Scientific Understanding

**What sections should I know before attempting to learn this section?**

—> Exponents

**How do we go from a non-scientific notation number to a scientific notation number?**

What happens if we go in the reverse direction? Let’s take a non-scientific notation number and turn it into scientific notation.

**VIDEO Scientific Notation Demonstrated Example 3**: Convert this non-scientific notation number below into scientific notation.

0.00000000873

What is the first non-zero number we encounter as we go from left to right above?

Answer: 8

What are all the significant figures or numbers after and including 8?

Answer: 873

Where would a decimal point go to make those digits into a number between 1 and 10?

Answer: 8.73

How many places do we have to move our decimal from our original number to get 8.73?

Answer: 9

Therefore, what is the exponent on the 10?

Answer: 9

Is the exponent positive or negative?

Answer: Negative (because we started off with a small number)

What does the scientific notation look like?

COMPLETE ANSWER: 8.73 * 10^{-9}

**VIDEO Scientific Notation Demonstrated Example 4**: Convert this non-scientific notation number below into scientific notation.

425000

What is the first non-zero number we encounter as we go from left to right above?

Answer: 4

What are all the significant figures or numbers after and including 4?

Answer: 425

Where would a decimal point go to make those digits into a number between 1 and 10?

Answer: 4.25

How many places do we have to move our decimal from our original number to get 4.25?

Answer: 5

Therefore, what is the exponent on the 10?

Answer: 5

Is the exponent positive or negative?

Answer: Positive (because we started off with a large number)

What does the scientific notation look like?

COMPLETE ANSWER: 4.25 * 10^{5}

**PRACTICE PROBLEMS**: Convert these numbers into scientific notation.

0.000713 | 7.13 * 10^{-4} |

98000 | 9.8 * 10^{4} |

31.2 | 3.12 * 10^{1} |

0.0000006508 | 6.508 * 10^{-7} |