warm up order each set of numbers from least to greatest. 1. 10, 10, 10, 10 2. 8, 8, 8, 8 3. 2, 2,...
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Warm UpOrder each set of numbers from least to greatest.
1. 10 , 10 , 10 , 10
2. 8 , 8 , 8 , 8
3. 2 , 2 , 2 , 2
4. 5.2 , 5.2 , 5.2 , 5.2
04 –1 –2
10 , 10 , 10 , 10 40–1–2
3 02 –2
8 , 8 , 8 , 8 320–2
13 –4 –6
–22 9 –1
5.2 , 5.2 , 5.2 , 5.2 92–1–2
2 , 2 , 2 , 2 31–4–6
Mathematicians and scientists often work with numbers that are
extremely large and numbers that are extremely small.
It can be challenging (and boring) to write out such
numbers over and over again.
Also, a calculator can only fit about 10 digits on its screen.
For example, suppose that you were studying the planet Pluto.
Pluto is 2,670,000,000 miles away from Earth.
2,670,000,000 is a huge number. Imagine how tedious it would be to write this number multiple times or do calculations with this number.
Mathematicians and scientists use a system called scientific notation to abbreviate numbers like these.
2,670,000,000
2,670,000,000 = 2.67 x 109
Mathematicians and scientists use a system called scientific notation to abbreviate numbers like these.
Scientific notation works by rewriting numbers as the product of
a number times 10 to a certain power.
The exponent tells about the size of the number.
A positive exponent means a BIG number.
A negative exponent means a small number.
Scientific notation has 3 parts.
ONLY 1 number in front of the
decimal!
Xmultiplication symbol – do not use multiplication dot
a power of 10
101.25
Scientific notation works by rewriting numbers as the product of a number
times 10 to a certain power.
45,000,000 = 4.5 x 107
Scientific notation works by rewriting numbers as the product of a number
times 10 to a certain power.
45,000,000 = 4.5 x 107
Notice that there is one digit in front of the decimal point.
Scientific notation works by rewriting numbers as the product of a number
times 10 to a certain power.
45,000,000 = 4.5 x 107
The exponent of “7” refers to the number of times that the decimal point “moved.”
Scientific notation works by rewriting numbers as the product of a number
times 10 to a certain power.
45,000,000 = 4.5 x 107
The exponent of “7” refers to the number of times that the decimal point “moved.”
Scientific notation works by rewriting numbers as the product of a number
times 10 to a certain power.
45,000,00 0 =4.5 x 106
one move
Scientific notation works by rewriting numbers as the product of a number
times 10 to a certain power.
45,000,0 00 =4.5 x 105
two moves
Scientific notation works by rewriting numbers as the product of a number
times 10 to a certain power.
45,000, 000 =4.5 x 104
three moves
Scientific notation works by rewriting numbers as the product of a number
times 10 to a certain power.
45,00 0,000 =4.5 x 103
four moves
Scientific notation works by rewriting numbers as the product of a number
times 10 to a certain power.
45,0 00,000 =4.5 x 102
five moves
Scientific notation works by rewriting numbers as the product of a number
times 10 to a certain power.
45, 000,000 =4.5 x 101
six moves
Scientific notation works by rewriting numbers as the product of a number
times 10 to a certain power.
4 5,000,000 =4.5 x 100
seven moves
Scientific notation works by rewriting numbers as the product of a number
times 10 to a certain power.
45,000,000 = 4.5 x 107
The exponent of “7” refers to the number of times that the decimal point “moved.”
Scientific notation can also be used to abbreviate numbers that
are really small.
.0022 is a really small number that can be rewritten using scientific notation.
.0022 = 2.2 x 10-3
.0022 is a really small number that can be rewritten using scientific
notation.
.0022 = 2.2 x 10-3
Notice that there is one digit in front of the decimal point.
The exponent of “-3” refers to the number of times that the decimal point “moved.”
.0022 is a really small number that can be rewritten using scientific notation.
.0022 = 2.2 x 10-3
.0022 is a really small number that can be rewritten using scientific notation.
