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Show Me With The Money
Presented by
A. Dávila, Ed.D.
Scientific Notation and
Standard Form
Created by
Dr. A. Dávila
Scientific Notation: a way of
writing a number as a product of
two factors
x
Scientific Notation: a way of
writing a number as a product of
two factors
The first factor has exactly one
nonzero digit to the left of the
decimal point
x
Scientific Notation: a way of
writing a number as a product of
two factors
The first factor has exactly one nonzero
digit to the left of the decimal point (less
then 10 but greater than 1)
The second factor is a
power of ten
x
10
Place Value Review
The value increases 10 times more than
the previous value.
The ones
is the starting
point (no
powers of ten)
Ones
1
0
10
multiply by 10
The value increases 10 times more than
the previous value.
Tens
10
from the ones
place
to the tens
place
(10 times more)
Tens
10
1 x 10
Tens
10
1 x 10
1
10
One power of ten
Various methods of representing the Tens Place
Tens
10
1
10
multiply by 10
The value increases 10 times more than
the previous value.
Hundreds
100
Hundreds
from the tens
to the hundreds 100
place
(10 times more) 10 x 10
Hundreds
100
10 x 10
10
2
two powers of ten
Various methods of representing the
Hundreds Place
Hundreds
100
2
10
multiply by 10
As you continue to the left (higher value
sections) in the place value chart, the value
increases 10 times more than the previous
value.
Thousands
1,000
Thousands
1,000
from the hundreds
10 0 x 10
to the thousands
place (10 times more)
Thousands
1,000
10 0 x 10
10 x 10 x 10
Thousands
1,000
10 0 x 10
10 x 10 x 10
10
3
three powers of ten
Various methods of representing
the Thousands Place
Thousands
1,000
3
10
multiply by 10
As you continue to the left (higher value
sections) in the place value chart, the value
increases 10 times more than the previous
value.
Ten-thousands
10,000
Ten-thousands
10,000
from the thousand 1000 x 10
to the ten thousands
place (10 times
more)
Ten-thousands
10,000
1000 x 10
100 x 10 x 10
Ten-thousands
10,000
1000 x 10
100 x 10 x 10
10 x 10 x 10 x 10
Ten-thousands
10,000
1000 x 10
100 x 10 x 10
10 x 10 x 10 x 10
4
10
four powers of ten
Various methods of representing the
Ten-thousands Place
Ten-thousands
10,000
4
10
multiply by 10
As you continue to the left (higher value
sections) in the place value chart, the value
increases 10 times more than the previous
value.
One Hundred Thousands
100,000
One Hundred Thousands
100,000
from the ten
thousands
to the hundreds
thousands
place (10 times
more)
10000 x 10
One Hundred Thousands
100,000
10000 x 10
1000 x 10 x 10
One Hundred Thousands
100,000
10000 x 10
1000 x 10 x 10
100 x 10 x 10 x 10
One Hundred Thousands
100,000
10000 x 10
1000 x 10 x 10
100 x 10 x 10 x 10
10 x 10 x 10 x 10 x 10
One Hundred Thousands
100,000
10000 x 10
1000 x 10 x 10
100 x 10 x 10 x 10
10 x 10 x 10 x 10 x 10
10
5
five powers of ten
Various methods of representing the
One Hundreds Thousands place
One Hundred Thousands
100,000
5
10
WHOLE NUMBERS
0
10
WHOLE NUMBERS
1
0
10 10
WHOLE NUMBERS
10
2
1
0
10 10
WHOLE NUMBERS
3
10 10
2
1
0
10 10
WHOLE NUMBERS
4
3
10 10 10
2
1
0
10 10
Powers of 10 for Whole Numbers
5
10
4
3
10 10 10
2
1
0
10 10
Powers of 10
for Decimal Places/Fractional
Parts
Decimal Fraction: a fraction in
which the denominator is some
power of ten
divide by 10
As you move to the left on the place value
chart the value decreases 10 times.
This is one-tenth. If we relate it to the USA
monetary, it has a value of 10¢.
Tenths
0.1
from the
ones
to the
tenths
place (10
times less)
Tenths
0.1
1 ÷ 10
Tenths
0.1
1 ÷ 10
1
1 x 10
Tenths
0.1
1 ÷ 10
1
1 x 10
The denominator 1
is power of ten 10
Tenths
0.1
1 ÷ 10
1
1 x 10
1
10
10
-1 one power of ten
(denominator)
Various methods of representing one-tenth
Tenths
0.1
1
10
10
-1
This is one-hundredths. If we relate it to the
USA monetary, it has a value of 1¢.
divide by 10
The value decreases 10 times.
Hundredths
0.01
Hundredths
0.01
from the
tenths
to the
hundredths
place (10
times less)
1
÷ 10
10
Hundredths
0.01
1
10
÷ 10
1 x 1
10 10
Hundredths
0.01
1
10
÷ 10
1 x 1
10 10
1
2
10
two powers of ten
(denominator)
Hundredths
0.01
1
10
÷ 10
1 x 1
10 10
1
2
10
-2
10
Hundredths
0.01
1
100
1
2
10
-2
10
divide by 10
As you move to the left on the place value
chart the value decreases 10 times.
This is one-tenth. If we relate it to the USA
monetary, it has a value of 10¢.
Thousandths
0.001
Thousandths
0.001
from the
hundredths
to the
thousandths
place (10
times less)
1
÷ 10
100
Thousandths
0.001
1
÷ 10
100
1 x 1
100 10
Thousandths
0.001
1
÷ 10
100
1 x 1
100 10
1
10 x 10 x 10
Thousandths
0.001
1
÷ 10
100
1 x 1
100 10
1
10 x 10 x 10
1
three powers of ten
3
10 (denominator)
Thousandths
0.001
1
÷ 10
100
1 x 1
100 10
1
3
10
10
-3
Thousandths
0.001
1
100
1
3
10
10
-3
F
R
A
C
T
I
O
N
A
L
PARTS
-3
10
F
R
A
C
T
I
O
N
A
L
PARTS
-2
10
-3
10
F
R
A
C
T
I
O
N
A
L
PARTS
-1
10
-2
10
-3
10
Write in
standard form
2 x 10
5
Write in
standard form
2 x 10
5
10
5
Write in
standard form
2 x 10
5
10
5
2 x 100000
Write in
standard form
2 x 10
5
2 x 100000
2
Write in
standard form
2 x 10
5
2 x 100000
20
Write in
standard form
2 x 10
5
2 x 100000
200
Write in
standard form
2 x 10
5
2 x 100000
2000
Write in
standard form
2 x 10
5
2 x 100000
20000
Write in
standard form
2 x 10
5
2 x 100000
200000
Write in
standard form
4
3.1 x 10
Write in
standard form
4
3.1 x 10
4
10
Write in
standard form
4
3.1 x 10
3.1 x 10000
4
10
Write in
standard form
4
3.1 x 10
3.1 x 10000
3.1
Write in
standard form
4
3.1 x 10
3.1 x 10000
31.
Write in
standard form
4
3.1 x 10
3.1 x 10000
310.
Write in
standard form
4
3.1 x 10
3.1 x 10000
3100.
Write in
standard form
4
3.1 x 10
3.1 x 10000
31000.
Write in
standard form
7.05 x 10
-3
-3
10
Write in
standard form
7.05 x 10
-3
-3
10
Write in
standard form
7.05 x 10
7.05 x
-3
_ 1_
1000
-3
10
Write in
standard form
7.05 x 10
7.05 x
7.05
-5
_ 1_
1000
-3
10
Write in
standard form
7.05 x 10
7.05 x
.705
-3
_ 1_
1000
-3
10
Write in
standard form
7.05 x 10
7.05 x
.0705
-3
_ 1_
1000
-3
10
Write in
standard form
7.05 x 10
7.05 x
.00705
-3
_ 1_
1000
Write in
scientific form
5,200,000
Scientific Notation: a way of
writing a number as a product of
two factors
x
Scientific Notation: a way of
writing a number as a product of
two factors
The first factor has exactly one
nonzero digit to the left of the
decimal point
x
Scientific Notation: a way of
writing a number as a product of
two factors
The first factor has exactly one
nonzero digit to the left of the
decimal point
The second factor is the
necessary power of ten
x
10
Write in scientific form
A number
greater than or
equal to one
Write in scientific form
A number
greater than or
equal to one
x
10
Power of 10
Write in scientific form
A number
greater than or
equal to one
x
10
Exponent
Power of 10
5
10
4
10
3
10
2
10
1
10
0
10
Write in scientific form
A number
greater than or
Equal to one
5
10
x
4
10
3
10
Exponent
10
2
10
Power of 10
1
10
0
10
Write in scientific form
A number
greater than or
equal to one
5
10
5.2
4
10
3
10
x
Exponent
10
2
10
Power of 10
1
10
0
10
Write in scientific form
A number
greater than or
equal to one
5
10
5.2
4
10
3
10
x
10
2
10
5
Exponent
Power of 10
1
10
0
10
Write in scientific form
0.0016
Write in scientific form
A number
greater than or
Equal to one
x
10
Exponent
Power of 10
10
-1
-2
10
-3
10
-4
10
Ten
Thousandths
Write in scientific form
A number
greater than or
Equal to one
10
-1
-2
10
-3
10
-4
10
Ten
Thousandths
Write in scientific form
A number
greater than or
Equal to one
1.6
10
-1
x
-2
10
Exponent
10
Power of 10
-3
10
-4
10
Ten
Thousandths
Write in scientific form
A number
greater than or
Equal to one
1.6
10
-1
x
-2
10
10
-3
Exponent
Power of 10
-3
10
-4
10
Ten
Thousandths
Write in scientific form
0.0216
Write in scientific form
A number
greater than or
Equal to one
x
10
Exponent
Power of 10
Write in scientific form
A number
greater than or
Equal to one
Write in scientific form
A number
greater than or
Equal to one
10
-1
-2
10
-3
10
Ten
Thousandths
Write in scientific form
A number
greater than or
Equal to one
10
-1
-2
10
-3
10
Ten
Thousandths
Write in scientific form
A number
greater than or
Equal to one
Exponent
2.16 x 10
10
-1
-2
10
Power of 10
-3
10
Ten
Thousandths
Write in scientific form
A number
greater than or
Equal to one
2.16 x 10
10
-1
-2
10
-2
Exponent
Power of 10
-3
10
Ten
Thousandths