Writing and Interpreting Numbers in Standard Form
We use standard form to easily write very, very large numbers and very, very small numbers.
A number is in standard form when it is written in the form:
a × 10n
a is a number greater than, or equal to 1, and less than 10.
n is an integer (whole number).
If n is positive, we are dealing with a large number. If n is negative, we have a small number (less
than 1).
The power of n tells us how many times we multiply by 10 (if n is positive) or divide by 10 (if n is
negative). Informally, we can say that n tells us how many places the digits have moved in relation
to the decimal point.
Example 1
Example 2
a. Write 39 000 in standard form.
a. Write 3.2 × 102 as an ordinary number.
We need to begin by choosing our value for
a. We want to keep the same digits in the
answer so we choose 3.9.
This is 3.2 × 10 × 10. The value for n is positive
so we know the number is going to be a large
one. Since n = 2, we move the digits 2 places.
3.2 × 102 = 320
39 000 can be written as 3.9 × 10 × 10 × 10 ×
10 or 3.9 × 104.
b. Write 1.8 × 10-3 as an ordinary number.
Look at where the decimal point would be in
the original number and where the decimal
point is in our new number.
The value for n is negative so we know the
number is going to be a small one.
We can count the difference in the number of
places to find the value of n.
As n = -3, we could divide 1.8 by 10 three
times.
39 000
4 places
Alternatively, we can move the digits 3 places.
1.8 × 10-3 = 0.0018
b. Write 0.0000467 in standard form.
We begin by choosing our value for a. We
want to keep the same digits in the answer so
we choose 4.67
This time, we have a small number (it’s less
than 1) so we are going to have a negative
value of n.
We can count the number of places the digits
have moved.
0.0000467
5 places
The digits have moved 5 places, therefore:
0.0000467 = 4.67 × 10-5
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Writing and Interpreting Numbers in Standard Form
Your Turn
1. Identify whether each of the following numbers is written in standard form. If a number is
not written in standard form, explain why.
a. 2 × 100.5
b. 10 × 104
c. 3 × 10-15
d. 0.9 × 10-2
e. 4.721431709 × 10-3
2. Write each number in standard form:
a. 7000
d. 38 000
g. 0.00981
b. 900 000
e. 0.002
h. 0.07024
c. 120
f. 0.000045
i. 98
3. Write each number in ordinary form:
a. 4 × 103
d. 9.01 × 104
g. 1.41 × 10-7
b. 2 × 107
e. 7 × 10-2
c. 3.1 × 102
f. 2.9 × 10-4
Challenge:
These numbers are not in standard form. Convert each one to standard form.
a. 31 × 104
b. 0.9 × 10-3
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