PRECISION AND SIGNIFICANT

FIGURES

1.1 To determine the degree of precision of a measurement.

Related Standard N.Q.A.1 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Introduction

Today we are going to talk about MEASUREMENT

What to do:1. Each pair of students is going to

measurean object in the unit of measure you

weregiven when you walked in.

2. Record your measurements on the board.

WHOSE MEASUREMENT IS CORRECT?

Who used the correct tool?

Hmmmm . . .

Are 7.5 grams and 7.50 grams the same?

What Scientists Do . . .

When scientists do experiments, they're always recording data and making measurements.

Sometimes the information they record is based on observation. This is called qualitative, meaning that it is based on an observation, but it's not directly measured and recorded numerically.

For example, 'The water in the beaker is warm' would be a qualitative observation. I didn't actually go and measure the temperature of the water in the beaker.

What Scientists Do . . .

The other type of information that scientists record is quantitative, meaning that it is based on a measurement, and it's reported numerically.

An example would be 'The water in the beaker is 87 degrees.' Notice how there's a number in the quantitative observation and not in the qualitative observation.

Precision

If you have ever measured something more than once, you may have noticed that each time you may get a slightly different result?

Any time you make a measurement there is some degree of uncertainty related to that measurement.

This is because no measuring device is perfect. Usually the more high-quality the measuring instrument is the more precise your measurement will be.

Precision

The precision of an instrument refers to the smallest repeatable digit that the instrument can measure to.

For example, if you are measuring the mass of a pen and one balance reads 7.5 grams while another (more precise balance) measures 7.50 grams, the second balance will give you a more precise measurement.

Reporting Measurements

When reporting these measurements, it's extremely important to report all the digits that are given.

In math class, you may have learned that 7.50 is equivalent to 7.5, but when it comes to making and recording a measurement, the zero at the end is just as important as the seven and the five.

This is because the zero tells the person reading the number that the balance measured out to the nearest hundredth place, which just happened to be a zero. It pretty much tells us that the second balance we used is a little more 'high-tech' than the first one because it measures out farther.

7.5 VS 7.50

This zero is so important that it is called a significant figure.

A significant figure is a number that plays a role in the precision of a measurement. If a number is significant, it means that it is kept track of when reporting measured results and making calculations.

It's very important to be able work with significant figures correctly so both the measurement and the precision of the instrument used are communicated.

So Which Digits Are Significant? ● ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are

ALWAYS significant.

● ALL zeros between non-zero numbers are ALWAYS significant.

● ALL zeros which are SIMULTANEOUSLY to the right of the decimal point AND at the end of the number are ALWAYS significant.

● ALL zeroes which are to the left of a written decimal point and are in a number > 10 are ALWAYS significant.

Sound Confusing? Watch this . . .

https://www.youtube.com/watch?v=GVRKRsegiCE

Practice

How many significant digits are present in each of the following numbers?

NumberNumber of Significant

DigitsRule(s)

48, 923

3.967

900.06

0.0004

8.1000

501.040

10.0

Can you answer these?

1. What is the difference between quantitative and qualitative?

2. Which measurement is most precise?a. 40 days and 3 yearsb. 36 inches and 3 feetc. 43.2 cm and 43 cm

3. How many significant digits are in each figure below?

a. 0.0001b. 1.000c. 10.00d. 1,000