Download 578298Scientific_Notation-GCF-LCM_Notes

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MCA Review – Scientific Notation
Scientific Notation: a way to represent very large or very small numbers
if it has the form c × 10n where c is
A number is written in
greater than or equal to
and less than
and n is a
number.
Standard form
2,860,000
Product form
2.86 × 1,000,000
Scientific notation
2.86 × 106
110,000
(
decimal places)
1.1 × 1
( zeros)
1.1 × 10 ?
(Exponent is
)
To Change from Standard Form to Scientific Notation:
1. Place decimal point such that there is one non-zero digit to the left of the
.
2. Count number of decimal places the decimal has "
" from the
original number. This will be the exponent of the 10.
3. If the original number was less than 1, the exponent is
; if the
original number was greater than 1, the exponent is
.
Examples:
Given: 4,750,000
Use: 4.75 (moved
Given: 0.000789
decimal places)
answer:
7.89 (moved
decimal places)
answer:
You try:
Change these numbers from standard form to scientific notation:
1.
61,500
2.
0.0000568
3.
10,000,000,000
To Change from Scientific Notation to Standard Form:
1. Move decimal point to
for positive exponent of 10.
2. Move decimal point to
for negative exponent of 10.
Examples:
Given: 1.015 x 10-8
Given: 5.024 x 103
answer: 0.00000001015
answer: 5,024
(
places to
)
(
places to
)
You try:
Change these numbers from scientific notation to standard form:
1.
6 x 107
2.
4.22715 x 108
3.
3.078 x 10-4
Comparing Numbers in Scientific Notation:
1. Compare the
is the
. The number with the greater the
number.
2. If the exponents are the same, then compare the
parts.
Example:
1.06 x 1016
or
2.4 x 1015
5.28 x 1012
or
5.3 x 1012
You try:
Copy and complete the statement using <, >, or =.
1.
9.74 x 1021
2.1 x 1022
2.
4.4 x 107
44,000,000
Greatest Common Factor (GCF)
: Numbers that go into a larger number
GCF: The greatest common
of two or more numbers.
2 ways to find GCF:
1. List all the factors
2. Prime Factorization (use a
numbers they have in common)
, then multiply only the prime
Making a list to find GCF:
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
GCF of 48, 24, 36 is
.
Prime Factorization to find GCF:
180
10
2
2
18
5
5
126
2
2
2
9
3
63
2
3
3
2
3
21
3
7
2×2×3×3×5
2×3×3×7
GCF of 180 & 126 is
.
Least Common Multiple (LCM)
: the product of the number by any nonzero whole number
LCM: The least common
of two or more numbers.
2 ways to find LCM:
1. List all the multiples
2. Prime Factorization (use a
, then multiply only the prime
numbers they have in common once, and then multiply all other numbers as well)
Making a list to find the LCM
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, …
Multiples of 6: 6, 12, 18, 24, 30, 36, …
LCM of 4 & 6:
Using Prime Factorization to find the LCM
180
10
2
2
18
5
5
126
2
2
2
9
3
63
2
3
3
2
3
2×2×3×3×5
2×3×3×7
LCM of 180 & 126 is
.
You try:
Find the GCF by listing the factors or using prime factorization:
1. 24, 63
2. 84, 216
Find the LCM by listing the multiples or using prime factorization:
1. 9, 24
2. 28, 46
21
3
7