6.1 Introduction & Large Numbers
Very large and very small numbers can be written in standard form and by writing these very large and small numbers in standard form, they are easier to deal with. Scientists often use standard form to measure distances between planets, the speed of waves (e.g. light), the size of atoms etc.
A number written in standard form will follow this form:
A number written in standard form will follow this form:
Where:
- A is a number between 1 and 10 (1 ≤ A < 10).
- n is the power of 10 (or the number of times that 10 is multiplied by itself). It is the number of places that the decimal points move.
When large numbers are written in standard form, they have a positive value for n. When small numbers are written in standard form, they have a negative value for n. Let’s first look at turning large numbers into standard form.
Large Numbers in Standard Form
When large numbers are written in standard form, they have a positive value for n. This is because the value for A is going to be less than the actual value for the number that we are changing into standard form. This means that we have to multiply A by 10 to a positive power in order to get the number that we are converting into standard form. Let’s get rid of standard form in the following number.
When large numbers are written in standard form, they have a positive value for n. This is because the value for A is going to be less than the actual value for the number that we are changing into standard form. This means that we have to multiply A by 10 to a positive power in order to get the number that we are converting into standard form. Let’s get rid of standard form in the following number.
A in the number above is 5.4 (and it is between 1 and 10) and n is four. 104 is 10 x 10 x 10 x 10, which is 10000. We therefore do:
Here are the powers of 10 for positive values of n:
- 100 = 1
- 101 = 10
- 102 = 100
- 103 = 1,000
- 104 = 10,000
- 105 = 100,000
Placing a Large Number into Standard Form
Write 64,000 in standard form.
The first step is to find a value for A between 1 and 10. This value will be 6.4. We then find what we multiply 6.4 by to get 64,000.
Write 64,000 in standard form.
The first step is to find a value for A between 1 and 10. This value will be 6.4. We then find what we multiply 6.4 by to get 64,000.
Therefore,
Another method to find the answer, is to look at how many places the decimal point has moved when we change 64,000 into 6.4. We can see that the decimal place has moved by 4 places, thus meaning that our answer for n is 4. This is the same as seeing how far the 6 is away from the units column; it is 4 places away, therefore meaning that n is 4.
Here is another example – write 3,500,000in standard form:
Our number for A is 3.5. 3 is 6 places away from the units column (or the decimal point moves 6 places), which means that n is 6. We can write 3,500,000 in standard form as:
Our number for A is 3.5. 3 is 6 places away from the units column (or the decimal point moves 6 places), which means that n is 6. We can write 3,500,000 in standard form as: