Sometimes we do not always need to give detailed answers to problems - we just want a rough idea. When we are faced with a long number, we could round it off to the nearest thousand, or nearest million. And when we get a long decimal answer on a calculator, we could round it off to a certain number of decimal places. Another method of giving an approximated answer is to round off using significant figures.
The word "significant" means "having meaning".
With the number 368249, the 3 is the most significant digit, because it tells us that the number is 3 hundred thousand and something. It follows that the 6 is the next most significant, and so on.
With the number 0.0000058763, the 5 is the most significant digit, because it tells us that the number is 5 millionths and something. The 8 is the next most significant, and so on.
Be careful with numbers such as 30245, as the 3 is the first significant figure and 0 the second, because of its value as a place holder.
We round off a number using a certain number of significant figures. The most common are 1, 2 or 3 significant figures.
Remember the rules for rounding up are the same as before:
When using significant figures in calculations, we need to take into account the measurements we have made.
If measurements have been made to one, two or three significant figures, we cannot have more significant figures in answers to any calculations we make.
Most animal and plant cells are 0.01 to 0.10 mm in size. The smallest thing seen with the naked eye is about 0.05 mm.
For all cells we need a microscope to see them in any detail.
The best unit to measure most cells is the micrometre, which has the symbol μm.
One metre can be broken down into the following measurements:
|Millimetre, mm||Micrometre, μm||Nanometre, nm|
|Division of a metre as a fraction|
|Division of a metre in standard form||1 × 10-3 m||1 × 10-6 m||1 × 10-9 m|
A unit we use in everyday lives is the centimetre, m, or 1 × 10-2 m.
Decimals allow us to clearly identify that a number is not whole. They show us fractions of numbers in a very clear way.
So 0.5 is halfway between 0 and 1. 0.25 is one quarter of the way and 0.75 is three quarters.
When writing and working with very large or very small numbers, we use standard form.
Standard form shows the size of numbers as powers of 10.
In a book, a micrograph of the cell measured 100 mm.
The real size of the cell shown is 0.05 mm.
To calculate the magnification:
It's important to work in the same units when calculating magnification. Sizes of most cells are given in micrometres, with the symbol μm.
To calculate magnification using the same formula in micrometres, convert the measurement of the cell above from millimetres (mm) into micrometres (μm):
Cell measurement = 100 mm
1 mm = 1000 μm
100 mm = 100 × 1000 μm
100 mm = 100 000 μm
The real size of the cell above in micrometres is 50 μm.
The magnification of the image:
From this, we know that the image has been magnified 2000 times.