Standard Form Notation
Positive indices and standard form - part 1
INTRODUCTION:
Using your calculator, try to work out 9 to the power 9. You should find
out either an E appearing on the display or a number which looks like 3.874208. If you have a calculator with a large display, you might have the complete answer shown: 387420489.
Most calculators cannot show this number because it is nine digits long. Usually a calculator display shows a maximum of eight digits. What does
the calculator do when it tries to show the answer?
Some calculators show an E for error, indicating that it cannot show
the number as it is too large. Scientific calculators use standard form
to show the number. This is a method of shortening large numbers in a standard form.
3.874208 means 3.8742 * 10 to the power of 8 or 3.8742 * 10 * 10 * 10
* 10 * 10 * 10 * 10 * 10.
In other words, we have to multiply the decimal by ten eight times to
show it as an ordinary number. Each time when we multiply by ten, the decimal moves one place to the right, so when we multiply by ten to the power of eight the decimal moves up eight places to the right.
Definition
In standard form notation, we have two parts to the number.
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The first part is a decimal with the decimal point after the first
digit.
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The second part is the power of ten by which we must multiply the
decimal to change it back into an ordinary number.
Exercise 1
Write the following numbers in ordinary form:
Solution:
4.271 * 105 = 4.271 * 10 * 10 * 10 * 10 * 10 = 427100 (each time when we multiply, the decimal moves one place to the right; we
multiplied by 105, therefore decimal moves up five places to
the right)
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