Significant Digits Notes

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:

The Four Rules for Significant Digits:1) All nonzero digits are significant

The Four Rules for Significant Digits:1) All nonzero digits are significant2) 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 significant2) Zeros that are after a decimal and after a

nonzero digit (or vice versa) are significantExamples: 4.00000 ← these zeros are sig digs

The Four Rules for Significant Digits:1) All nonzero digits are significant2) Zeros that are after a decimal and after a

nonzero digit (or vice versa) are significantExamples: 4.00000 ← these zeros are sig digs

.400000 ← these zeros are sig digs

The Four Rules for Significant Digits:1) All nonzero digits are significant2) Zeros that are after a decimal and after a

nonzero digit (or vice versa) are significantExamples: 4.00000 ← these zeros are sig digs

.400000 ← these zeros are sig digs

Nonexamples: 400000 ← these zeros are NOT sig digs

The Four Rules for Significant Digits:1) All nonzero digits are significant2) Zeros that are after a decimal and after a

nonzero digit (or vice versa) are significantExamples: 4.00000 ← these zeros are sig digs

.400000 ← these zeros are sig digs

Nonexamples: 400000 ← these zeros are NOT sig digs

.000004 ← these zeros are NOT sig digs

The Four Rules for Significant Digits:1) All nonzero digits are significant2) Zeros that are after a decimal and after a

nonzero digit (or vice versa) are significantExamples: 4.00000 ← these zeros are sig digs

.400000 ← these zeros are sig digs

Nonexamples: 400000 ← these zeros are NOT sig digs

.000004 ← these zeros are NOT sig digs

Mixed: .00400 ← only 2 of these zeros are sig digs

The Four Rules for Significant Digits:1) All nonzero digits are significant2) Zeros that are after a decimal and after a

nonzero digit (or vice versa) are significant3) Zero between significant digits (zeros or

nonzeros) are also significantExamples: 4000005 ← these zeros are sig

digs

The Four Rules for Significant Digits:1) All nonzero digits are significant2) Zeros that are after a decimal and after a

nonzero digit (or vice versa) are significant3) Zero between significant digits (zeros or

nonzeros) are also significantExamples: 4000005 ← these zeros are sig digs

400.0005 ← these zeros are sig digs

The Four Rules for Significant Digits:1) All nonzero digits are significant2) Zeros that are after a decimal and after a

nonzero digit (or vice versa) are significant3) Zero between significant digits (zeros or

nonzeros) are also significantExamples: 4000005 ← these zeros are sig digs

400.0005 ← these zeros are sig digs

.4000005 ← these zeros are sig digs

The Four Rules for Significant Digits:1) All nonzero digits are significant2) Zeros that are after a decimal and after a

nonzero digit (or vice versa) are significant3) Zero between significant digits (zeros or

nonzeros) are also significantExamples: 4000005 ← these zeros are sig digs

400.0005 ← these zeros are sig digs

.4000005 ← these zeros are sig digs

The Four Rules for Significant Digits:1) All nonzero digits are significant2) Zeros that are after a decimal and after a

nonzero digit (or vice versa) are significant3) Zero between significant digits (zeros or

nonzeros) are also significantExamples: 4000005 ← these zeros are sig digs

400.0005 ← these zeros are sig digs

.4000005 ← these zeros are sig digs

Nonexample: 0.0000045 ← these zeros are NOT sig digs

The Four Rules for Significant Digits:1) All nonzero digits are significant2) Zeros that are after a decimal and after a

nonzero digit (or vice versa) are significant3) Zero between significant digits (zeros or

nonzeros) are also significantExamples: 4000005 ← these zeros are sig digs

400.0005 ← these zeros are sig digs

.4000005 ← these zeros are sig digs

Nonexample: 0.0000045 ← these zeros are NOT sig digs

Mixed: 0.004005 ← only 2 of these zeros are sig digs

The Four Rules for Significant Digits:1) All nonzero digits are significant2) Zeros that are after a decimal and after a

nonzero digit (or vice versa) are significant3) Zero between significant digits (zeros or

nonzeros) are also significant4) 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 significant2) Zeros that are after a decimal and after a

nonzero digit (or vice versa) are significant3) Zero between significant digits (zeros or

nonzeros) are also significant4) 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?

Significant Digits Practice

Copy down these numbers, then circle the sig digs in each of them:84.100.03910077.66700.06078008.528000.000900.006

7080300500.020640004009200001600.005000.000000100200

Copy down these numbers, then round them to the stated amount of sig digs:84.10 to 3 S.D.84.10 to 1 S.D.0.039100 to 2 S.D.0.9876 to 3 S.D.

0.9876 to 1 S.D.7080 to 3 S.D.30050 to 3 S.D.500 to 2 S.D.

How many Significant Digits is in:

84.10

How many Significant Digits is in:

84.10

4

How many Significant Digits is in:

0.039100

How many Significant Digits is in:

0.039100

5

How many Significant Digits is in:

77.6670

How many Significant Digits is in:

77.6670

6

How many Significant Digits is in:

0.060

How many Significant Digits is in:

0.060

2

How many Significant Digits is in:

78000

How many Significant Digits is in:

78000

2

How many Significant Digits is in:

8.52800

How many Significant Digits is in:

8.52800

6

How many Significant Digits is in:

0.00090

How many Significant Digits is in:

0.00090

2

How many Significant Digits is in:

0.006

How many Significant Digits is in:

0.006

1

How many Significant Digits is in:

7080

How many Significant Digits is in:

7080

3

How many Significant Digits is in:

30050

How many Significant Digits is in:

30050

4

How many Significant Digits is in:

0.0206

How many Significant Digits is in:

0.0206

3

How many Significant Digits is in:

4000400

How many Significant Digits is in:

4000400

5

How many Significant Digits is in:

9200001

How many Significant Digits is in:

9200001

7

How many Significant Digits is in:

600.00

How many Significant Digits is in:

600.00

5

How many Significant Digits is in:

500

How many Significant Digits is in:

500

1

How many Significant Digits is in:

0.000000100200

How many Significant Digits is in:

0.000000100200

6

Round the following number to the amount of Significant Digits:

84.10 to 3 S.D.

Round the following number to the amount of Significant Digits:

84.10 to 3 S.D.

84.1

Round the following number to the amount of Significant Digits:

84.10 to 1 S.D.

Round the following number to the amount of Significant Digits:

84.10 to 1 S.D.

80

Round the following number to the amount of Significant Digits:

0.039100 to 2 S.D.

Round the following number to the amount of Significant Digits:

0.039100 to 2 S.D.

0.039

Round the following number to the amount of Significant Digits:

0.9876 to 3 S.D.

Round the following number to the amount of Significant Digits:

0.9876 to 3 S.D.

0.988

Round the following number to the amount of Significant Digits:

0.9876 to 1 S.D.

Round the following number to the amount of Significant Digits:

0.9876 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:

30050 to 3 S.D.

Round the following number to the amount of Significant Digits:

30050 to 3 S.D.

30100

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 102