measurement & significant figures what time is it? someone might say: “9:00” or “9:02”...

Measurement & Significant Figures

What time is it?Someone might say:

“9:00” or “9:02” or “9:02:22”

All of these are appropriate for different situations

But why is it we can read so many different times

from a clock?

Each time given depends on…

what type of clock a person is reading!

The clock here shows the hours and 5 minute increments.

What time is it on this clock?

10:10:00 10:10

Can we really read seconds from this clock?

This clock has no second hand, so we don’t know if it is 10:10:00 or 10:10:30.

This clock has a limit to what time it can tell.

You’re RIGHT!!!

This clock has no second hand, so we don’t know if it is 10:10:00 or 10:10:30.

This clock has a limit to what time it can tell.

Each time given depends on…

what type of clock a person is reading!

The clock here shows the hours and each minute

increment.

If the minute hand was here,

What time is it?

10:10 10:12

10:12:00

Not Exactly…

This clock has minute increments. So the time

can be read more accurately.

TRYAGAIN!

GREAT!!!!

This clock has minute increments so you can tell

it is exactly on the 12.

But it still doesn’t have a second hand, so we can’t

include seconds in our time.

Not Exactly…

The clock here shows the hours and each minute

increment.

But the clock still does not display time in seconds.

TRY AGAIN!

Each time given depends on…

what type of clock a person is reading!

The clock here shows the hours, minutes, and

seconds.

If the minute hand was here

What time is it?

10:10 10:12

10:12:32

Not Exactly…

This clock has minute increments and a sec hand.

So the time can be read more accurately.

TRY AGAIN!

Not Exactly…

This clock has minute increments and a sec hand.

So the time can be read more accurately.

TRY AGAIN!

Fantastic!!!!

This clock has minute increments and a second

hand.

The time can be read more accurately on this clock!

When we read time…we are taking a measurement!

How exact our measurement is depends on the equipment or instrument we use to take that measurement.

Let’s look at another example:

The person reading this green object records

the length as 4.81950. Based on the instrument

they are using, is this a valid measurement?

Yes No

Excellent!!!

This ruler does not have enough increments to measure the object to 5 decimal places. A measurement of 4.8 would be more accurate.

Take Another Look…

How many increments are listed on the ruler?

Can you see enough increments to read out 5 decimal places? No!

Therefore, a measurement of 4.8 would be more accurate.

Now you try…

How long is the grey block above?

What is the length of this gray block in

cm?

11.6 11.711.6511.71

Let’s look Closer …

This is the line for .6

Looking at the red line, you can see that there is still some of the grey block that passes the line. Therefore, 11.6 is too small of a measurement for this block.

TRY AGAIN!

Let’s look Closer …

This is the line for .7

Looking at the red line, you can see that the grey block does not reach the line. Therefore, the measurement 11.7 is too big for this block.

TRY AGAIN!

Great Job!!!

This is the line for .6

Looking at the red line, you can see the line lies right between .6 and .7! Therefore, the correct measurement needs to include the .6 but also an extra digit to indicate the block passes the .6 but does not reach .7… so 11.65 does just that!

Let’s look Closer …

This is the line for .7

Looking at the red line, you can see that the grey block does not reach the line. Therefore, the measurement 11.71 is too big for this block.

TRY AGAIN!

Graduated Cylinders

Are used to measure the volume of a liquid

Always, record the measurements from the bottom of the meniscus.

The meniscus occurs from liquid being in the graduated cylinder.

To ensure an accurate measurement, you should always read from the bottom of the meniscus.

Look at the graduated

cylinder at the right.

What would be the volume of the

liquid?54 53

54.1 52.9

TRY AGAIN!

The yellow line indicates the increment for 54. Is the bottom of the meniscus at this line?

No it isn’t.

TRY AGAIN!

The yellow line indicates the increment for 53. Is the bottom of the meniscus at this line?

Almost, but you can still see a bit of the liquid line.

TRY AGAIN!

The yellow line indicates the increment for 51.2. Is the bottom of the meniscus at this line?

No it isn’t.

The yellow line indicates the increment for 52.9 You can no longer see the meniscus. But the liquid level is not quite at 53 because you can see the 53 increment right above the yellow line.

