We will be using the SI units in this course. SI units are the internationally agreed upon units. Historically these units are based on the metric system which was developed in France at the time of the French Revolution.

Definition 2: SI Units

The name SI units comes from the French Système International d'Unités, which means international system of units.

There are seven base SI units. These are listed in Table 1. All physical quantities have units which can be built from these seven base units. So, it is possible to create a different set of units by defining a different set of base units.

These seven units are called base units because none of them can be expressed as combinations of the other six. This is identical to bricks and concrete being the base units of a building. You can build different things using different combinations of bricks and concrete. The 26 letters of the alphabet are the base units for a language like English. Many different words can be formed by using these letters.

The SI Units are not the only units available, but they are most widely used. In Science there are three other sets of units that can also be used. These are mentioned here for interest only.

For the following symbols of units that you will come across later in this book, write whether you think the unit is named after a person or not.

Click here for the solution.

Certain numbers may take an infinite amount of paper and ink to write out. Not only is that impossible, but writing numbers out to a high precision (many decimal places) is very inconvenient and rarely gives better answers. For this reason we often estimate the number to a certain number of decimal places. Rounding off or approximating a decimal number to a given number of decimal places is the quickest way to approximate a number. For example, if you wanted to round-off 2,65252722,6525272 to three decimal places then you would first count three places after the decimal. 2,652|52722,652|5272 All numbers to the right of || are ignored after you determine whether the number in the third decimal place must be rounded up or rounded down. You round up the final digit (make the digit one more) if the first digit after the || was greater or equal to 5 and round down (leave the digit alone) otherwise. So, since the first digit after the || is a 5, we must round up the digit in the third decimal place to a 3 and the final answer of 2,65252722,6525272 rounded to three decimal places is 2,653.

In a calculation that has many steps, it is best to leave the rounding off right until the end. For example, Jack and Jill walk to school. They walk 0,9 kilometers to get to school and it takes them 17 minutes. We can calculate their speed in the following two ways.

Method 1:

You will see that we get two different answers. In Method 1 no rounding was done, but in Method 2, the time was rounded to 2 decimal places. This made a big difference to the answer. The answer in Method 1 is more accurate because rounded numbers were not used in the calculation. Always only round off your final answer.

In Science one often needs to work with very large or very small numbers. These can be written more easily in scientific notation, in the general form

where dd is a decimal number between 0 and 10 that is rounded off to a few decimal places. ee is known as the exponent and is an integer. If e>0e>0 it represents how many times the decimal place in dd should be moved to the right. If e<0e<0, then it represents how many times the decimal place in dd should be moved to the left. For example 3,24×1033,24×103 represents 3240 (the decimal moved three places to the right) and 3,24×10-33,24×10-3 represents 0,003240,00324 (the decimal moved three places to the left).

If a number must be converted into scientific notation, we need to work out how many times the number must be multiplied or divided by 10 to make it into a number between 1 and 10 (i.e. the value of ee) and what this number between 1 and 10 is (the value of dd). We do this by counting the number of decimal places the decimal comma must move.

For example, write the speed of light in scientific notation, to two decimal places. The speed of light is 299 792 458 m··s-1-1. First, find where the decimal comma must go for two decimal places (to find dd) and then count how many places there are after the decimal comma to determine ee.

In this example, the decimal comma must go after the first 2, but since the number after the 9 is 7, d=3,00d=3,00. e=8e=8 because there are 8 digits left after the decimal comma. So the speed of light in scientific notation, to two decimal places is 3,00 ×× 1088 m··s-1-1.

In a number, each non-zero digit is a significant figure. Zeroes are only counted if they are between two non-zero digits or are at the end of the decimal part. For example, the number 2000 has 1 significant figure (the 2), but 2000,0 has 5 significant figures. You estimate a number like this by removing significant figures from the number (starting from the right) until you have the desired number of significant figures, rounding as you go. For example 6,827 has 4 significant figures, but if you wish to write it to 3 significant figures it would mean removing the 7 and rounding up, so it would be 6,83.

Work in groups of 5 to discuss other possible situations where using the incorrect set of units can be to your disadvantage or even dangerous. Look for examples at home, at school, at a hospital, when travelling and in a shop.

Read the following extract from CNN News 30 September 1999 and answer the questions below.

NASA: Human error caused loss of Mars orbiter November 10, 1999

Failure to convert English measures to metric values caused the loss of the Mars Climate Orbiter, a spacecraft that smashed into the planet instead of reaching a safe orbit, a NASA investigation concluded Wednesday. The Mars Climate Orbiter, a key craft in the space agency's exploration of the red planet, vanished on 23 September after a 10 month journey. It is believed that the craft came dangerously close to the atmosphere of Mars, where it presumably burned and broke into pieces. An investigation board concluded that NASA engineers failed to convert English measures of rocket thrusts to newton, a metric system measuring rocket force. One English pound of force equals 4,45 newtons. A small difference between the two values caused the spacecraft to approach Mars at too low an altitude and the craft is thought to have smashed into the planet's atmosphere and was destroyed. The spacecraft was to be a key part of the exploration of the planet. From its station about the red planet, the Mars Climate Orbiter was to relay signals from the Mars Polar Lander, which is scheduled to touch down on Mars next month. “The root cause of the loss of the spacecraft was a failed translation of English units into metric units and a segment of ground-based, navigation-related mission software,” said Arthus Stephenson, chairman of the investigation board. Questions:

Very often in Science you need to convert speed and temperature. The following two rules will help you do this:

Converting speed When converting km··h-1-1 to m··s-1-1you divide by 3,6. For example 72 km··h-1-1÷÷ 3,6 = 20 m··s-1-1.

When converting m··s-1-1to km··h-1-1, you multiply by 3,6. For example 30 m··s-1-1××3,6 = 108 km··h-1-1.

Converting temperature Converting between the kelvin and celsius temperature scales is easy. To convert from celsius to kelvin add 273. To convert from kelvin to celsius subtract 273. Representing the kelvin temperature by TKTK and the celsius temperature by ToCToC,

Try to get an idea of the typical values for the following physical quantities and write your answers into the table: