You will often be required to gather date by making measurements. To measure means to determine the dimension, capacity, weight, etc., of materials by comparison with a given standard. Man has prepared several standards and the English and the Metric Systems of Measurements maybe cited as examples. At present, however, a concerted effort is being made to adopt the SI units (Le Systems International d’ Unites) for all scientific works. During this period of change from the English to the new system, you need to be familiar with both.

**Precision in Measurement**

The precision of an experimental result means the agreement between such result and another obtained by duplicate measurement under similar conditions. The student should always report his results in such a way as to give the correct information about the precision of his measuring instrument. He does this by recording his data with the correct number of significant figures.

**Accuracy in Measurement**

The accuracy of an experimental result means the degree of agreement between it and the true value. Greater accuracy maybe obtained by making more that 1 trial and getting the average value of these trials. A result maybe judged accurate if its percentage of error is small.

Difference between Experimental Value and True Value

% error = ——————————————————————– x 100

True Value

**Significant Figures**

Significant figures are numbers which express the result of a measurement such that only the last digit is doubtful. The proper number of significant figures indicates how accurately the measurements are made. In a given numerical result, the following digits are considered significant.

1. All none-zero digits

2. Zero between two non-zero digits

3. In decimal numbers greater than 1, zeros before and after the decimal point.

4. In decimal numbers less than 1, zeros after the first non-zero digit. Zeros before the decimal point and preceding digits are not significant.

5. Zeros before and unexpressed decimal point may or may not be significant. Confusion is avoided by writing the number in exponential form.

6. Terminal zeros with a specified notation on the last digit (using a bar above the last 0 or with an expressed decimal point).

7. Zeros in money.

**Round off of Numbers**

1. When the number to be dropped is less than 5, the preceding number remains unchanged.

2. When the number to be dropped is greater than 5, 1 is added to the preceding number.

3. When the number to be dropped is exactly 5, if the preceding number is ever, it remains unchanged; if the preceding number is odd, 1 is added to it.

Note: Number dropped may be taken a 5, 50, 500…….

**Scientific Notation**

In scientific notation, very large numbers and very small numbers are conveniently expressed as powers of 10. To convert a decimal number greater than 1 to scientific notation, move the decimal point to the left until the decimal point is in its standard position and multiply by a power of 10 (positive exponent). To convert a decimal number less than 1 to a scientific notation, move the decimal point to the right until the decimal point is in its standard position and multiply by a power of 10 (negative exponent).

**Procedure in Measurement**

**A. Dimension**

With the use of a foot rule, measure in cm. the length, width thickness of the regular solids provided b y your instructor.

**B. Measurement of Volume**

Practice measuring 100 ml of dilute water by the use of graduated cylinder, adding and removing water from its until the lower meniscus coincides with the 100 ml graduation. Read the volume of the liquid by holding the cylinder vertically at eye level and look at the lower meniscus (convex curve). Make three (3) trials.

Now practice measuring 100 ml of dilute KMn0_{4} using the same graduated cylinder. This time get the reading of which is the upper meniscus, the part where the liquid gets is contact with the glass.

**C. Measurement of Density**

1. **Density of Liquid**

Weigh a clean and dry graduated cylinder in the balance and record the weight. Pour 20 ml of a sample of liquid (to be assigned by your instructor) to the cylinder and record the volume. Weigh the cylinder and its contents. Calculate the weight and density of the liquid. Get the correct density of the liquid from your instructor. Calculate the % error.

**2. ****Density of a Solid**

Weigh a pebble or any irregular solid in the weighing balance. Pour 20 ml of water into clean dry graduated cylinder. Record this as initial volume. Then drop the pebble or any solid to the cylinder and record the final volume obtained. Calculate the volume of the solid and its density.

**D. Measurement of Temperature**

Place a thermometer in a beaker with tap water. After a minute, read the thermometer and record the temperature of the water in ^{o}C and convert this to ^{o}F. When making the reading, do not let the thermometer bulb touch the sides or the bottom of the beaker.