Measurements in Science

In science, we describe a measurement as having a certain number of “significant digits”

These are called significant digits, significant figures, or sometimes just “Sig Figs”.

Significant Figures or “Sig Figs”

Remember: significant figures, significant digits, and sig figs mean the same

This clock reads “9:02:22”

In this measurement,

all the numbers are important to the specific

time.

Therefore, this time has 5 significant digits or

figures.

Remember…

This is the line for .6

This block has a measurement of 11.65.

Each digit in the measurement is significant. Therefore, this measurement has 4 significant figures or “sig figs”

When reading the bottom of this meniscus, the liquid is right at the 32 increment. However, to indicate this, the measurement needs a .0 added.

There are 3 sig figs in this measurement

Determining Sig Figs

There are rules that dictate the number of significant digits in a measurement.

Let’s take a look at the rules!!!

Sig Fig Rules: Significant

Non-Zeros:

.399 = 3 Sig Figs

Examples:

14679.48 = 7 Sig Figs

1) All non-zeros are significant (1-9)

Sig Fig Rules: Significant

Zeros

8040.5 = 5 Sig Figs

Examples:

1000025 = 7 Sig Figs

2) Zeros appearing between non-zero digits are significant

Sig Fig Rules: Significant

Zeros:

12.00 = 4 Sig Figs

Examples:

.567000 = 6 Sig Figs

3) Zeros at the end of a number and to the right of a decimal point are significant

Sig Fig Rules: Significant

Zeros:

1100. = 4 Sig Figs

Examples:

134000. = 6 Sig Figs

4) Zeros at the end of a number and to the left of a decimal point are significant

Sig Fig Rules: Non-SignificantZeros:

9000 = 1 Sig Figs

Examples:

0.08532 = 4 Sig Figs

5) Place keeping zeros are not significantA) In front of non-zero digits

B) End of a number without a decimal

Not Significant

Now Let’s Practice!!!

How many sig figs does the following number have?

246783972

8 9

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

TRY AGAIN

246783972

Great!!! Now which Rule did you use?

1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant 3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant 5. Place keeping zeros are NOT significant:

a)In front of non-zero digitsb)End of a number without a decimal

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

Are there zeros in your value? Where are they located?

If the zeros are not between to non-zero digits, you used a different rule.

TRY AGAIN

246783972

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

Are there zeros in your value? Where are they located? Is there a decimal present?

If there is no decimal or if the zeros are not to the right of the decimal, then you used a different rule.

TRY AGAIN

246783972

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

Are there zeros in your value? Where are they located? Is there a decimal present?

If there is no decimal or the zeros are not to the left of the decimal, you used a different rule.

TRY AGAIN

246783972

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

Are there zeros in your value? Where are they located? Is there a decimal present? If the zeros are in front of any non-zero digit, or if the zeros are at the end of a number without a decimal, you used a different rule.

TRY AGAIN

246783972

Great!!! Let’s Try Another One…

How many sig figs does the following number have?

0.0000784

7 3 8

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

TRY AGAIN

0.0000784

Awesome!!! Now which Rule did you use?

1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant 3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant 5. Place keeping zeros are NOT significant:

a)In front of non-zero digitsb)End of a number without a decimal

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

Are all the digits between 1-9?

If there is one zero, you used a different rule.

TRY AGAIN

0.0000784

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

Are there zeros in your value? Where are they located?

If the zeros are not between to non-zero digits, you used a different rule.

0.0000784

TRY AGAIN

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

Are there zeros in your value? Where are they located? Is there a decimal present?

If there is no decimal or if the zeros are not at the end of a number and to the right of the decimal, then you used a different rule.

0.0000784

TRY AGAIN

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

Are there zeros in your value? Where are they located? Is there a decimal present?

If there is no decimal or the zeros are not to the left of the decimal, you used a different rule.

0.0000784

TRY AGAIN

You really know your stuff!Let’s Try Another…

How many sig figs does the following number have?

6300045

2 4 7

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

TRY AGAIN

6300045

Fantastic!!! Now which Rule did you use?

1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant 3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant 5. Place keeping zeros are NOT significant:

a)In front of non-zero digitsb)End of a number without a decimal

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

Are all the digits between 1-9?

