You will need your own paper. Purpose: Significant digits (or significant figures) is a communication tool to express where you rounded any particular.

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Presentation transcript:

You will need your own paper

Purpose: Significant digits (or significant figures) is a communication tool to express where you rounded any particular number. Question (do not need to copy): If you won one million dollars, where would you want that rounded? The person paying would want to round it at the millions place, then they only have to pay you $500,000. Significant digits communicates where the rounding occurred! (end of do not need to copy)

In science we round for our measurements. We always estimate a digit between the lines on a measurement tool, and with significant digits we can communicate how accurate a measurement tool we used.

The Four Rules for Significant Digits:

1) All nonzero digits are significant

The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant

The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant Examples: ← these zeros are sig digs

The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant Examples: ← these zeros are sig digs ← these zeros are sig digs

The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant Examples: ← these zeros are sig digs ← these zeros are sig digs Nonexamples: ← these zeros are NOT sig digs

The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant Examples: ← these zeros are sig digs ← these zeros are sig digs Nonexamples: ← these zeros are NOT sig digs ← these zeros are NOT sig digs

The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant Examples: ← these zeros are sig digs ← these zeros are sig digs Nonexamples: ← these zeros are NOT sig digs ← these zeros are NOT sig digs Mixed: ← only 2 of these zeros are sig digs

The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant 3)Zero between significant digits (zeros or nonzeros) are also significant Examples: ← these zeros are sig digs

The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant 3)Zero between significant digits (zeros or nonzeros) are also significant Examples: ← these zeros are sig digs ← these zeros are sig digs

The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant 3)Zero between significant digits (zeros or nonzeros) are also significant Examples: ← these zeros are sig digs ← these zeros are sig digs ← these zeros are sig digs

The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant 3)Zero between significant digits (zeros or nonzeros) are also significant Examples: ← these zeros are sig digs ← these zeros are sig digs ← these zeros are sig digs

The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant 3)Zero between significant digits (zeros or nonzeros) are also significant Examples: ← these zeros are sig digs ← these zeros are sig digs ← these zeros are sig digs Nonexample: ← these zeros are NOT sig digs

The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant 3)Zero between significant digits (zeros or nonzeros) are also significant Examples: ← these zeros are sig digs ← these zeros are sig digs ← these zeros are sig digs Nonexample: ← these zeros are NOT sig digs Mixed: ← only 2 of these zeros are sig digs

The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant 3)Zero between significant digits (zeros or nonzeros) are also significant 4)Any other zeros are NOT signficiant digits, but still MUST be shown to keep the decimal place correct

The Four Rules for Significant Digits: 1)All nonzero digits are significant 2)Zeros that are after a decimal and after a nonzero digit (or vice versa) are significant 3)Zero between significant digits (zeros or nonzeros) are also significant 4)Any other zeros are NOT signficiant digits, but still MUST be shown to keep the decimal place correct Example : 1,000,000 ← only the “1” is a sig dig, so the one is where the rounding occurred (could have been 4,000,000 rounded down or 500,000 rounded up - we don’t know, but we know where it was rounded)

Self-Check (do not need to copy): How would you write one million to be as sure as possible of getting all your money?

Copy down these numbers, then circle the sig digs in each of them:

Copy down these numbers, then round them to the stated amount of sig digs: to 3 S.D to 1 S.D to 2 S.D to 3 S.D to 1 S.D to 3 S.D to 3 S.D. 500 to 2 S.D.

How many Significant Digits is in: 84.10

How many Significant Digits is in:

How many Significant Digits is in:

How many Significant Digits is in:

How many Significant Digits is in:

How many Significant Digits is in:

How many Significant Digits is in: 0.060

How many Significant Digits is in:

How many Significant Digits is in: 78000

How many Significant Digits is in:

How many Significant Digits is in:

How many Significant Digits is in:

How many Significant Digits is in:

How many Significant Digits is in:

How many Significant Digits is in: 0.006

How many Significant Digits is in:

How many Significant Digits is in: 7080

How many Significant Digits is in:

How many Significant Digits is in: 30050

How many Significant Digits is in:

How many Significant Digits is in:

How many Significant Digits is in:

How many Significant Digits is in:

How many Significant Digits is in:

How many Significant Digits is in:

How many Significant Digits is in:

How many Significant Digits is in:

How many Significant Digits is in:

How many Significant Digits is in: 500

How many Significant Digits is in: 500 1

How many Significant Digits is in:

How many Significant Digits is in:

Round the following number to the amount of Significant Digits: to 3 S.D.

Round the following number to the amount of Significant Digits: to 3 S.D. 84.1

Round the following number to the amount of Significant Digits: to 1 S.D.

Round the following number to the amount of Significant Digits: to 1 S.D. 80

Round the following number to the amount of Significant Digits: to 2 S.D.

Round the following number to the amount of Significant Digits: to 2 S.D

Round the following number to the amount of Significant Digits: to 3 S.D.

Round the following number to the amount of Significant Digits: to 3 S.D

Round the following number to the amount of Significant Digits: to 1 S.D.

Round the following number to the amount of Significant Digits: to 1 S.D. 1

Round the following number to the amount of Significant Digits: 7080 to 3 S.D.

Round the following number to the amount of Significant Digits: 7080 to 3 S.D. 7080

Round the following number to the amount of Significant Digits: to 3 S.D.

Round the following number to the amount of Significant Digits: to 3 S.D

Round the following number to the amount of Significant Digits: 500 to 2 S.D.

Round the following number to the amount of Significant Digits: 500 to 2 S.D. 5.0 x 10 2