.0022 = 2.2 x 10-3
.0022 is a really small number that can be rewritten using scientific notation.
0 022 = 2.2 x 10-2
1 move
.0022 is a really small number that can be rewritten using scientific notation.
00 22 = 2.2 x 10-1
2 moves
.0022 is a really small number that can be rewritten using scientific notation.
002 2 = 2.2 x 100
3 moves
.0022 is a really small number that can be rewritten using scientific notation.
.0022 = 2.2 x 10-3
3 moves
to the leftThe exponent is negative because multiplying by .001 will move the decimal to the left 3 times.
Rules to Write in Standard NotationIf the exponent is positive, move the decimal point as
many places to the right as indicated by the exponent.
1.120000
1.12 x 106
. 1,120,000 positive exponent large number
If the exponent is negative, move the decimal point as many places to the left as indicated by the exponent.
4.3 x 10-4 0004.3
.00043
negative exponent small number
.
Example 1 Write in standard notation (decimal form).1. Write problem.
3.0259 x 108
2. Write standard form.
000,590,302
PracticeA. 6.7 x 105
B. 1.38 x 10-4
C. 6.12 x 10-5
D. 5.4 x 104
= 670,000 = .000138 = .0000612 = 54,000
Rules to Write in Scientific NotationMove the decimal point to create a number greater than or
equal to 1 and less than 10. Count the decimal positions to identify the exponent. If the original number is greater than or equal to 1, the exponent is positive. If the original number is between zero and 1, the exponent is negative.
3.25 x 1063,250,000• use a positive exponent original
number is > 1
0.000817 8.17 x 10-
4
use a negative exponent original
number is between 0 and 1
•
•
Example 2 Write in scientific notation.
1. Write problem.
42,000,000
2. Write scientific notation.
710 x 2.4
PracticeA. 0.000052B. 3,107,000C. 970,000,00
0D. 0.0063
= 5.2 x 10-5 = 3.107 x 106 = 9.7 x 108
= 6.3 x 10-3
What do you already know about the sign
of the exponent?
LOL Moment!
Operations with Scientific Notation 36 10 x 410 x 3
Group the whole/decimal numbers together.
4 x 3
Group the powers of 10 together.
36 10 x10
Simplify within each group.
12
Write the whole/decimal number in scientific notation.
10 x 2.1 1
Combine the powers of ten.
9110 x 2.1
3610 x
910 x 12 10 x 9
1010 x 2.1
Perform the indicated operation. Write the result in scientific notation.
53 10 x 210 x 3
2. Group the whole/decimal numbers together.
2 x 3
Group the powers of 10 together.
53 10 x10
3. Simplify within each group.
6
4. Combine the powers of ten.
1. Write problem.5310 x
810 x 6
What do you know about the size of
this number?
Perform the indicated operation. Write the result in scientific notation.
64 10 x 610 x 4
2. Group the whole/decimal numbers together.
6 x 4
Group the powers of 10 together.
64 10 x10
3. Simplify within each group.
24
4. Write the whole/decimal number in scientific notation.
110 x 4.2
5. Combine the powers of ten.
10110 x 4.2
1. Write problem.6410 x
1010 x 24 1010 x
1110 x 4.2
What do you know about the size of
this number?
Perform the indicated operation. Write the result in scientific notation.
48 10 x 810 x 1.7
2. Group the whole/decimal numbers together.
8 x .17
Group the powers of 10 together.
48 10 x10
3. Simplify within each group.
8.56
4. Write the whole/decimal number in scientific notation.
110 x 5.68
5. Combine the powers of ten.
4110 x 68.5
1. Write problem.4810 x
410 x 8.56 410 x
310 x 68.5
What do you know about the size of
this number?
Perform the indicated operation. Write the result in scientific notation.
39 10 x 4.010 x 2.1
2. Group the whole/decimal numbers together.
0.4 x 2.1
Group the powers of 10 together.
