Use index notation and index laws for positive and negative powers
Index Notation is just a way of writing a really big or really small number that has a lot of zeros.
For example, consider the mass of the earth in grams, which is 5,974,200,000,000,000,000,000,000,000. We have 5 numbers, and a bunch of zeros.
To make it easier we can write this as 5.9742 x 1027
1027 means that we move the decimal point 27 times to the right (it's a positive number). Since we have 9,7,4 and 2 after the decimal point already, that gives us 23 zeros (if you count it above you'll see this is correct!)
This is an example of a positive power (positive for the positive n value which is 27 here)
By following index laws we know that a standard index form number is ALWAYS written as: A x 10 n
When turning a ridiculously large number in to a standard index form in your Maths GCSE exam we must remember:
- the number infront of the decimal point must always be between 1 and 10.
- we must include all the significant figures in for A and finally there is always a 10 when expressing a number in standard form
Another example is:
The mass of an electron: 0.000000000000000000000000000000910938188.
This is written as the following in standard index form:
9.1098188 x 10-31 Which is a negative power
As we discussed previously when writing a number in it's standard index form we must always include all of the significant figures in the original number, make sure that the number infront of the decimal point is between the numbers 1 and 10 and finally there is also a 10 in the expression.
The negative power of 31 shows how many times decimal point was moved to the left to get to our new number of 9.1098188.
Also remember that index laws is sometimes referred to as the laws of indices, do not worry it means the same thing!
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