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Powers of 10
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What
are
powers
of
10
?
Powers
of
10
are numbers like 10, 100, and
1
,
000
.
Powers of 10 can always be written with an
exponent
.
Look
at the table. Do you see a pattern in the number of zeros and the
exponent?
Exponent
Power
of
10
Value
Number
of
zeros
1
10
1
=
10
1
0
1
2
10
2
=
10
×
10
1
00
2
3
10
3
=
10
×
10
×
10
1,
000
3
4
10
4
=
10
×
10
×
10
×
10
1
0
,
000
4
The
exponent matches the number of zeros! You can use that pattern to write powers of
10.
Let's
try it with
1,000,000.
There
are 5 zeros, so the exponent is
5.
1
0
0
,
0
0
0
=
10
5
You
can use the pattern to evaluate powers of 10, too. Let's try it with
10
8
.
There will be 8
zeros.
10
8
=
1
0
0
,
0
0
0
,
0
0
0
You
can check the answer by using repeated
multiplication.
Fun
Fact
Did
you
know
that
1
is
a
power
of
10
?
It
is
10
0
!
Try some practice problems!
Practice now
Write powers of ten with exponents
Powers
of
10
with
negative
exponents
You
can also have powers of ten with negative exponents. For example, 0.01 is a power of 10. You can write it as
10
–
2
.
You
can write a negative exponent as a positive exponent under a numerator of 1. So,
10
–
2
is the same as
1
10
2
=
1
100
=
0.01
.
Look
at the table. Do you see a pattern in the number of decimal places and the
exponent?
Exponent
Power
of
10
Value
Number
of decimal
places
-1
10
–
1
=
1
10
0.
1
1
-2
10
–
2
=
1
10
×
10
0.
01
2
-3
10
–
3
=
1
10
×
10
×
10
0.
001
3
-4
10
–
4
=
1
10
×
10
×
10
×
10
0.
0001
4
The
exponent matches the number of decimal places! You can use that pattern to write powers of 10 with negative
exponents.
Let's
try it with
10
–
6
.
The
exponent is
–
6
.
There will be 6 decimal
places.
10
–
6
=
0.
0
0
0
0
0
1
You
can use the pattern in the other direction, too. Let's try it with 0.0000001.
There
are 7 decimal places. The exponent will be
–
7
.
0.
0
0
0
0
0
0
1
=
10
–
7
Tip
Remember
,
for
a
positive
exponent
,
count
the
number
of
zeros
.
For
a
negative
exponent
,
count
the
number
of
decimal
places
.
Related
Skills
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Powers of ten
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