1) Scientific notation is used to express very small and very large numbers in a standardized way to make calculations easier. 2) Numbers in scientific notation are written as the product of a coefficient and a power of 10. 3) To convert a number to scientific notation, the decimal is moved to give a coefficient between 1 and 10, and the power of 10 indicates how many places the decimal was moved. A positive exponent means the decimal was moved left, and a negative exponent means it was moved right.

1. (Standard Form)

2. Is used to express very small and very
large numbers to make problem solving
easier.
For example
• The distance from the
earth to the sun is
150,000,000,000 meters.
• The mass of a grain of
sand is 0.00000003 grams.
2

3. Numbers in scientific notation are written
as the product of two other numbers:
• A coefficient
• A power of 10 (exponent)
3

4. The number 𝟕𝟔𝟓, 𝟎𝟎𝟎 written in Scientific Notation is 𝟕. 𝟔𝟓 × 𝟏𝟎𝟓
The coefficient is 𝟕. 𝟔𝟓
The coefficient must be 1 or greater
but also less than 10.
7.65 satisfies this condition.
The power of 10 (exponent) is 𝟓
The exponent represents the number of
times the coefficient must be multiplied
by 10 to give us the original number.
Another way to explain it is that:
It is the number of times the decimal
point must be moved to the left to
express the number in scientific notation.
4

5. The number 𝟎. 𝟎𝟎𝟎𝟓𝟖𝟐 written in Scientific Notation is 𝟓. 𝟖𝟐 × 𝟏𝟎−𝟒
The coefficient is 𝟓. 𝟖𝟐
The coefficient must be 1 or greater
but also less than 10.
5.82 satisfies this condition.
The power of 10 (exponent) is −𝟒
The exponent represents the number of
times the coefficient must be multiplied
by 10 to give us the original number.
Another way to explain it is that:
It is the number of times the decimal
point must be moved to the right to
express the number in scientific notation.
5

6. When the number is very small, the
exponent is NEGATIVE.
When the number is very large, the exponent
is POSITIVE.
6

7. A number that is greater than or equal to 1 but
less than 10, will have an exponent of zero.
Example:
𝟑. 𝟔𝟕 in scientific notation is simply 𝟑. 𝟔𝟕 × 𝟏𝟎𝟎
7

8. 8
1) Move the decimal to the immediate
right of the first non-zero number
2) Count the number of spaces the
decimal point was moved to get the
value of the exponent.
3) If the point was moved to the right,
the exponent will be negative.
4) If the point was moved to the left, the
exponent will be positive.

9. Write in Scientific Notation
1. 0.000671
2. 59200
3. 93100000
4. 0.00825
5. 0.0158
6. 3.2
7. 90.45

10. 1. 0.000671 = 𝟔. 𝟕𝟏 × 𝟏𝟎−𝟒
2. 59200 = 𝟓. 𝟗𝟐 × 𝟏𝟎𝟒
3. 93100000 = 𝟗. 𝟑𝟏 × 𝟏𝟎𝟕
4. 0.00825 = 𝟖. 𝟐𝟓 × 𝟏𝟎−𝟑
5. 0.0158 = 𝟏. 𝟓𝟖 × 𝟏𝟎−𝟐
6. 3.2 = 𝟑. 𝟐 × 𝟏𝟎𝟎
7. 90.45 = 𝟗. 𝟎𝟒𝟓 × 𝟏𝟎𝟏

11. 11
• 1.95 × 102
= 𝟏𝟗𝟓
• 3.87 × 10−4
= 𝟎. 𝟎𝟎𝟎𝟑𝟖𝟕
• 4.26 × 100 = 𝟒. 𝟐𝟔
• 2.18 × 10−1 = 𝟎. 𝟐𝟏𝟖
• 1.159 × 105
= 𝟏𝟏𝟓 𝟗𝟎𝟎
Write the following as whole numbers
or decimals.

12. YOU DID IT!!
THE END. 12