Measurement, Significant Digits and Recording Data in Science

Along with the knowledge, we need to understand the scientific method, how to collect data, analyze data and explain our results.

In science, we use SI (Scientifique Internationale) Units. They are metric units, some of which are used everyday, or specifically in the areas of science.

Units

Distance –

Mass –

Volume –

Temperature –

Time –

Force –

Heat –

Amount of Matter –

All other units are derivatives of the SI units.

Ex. 1 km = 1000 m

“kilo” = 1000 x the unit

Examples

SI Units and Conversion Sheet

PrefixSymbolMeaningFactor

GigaGbillion times a unit1 x 109

MegaMmillion times a unit1 x 106

Kilokthousand times a unit1 x 103

Hectohhundred times a unit1 x 102

Decadaten times a unit1 x 101

Base Units(m, L, g, s, mol, etc.)

Decidtenth of a unit1 x 10-1

Centichundreth of a unit1 x 10-2

Millimthousandth of a unit1 x 10-3

Microumillionth of a unit1 x 10-6

Nanonbillionth of a unit1 x 10-9

Expressing Accuracy of our Measuring Device

With every measuring device we have a degree of uncertainty, or when we are in between graduations or “ticks”. At this point we estimate what the degree of uncertainty is.

Using a Ruler – Measure a piece of white paper

The amount of liquid in a graduated cylinder

Significant Digits / Figures and Scientific Notation

Significant digits or sig. figs. are used to express the accuracy of your measuring device, and our answer.

For example, if you have a ruler that can only measure to the nearest half a cm, you can only express your measurement as 5.5 cm, as you had to estimate the half. This would only have 1 sig. fig. after the decimal place or 2 sig. figs. total.

A device that only measures to the nearest digit, could only express its accuracy as 1 cm or 10 cm, depending. In this case, the measurement only has 1 sig. fig., as the zero is only holding the place value, and does not contribute to the accuracy of the measurement. The same goes for decimals like 0.01 cm. There is only one sig. fig., as the zero is a placeholder. If the measurement was 0.010 cm this means the measuring device can measure to the nearest 0.001 cm and is more accurate. Therefore, you can express the measurement with two significant digits.

Confused? Don’t be. Here are the rules.

Rules of Significant Figures

  1. Zeros which are used to locate the decimal point are not significant. They are simply placeholders

3 cm = 0.03 m (Both have 1 significant digit)

300 km (only has one significant digit [Zeros are simply placeholders])

  1. All numbers other than zero, and zeros in between non-zero digits are significant

567.25 m = 5 sig. figs.609.2 cm = 4 sig. figs.

  1. Zeros after a decimal point are significant, as they are being used to express the accuracy of your measurement

6.70 s = 3 sig. figs.9.00 s = 3 sig. figs.

  1. When it comes to adding and subtracting measurements, and you use two different measuring devices (this rarely happens), you express your answer to the degree of the least accurate measurements number of decimal places.

28.16 cm + 5.423 cm + 0.0004 cm = 33.5834 cm

The answer is expressed as 33.58 cm

  1. When you multiply or divide measurements, and you use two or more different measuring devices, you express your answer to the degree of the least accurate measurements number of sig. figs.

0.24 g / 1.346 cm3 = 0.1783 g/cm3

The answer is expressed as 0.18 g/cm3

*****Even if you find an average, the number you divide by is not a measurement and does not affect the number of significant digits.

An easy way to use as many significant figures as possible is to use Scientific Notatation.

Do you know this number, 300,000,000 m/sec.?

It's the Speed of light!

Do you recognize this number, 0.000 000 000 753 kg. ?

This is the mass of a dust particle!

Or, do you recognize this number, 602 000 000 000 000 000 000 000 atoms / mol

This is Avagadro’s Number, or the number of atoms, molecules or formula units in one mol of any substance, used in Chemistry.

