Video lessons with examples and solutions to help math students learn to
convert from Standard Notation to Scientific Notation.

In these lessons, we will learn

Scientists have developed 'scientific notation' as a shorter method to express very large and very small numbers.

Scientific Notation is based on powers of the base number 10.

The number 123,000,000,000 in scientific notation is written as:

This video shows how to change a very large number or very small number into scientific notation.

The following video shows an example of converting a number in standard notation to a number in scientific notation.

## Multiplication
of numbers in scientific notation

Introduction to Scientific Notation and Multiplication in Scientific Notation

- what is scientific notation
- how to convert from decimal notation to scientific notation
- how to multiply and divide numbers in scientific notation

Scientists have developed 'scientific notation' as a shorter method to express very large and very small numbers.

Scientific Notation is based on powers of the base number 10.

The number 123,000,000,000 in scientific notation is written as:

The first
number 1.23 is called the **coefficient**. It must be greater than or equal
to 1 and less than 10. The second number is called the **base** which must
always be 10 in scientific notation. The **exponent** indicates the power to which 10 must be raised to bring the number to its proper magnitude.

To write a **very
large number** in scientific notation:

1. Move the decimal point to theleftuntil after the first digit. (e.g. 1.23 000 000 000)

2. The number of places moved by the decimal point would be the exponent. (e.g. 11)

3. Then drop the zeroes. (e.g.)

To enter scientific notation in the calculator, use the EXP key.

For example: Enter 1.23 EXP 11 for

A **very small number** will have a **negative exponent**, for example:

0.000 000 00712 will be written as 7.12 × 10

^{-9}

To
write a **very small number** in scientific notation:

1. Move the decimal point needs to the

rightuntil after the first non-zero digit. (e.g. 7.12)

2. The number of places moved by the decimal point would be the negative exponent. (e.g. -9)

The following video shows an example of converting a number in standard notation to a number in scientific notation.

To multiply numbers in scientific notation:

1. Multiply the coefficients

2. Add the exponentsFor example:

(2.1 × 10

^{-2}) × (3.2 × 10^{4})

= 2.1 × 3.2 × 10^{-2+4 }

= 6.72 × 10^{2}

This video shows how to convert from decimal notation to scientific notation and how to multiply and divide numbers in scientific notation.

Introduction to Scientific Notation and Multiplication in Scientific Notation

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