39 10 x10
3. Simplify within each group.
48.0
4. Write the whole/decimal number in scientific notation.
110 x 8.4
5. Combine the powers of ten.
6110 x 8.4
1. Write problem. 3910 x
610 x 48.0 610 x
510 x 8.4
What do you know about the size of
this number?
Perform the indicated operation. Write the result in scientific notation.
24 10 x .8510 x .52
2. Group the whole/decimal numbers together.
5.8 x .52
Group the powers of 10 together.
24 10 x10
3. Simplify within each group.
50.14
4. Write the whole/decimal number in scientific notation.
110 x 45.1
5. Combine the powers of ten.
6110 x 45.1
1. Write problem.2410 x
610 x 50.14 610 x
710 x 45.1
What do you know about the size of
this number?
210 x
Perform the indicated operation. Write the result in scientific notation.
3
5
10 x 2
10 x 6
2. Group the whole/decimal numbers together.
2 6
Group the powers of 10 together.
3
5
10
10
3. Simplify within each group.
3
1. Write problem.
What is left over and
where is it located?
Perform the indicated operation. Write the result in scientific notation.
2
6
10 x 8
10 x 5
2. Group the whole/decimal numbers together.
85
Group the powers of 10 together.
2
6
10
10 x
3. Simplify within each group.
625.
4. Write the whole/decimal number in scientific notation.5. Combine the powers of ten.
110 x 25.6
1. Write problem.
410 x 410 x
310 x 25.6
Perform the indicated operation. Write the result in scientific notation.
6
2
10 x 810 x 5
2. Group the whole/decimal numbers together.
85
Group the powers of 10 together.
6
2
1010 x
3. Simplify within each group.
625.
4. Write the whole/decimal number in scientific notation.
110 x 25.6
5. Combine the powers of ten.
4110 x 6.25
1. Write problem.
2
6
1010 x
410 x .625 410 x
310 x 6.25What do you know about the size of
this number?
Perform the indicated operation. Write the result in scientific notation.
1. Write problem. 24-10 x 5
2. Use power of product property.
242 10 x5
3. Write the whole/decimal number in scientific notation.
110 x 2.5
4. Combine the powers of ten. -710 x 2.5
810 x 25 810 x
What do you know about the size of
this number?
4) Write the missing exponent.
1) 3 x 10?
2) 6.8 x 10?
3) 3.5 x 10?
4) 2.45 x 10?
= 30,000
= 680,000
= .0035
= .0000245
1) 3 x 104
2) 6.8 x 10?
3) 3.5 x 10?
4) 2.45 x 10?
= 30,000
= 680,000
= .0035
= .0000245
4) Write the missing exponent.
1) 3 x 104
2) 6.8 x 105
3) 3.5 x 10?
4) 2.45 x 10?
= 30,000
= 680,000
= .0035
= .0000245
4) Write the missing exponent.
1) 3 x 104
2) 6.8 x 105
3) 3.5 x 10-3
4) 2.45 x 10?
= 30,000
= 680,000
= .0035
= .0000245
4) Write the missing exponent.
1) 3 x 104
2) 6.8 x 105
3) 3.5 x 10-3
4) 2.45 x 10-5
= 30,000
= 680,000
= .0035
= .0000245
4) Write the missing exponent.
5) Write each number in scientific notation.
1) 357,000
2) 6,250,000
3) .00045
4) .0027
5) Write each number in scientific notation.
1) 357,000
2) 6,250,000
3) .00045
4) .0027
= 3.57 x 105
5) Write each number in scientific notation.
1) 357,000
2) 6,250,000
3) .00045
4) .0027
= 3.57 x 105
= 6.25 x 106
5) Write each number in scientific notation.
1) 357,000
2) 6,250,000
3) .00045
4) .0027
= 3.57 x 105
= 6.25 x 106
= 4.5 x 10-4
5) Write each number in scientific notation.
1) 357,000
2) 6,250,000
3) .00045
4) .0027
= 3.57 x 105
= 6.25 x 106
= 4.5 x 10-4
= 2.7 x 10-3
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