Scientists have developed a shorter method to express very large numbers. This method is called scientific notation. Scientific Notation is based on powers of the base number 10.

The number 123,000,000,000 in scientific notation is written as:

The first number 1.23 is called the coefficient. It must be greater than or equal to 1 and less than 10.

The second number is called the base. It must always be 10 in scientific notation. The base number 10 is always written in exponent form. In the number 1.23 x 1011 the number 11 is referred to as the exponent or power of ten.

To write a number in scientific notation:

Put the decimal after the first digit and drop the zeroes.

In the number 123,000,000,000 The coefficient will be 1.23

To find the exponent count the number of places from the decimal to the end of the number.

In 123,000,000,000 there are 11 places. Therefore we write 123,000,000,000 as:

This number means it is 1.23 x 100 000 000 000 (or 1 x 1011)!!!

For small numbers, the opposite is done. For example, 0.00000089567

The coefficient is 8.95. You count back how many spaces you move to get to the original place of the decimal. You need to move 7 spaces. The exponent is -7, as this is a decimal, and you are really saying, 8.95 x 0.000 000 1 (or 1 x 10 -7).

Therefore, the answer is:

REMEMBER, ONLY THREE SIGS. ARE USED FOR SCIENTIFIC NOTATION

Try these:

Convert the following to scientific notation:

23 780 km0.00456 kg0.000 000 006 00 m

1.78 cm **7 899 000 000 bytes0.000 345 g

Convert the following from scientific notation:

6.78 x 10 6 m6.78 x 10 -6 cm8.90 x 10 1 kg

4.01 x 10 4 km5.55 x 10 5 cm1.00 x 10 -3 m

****Convert the one in bold to mm ****Convert the speed of light, mass of a dust particle and Avagadro’s Number to Scientific Notation

Questions

  1. Tommy wants to find the density of a block of wood. The mass of the block is 34.563 g. The block is represented below.
  2. Using your ruler, measure the length, width and height of the block. Record your data to the appropriate amount of significant figures.
  3. Find the density of the block, using the correct amount of significant figures.

  1. Convert the following. (5 x 1 mark each = 5 marks)

a) 78.9 m to kmb) 6.78 kg to g

c) 678 nm to md) 7.98 dm3 to cm3

e)80.00 km/h to m/s

  1. Do the measurement activity on the next sheet.

Measurement Activity

Make sure you pay attention to the amount of sig. figs, and your accuracies. Show your work for all calculations.

Part 1– Apparatus – meter stick

  1. Measure the width of the table top with the meter stick. Record your answer in centimeters. Take 3 measurements in three different spots and take the average.
  2. Measure the length of the table top with the meter stick. Record your answer in centimeters. Take 3 measurements in three different spots and take the average.
  3. Take the averages and find the area of the table top.
  4. Convert your area from cm2 to m2.

Part 2 – Measuring Reaction time

  1. Using the computers in the classroom, go to
  2. Record three trials. Fill in the data table attached.
  3. Find the average reaction time.

Part 3 – Apparatus – meter stick, balance

  1. Ask your partner to take off their right shoe.
  2. Measure the sole of the shoe from heel to toe. Record.
  3. Take the balance and find the mass of the shoe.
  4. Calculate the mass to size ratio of the shoe.

Part 4 –Density of Water – Apparatus – 10 ml graduated cylinder, balance

  1. Find the density for three separate volumes of water. Find the average density of the water.
  2. The literature value for the density of water is 1.00 g/ml. What is your percent error?
  3. What can you conclude about density, the volume of a substance and its mass?

Part 1 – Area of the Table

trial / Length (cm) / Width (cm)
1
2
3
Avg.
Area (cm2)

Work

Part 2 – Reaction TimeWork

Trial / Time (s)
1
2
3
Avg.

Part 3 – Mass vs. size of shoe

Length of Shoe (cm) / Mass of Shoe (g) / Ratio (g/cm)

Work