31 × 105 in terms of 103 by moving the decimal point two places to the right and subtracting 2
from the power of 10.
Next, add the numbers by adding the numbers multiplied by the power of 10 and keeping the power of 10
the same.
Then, write the answer in scientific notation by moving the decimal two places to the left and adding 2 to
the power of 10.
Example 2: Simplify the following expression.
Solution:
First, write 4.26 × 10-2 in terms of 10-3 by moving the decimal point one place to the right and subtracting 1
from the power of 10.
Next, subtract the numbers by subtracting the numbers multiplied by the power of 10 and keeping the
power of 10 the same.
Then, write the answer in scientific notation by moving the decimal point one place to the left and adding 1
to the power of 10.
Multiply in Scientific Notation
Multiply the numbers multiplied by the power of ten and add the exponents of 10.
Divide in Scientific Notation
Divide the numbers multiplied by the power of ten and subtract the exponents of 10.
If necessary, move the decimal point and change the exponent of 10 so that the answer is in scientific
notation.
Example 3: Simplify the following expression.
Solution: First, group the numbers multiplied by the powers of 10 and the powers of 10. Then, multiply
the numbers in the first set of parentheses and add the exponents of 10 to multiply the powers of 10 in the
second set of parentheses.
Example 4: Simplify the following expression.
Solution: First, group the numbers multiplied by the powers of 10 and the powers of 10. Then, divide the
numbers in the first set of parentheses and subtract the exponents of 10 to divide the powers of 10 in the
second set of parentheses.