If there is one zero, you used a different rule.

TRY AGAIN

6300045

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

Are there zeros in your value? Where are they located? Is there a decimal present?

If there is no decimal or if the zeros are not to the right of the decimal, then you used a different rule.

6300045

TRY AGAIN

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

Are there zeros in your value? Where are they located? Is there a decimal present?

If there is no decimal or the zeros are not to the left of the decimal, you used a different rule.

6300045

TRY AGAIN

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

Are there zeros in your value? Where are they located? Is there a decimal present? If the zeros are in front of any non-zero digit, or if the zeros are at the end of a number without a decimal, you used a different rule.

6300045

TRY AGAIN

Yes!!! You got it!!Do Another…

How many sig figs does the following number have?

6700000000000000000000000000000000

34 17 2

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

TRY AGAIN

6700000000000000000000000000000000

Great Job!!! Now which Rule did you use?

1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant 3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant 5. Place keeping zeros are NOT significant:

a)In front of non-zero digitsb)End of a number without a decimal

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

Are all the digits between 1-9?

If there is one zero, you used a different rule.

TRY AGAIN

6700000000000000000000000000000000

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

Are there zeros in your value? Where are they located?

If the zeros are not between to non-zero digits, you used a different rule.

6700000000000000000000000000000000

TRY AGAIN

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

Are there zeros in your value? Where are they located? Is there a decimal present?

If there is no decimal or if the zeros are not to the right of the decimal, then you used a different rule.

6700000000000000000000000000000000

TRY AGAIN

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

Are there zeros in your value? Where are they located? Is there a decimal present?

If there is no decimal or the zeros are not to the left of the decimal, you used a different rule.

6700000000000000000000000000000000

TRY AGAIN

Great Work!! Here’s Another…

How many sig figs does the following number have?

1300000000000.

2 13 8

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

TRY AGAIN

1300000000000.

Nice Work!!! Now which Rule did you use?

1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant 3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant 5. Place keeping zeros are NOT significant:

a)In front of non-zero digitsb)End of a number without a decimal

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

Are all the digits between 1-9?

If there is one zero, you used a different rule.

TRY AGAIN

1300000000000.

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

Are there zeros in your value? Where are they located?

If the zeros are not between to non-zero digits, you used a different rule.

1300000000000.

TRY AGAIN

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

Are there zeros in your value? Where are they located? Is there a decimal present?

If there is no decimal or if the zeros are not to the right of the decimal, then you used a different rule.

1300000000000.

TRY AGAIN

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

Are there zeros in your value? Where are they located? Is there a decimal present? If the zeros are in front of any non-zero digit, or if the zeros are at the end of a number without a decimal, you used a different rule.

1300000000000.

TRY AGAIN

Hooray!!! Just one More…

How many sig figs does the following number have?

3.400

4 2

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

TRY AGAIN

3.400

Great!!! Now which Rule did you use?

1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant 3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant 5. Place keeping zeros are NOT significant:

a)In front of non-zero digitsb)End of a number without a decimal

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

Are all the digits between 1-9?

If there is one zero, you used a different rule.

TRY AGAIN

3.400

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

Are there zeros in your value? Where are they located?

If the zeros are not between to non-zero digits, you used a different rule.

3.400

TRY AGAIN

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

Are there zeros in your value? Where are they located? Is there a decimal present?

If there is no decimal or the zeros are not to the left of the decimal, you used a different rule.

3.400

TRY AGAIN

Remember your Rules: 1. All non-zeros are significant (1-9)

2. Zeros appearing between non-zero digits are significant

3. Zeros at the end of a number and to the right of a decimal point are significant

4. Zeros at the end of a number and to the left of a decimal point are significant

5. Place keeping zeros are NOT significant:

a) In front of non-zero digits

b) End of a number without a decimal

Are there zeros in your value? Where are they located? Is there a decimal present? If the zeros are in front of any non-zero digit, or if the zeros are at the end of a number without a decimal, you used a different rule.

3.400

TRY AGAIN

YAY!!! You Did It!!!

Great Work!!!!

When taking measurements or using measurements in science,

Remember to use significant figures.

Significant figures or digits will be important to many of the concepts and topics you will learn in chemistry

this year.