Learning Scientific Notation

Learning Scientific Notation

Scientific Notation is way to write really large or really small numbers.

Writing Numbers in Scientific Notation

Scientific Notation involves a number in front (called the Base) multiplied by a power of ten.

The base number must be at least 1 (1 or bigger - can be one) and less than 10.

In other words the base number can only have one number (other than zero) in front of the decimal.

When we write a number in scientific notation, we will move the decimal to fit this description.

The power of 10 (10 to an exponent) will tell us how many places to move the decimal to get back to where it originally was.

Determining the Exponent of 10

If our original number is larger than 10

**then we must move the decimal to the right to get back to where it was originally.

**the exponent will be positive.

If our original number is less than 1

**then we must move the decimal to the left to get back to where it was originally.

**the exponent will be negative.

Examples of Writing the Base Number

If a number does not have a decimal, the decimal is really at the end.

We want one number in front of the decimal that is not zero.

We only write zeros that hold place values. We don't write zeros that happen at the beginning or end.

Examples of Writing Numbers in Scientific Notation

The picture shows the number with the decimal where it originally is and also shows the red arrows showing how many times you move the decimal to get it back to the original number.

More Examples of Numbers that are changed into Scientific Notation

• A number larger than 10 - has a positive exponent.

• A number smaller than 1 - has a negative exponent.

Multiple Choice

If I were to change 3,420 into scientific notation, what would the base become? What is the first number?

• 3.42

• 342

• 34.2

• 3.420

Multiple Choice

If I were to write .000408 in scientific notation, what would the base become? What is the first number?

• .408

• 40.8

• 4.08

• 4.8

Multiple Choice

Write 45,000,000 in scientific notation.

• $45.0\ \times\ 10^6$

• $4.5\ \times10^7$

• $4.0\ \times10^7$

• $4.05\ \times\ 10^8$

Multiple Choice

Write .00000375 in scientific notation.

• $3.75\ \times\ 10^{-6}$

• $37.5\ \times\ 10^{-5}$

• $3.75\ \times\ 10^6$

• $0.375\ \times\ 10^{-10}$

Multiple Choice

Rewrite

 $4.052\ \times\ 10^8$  in expanded form.  Change from scientific notation.

• 405,200,000,000

• .00000004052

• 405,200,000

• 40,520,000

Multiple Choice

Write 3,406,700,000 in scientific notation.

• $34.067\ \times\ 10^8$

• $3.467\ \times\ 10^9$

• $3.4067\ \times\ 10^9$

• $3.4\ \times10^9$