Science 1222 Lab Measurement # Laboratory # Measurements

## Values read from the measuring instrument are expressed with numbers known as significant figures.

### Examples:

• 203.4 cm: least count of ruler was 1 cm, tenth of centimeter was estimated.

• 4.07 cm: least count was 0.1 cm. hundredth of centimeter was estimated.

## You cannot increase the precision of measurement by doing arithmetic operations such as addition, subtraction, multiplication, division. This can be confusing because the calculator will return a large number of decimal places, especially when performing division.

### Examples:

• 12.34 cm + 9.8 cm = 22.14 cm., which should be rounded to 22.1 cm. sinc 9.8 has the greater number of decimal places.
• 16.315 cm x 21.84 cm = 356.3196 cm2 is rounded to four s.f. and becomes 356.3 cm2 because there are four s.f. in 16.31
• 37.91 divided by 6.3 = 6.0174603175 which becomes 6.0 because 6.3 has only two s.f.

## Rounding

### Round off the following numbers to two significant figures.

• 247 is rounded to 250- Since the last digit on the right is greater than 5, drop it and increase the preceding digit by one, for the result 250.

• 243 is rounded to 240 - Since the last digit on the right is less than 5, drop it and insert zero instead, for the result 240.

• 27.16 is rounded to 27. Since the last digit on the right is greater than 5, drop it and increase the preceding digit. This leaves, for the result 28.

### - Zero is always a significant digit when it is between the decimal point and another digit.

• Example: 14.002 has 5 significant figures.

• Example: 60.2 has 3 significant figures

### - Zero is significant if it is to the right of the decimal point

• Example: 29.20 has 4 significant figures

• Example: 7.020 has 4 significant figures

### - Zero is usually not a significant digit if there is no decimal point.

• Example: 240 has 2 significant figures
• Example: 1000 has 1 significant figure

### One exception is when a zero is obtained by rounding

• Example: 249.8 is rounded to 3 significant figures to become 250. Here the zero is significant.

## Units of Measurement

### Below are common units used in the metric system (also called the SI system.) Units in capital letters are the common ones.

LENGTH
Unit Abbreviation Meters
MILLIMETER

mm

0.001

CENTIMETER

cm

0.01

METER

1.0

KILOMETER

km

1000.0

MASS
Unit Abbreviation grams
MILLIGRAM

mg

0.001

GRAM

KILOGRAM

kg

1000