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:

Example 1

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.

Example 2

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.

Example 3

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.

Example 4

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.

Example 5

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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