# Scientific Notation

# Scientific Notation

Scientific notation is a special method for writing numbers that are **VERY LARGE** or **VERY SMALL**. This notation has been used for years, and is especially appropriate for our high tech age.

These numbers are used to describe distances into vast space, small size at atomic level, amounts of memory on computers, data transfer rates for phones, and much more. Using calculators or computers, you can easily encounter answers in scientific notation.

In scientific notation, numbers like 24520000 would become 2.452 x 10^{7}. Conversion is done as follows:

- Identify where the decimal point is, insert it if it is missing (add it to the end of a whole number).
- Count how many digits must by passed to move the decimal point between the two most significant digits.
- Rewrite the number, moving the decimal point between the two most significant non-zero digits, dropping trailing zeros.
- Add "x 10" after the rewritten number
- Use the count as an exponent to the 10. Include a negative sign in the exponent if the decimal point would have to move left to return to its original position.

Additionally, since calculators have trouble displaying exponents, calculators have a slightly different method for showing scientific notation. In the event you read a calculator and it shows 2.375 e+9, this is actually 2.375 x 10^{9}. In this case, "e" replaces the "x 10" and is derived from the word "exponent," implying the following number is the exponent of 10.

# Check Your Understanding

For the following, look at the number and convert it to scientific notation in your mind. Then, click the dropdown to confirm your answer.

- 197000000000
- 2345.5
- 0.00000521
- 0.002
- 9100000000

By the way, when you talk about milliseconds, gigabytes of memory, kilometers and more ... you are talking in scientific notation. if you have a 7.2 Megabit camera, you have 7.2 x 10^{6} bits in your camera to create the picture. If you have a 5 Terabyte harddrive, you have a 5 x 10^{12} bytes in your hard drive. The following chart shows some of the typical prefixes to words we use ... implying you are using scientific notation in your daily conversation.

Number Exponential Form Symbol Prefix
1,000,000,000,000 10^{12} T tera
1,000,000,000 10^{9} G giga
1,000,000 10^{6} M mega
1,000 10^{3} k kilo
1 10^{0}
0.01 10^{-2} c centi
0.001 10^{-3} m milli
0.000001 10^{-6} µ(Greek mu) micro
0.000000001 10^{-9} n nano
0.000000000001 10^{-12} p pico

# Scientific Notation

Scientific notation is a special method for writing numbers that are **VERY LARGE** or **VERY SMALL**. This notation has been used for years, and is especially appropriate for our high tech age.

These numbers are used to describe distances into vast space, small size at atomic level, amounts of memory on computers, data transfer rates for phones, and much more. Using calculators or computers, you can easily encounter answers in scientific notation.

In scientific notation, numbers like 24520000 would become 2.452 x 10^{7}. Conversion is done as follows:

- Identify where the decimal point is, insert it if it is missing (add it to the end of a whole number).
- Count how many digits must by passed to move the decimal point between the two most significant digits.
- Rewrite the number, moving the decimal point between the two most significant non-zero digits, dropping trailing zeros.
- Add "x 10" after the rewritten number
- Use the count as an exponent to the 10. Include a negative sign in the exponent if the decimal point would have to move left to return to its original position.

Additionally, since calculators have trouble displaying exponents, calculators have a slightly different method for showing scientific notation. In the event you read a calculator and it shows 2.375 e+9, this is actually 2.375 x 10^{9}. In this case, "e" replaces the "x 10" and is derived from the word "exponent," implying the following number is the exponent of 10.

# Check Your Understanding

For the following, look at the number and convert it to scientific notation in your mind. Then, click the dropdown to confirm your answer.

- 197000000000
- 2345.5
- 0.00000521
- 0.002
- 9100000000

By the way, when you talk about milliseconds, gigabytes of memory, kilometers and more ... you are talking in scientific notation. if you have a 7.2 Megabit camera, you have 7.2 x 10^{6} bits in your camera to create the picture. If you have a 5 Terabyte harddrive, you have a 5 x 10^{12} bytes in your hard drive. The following chart shows some of the typical prefixes to words we use ... implying you are using scientific notation in your daily conversation.

Number | Exponential Form | Symbol | Prefix |

1,000,000,000,000 | 10^{12} | T | tera |

1,000,000,000 | 10^{9} | G | giga |

1,000,000 | 10^{6} | M | mega |

1,000 | 10^{3} | k | kilo |

1 | 10^{0} | ||

0.01 | 10^{-2} | c | centi |

0.001 | 10^{-3} | m | milli |

0.000001 | 10^{-6} | µ(Greek mu) | micro |

0.000000001 | 10^{-9} | n | nano |

0.000000000001 | 10^{-12} | p | pico |