- Education and Science
How to write small numbers using standard form notation (negative exponents)
Just to recap, a number in standard form takes the form:
a × 10n
If you are writing small numbers in standard form n is a negative exponent (power) as this means you are actually dividing a by 10 to give you the original number. Also, remember that a must take a value between 1 and 10. Let’s take a look at a few examples of converting small numbers into standard form:
Write 0.0056 in standard form.
Since a must be number between 1 and 10, a must be 5.6.
Now, to get 0.0056, 5.6 must be divided by 1000 (the same as 10³).
So 0.0056 in standard form is 5.6 × 10⁻³.
Write 0.0005 in standard form.
Since a must be number between 1 and 10, a must be 5 (or 5.0)
Now, to get 0.0005, 5 must be divided by 10,000 (the same as 10⁴).
So 0.0005 in standard form is 5 × 10⁻⁴.
Write 0.000000924 in standard form.
Since a must be number between 1 and 10, a must be 9.24.
Now, to get 0.000000924, 9.24 must be divided by 10,000,000 (the same as 10⁷).
So 0.000000924 in standard form is 9.24 × 10⁻⁷.
A cell has a length of 0.081mm. Write this value in standard form.
Since a must be number between 1 and 10, a must be 8.1.
Now, to get 0.081, 8.1 must be divided by 100 (the same as 10²).
So the length of the cell in standard form is 8.1 × 10⁻².
Write 0.0089648364 in standard form (to 3 significant figure)
First round the number off to 3 significant figures:
0.0089648364 = 0.00896 rounded to 3 significant figures.
Since a must be number between 1 and 10, a must be 8.96.
Now, to get 0.00896, 8.96 must be divided by 1000 (the same as 10³).
So 0.00896 in standard form is 8.96 × 10⁻³.
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