```Divisibility Rules
Tuesday WarmUps
Tips & Reminders
Scientific/Standard
Notation
Place Value
Whole Numbers
Scientific notation is a way to write
very large numbers in a type of
“shorthand”. It is written in the form
of c X 10n, where c is a decimal
number greater than 1 and less than
10, and n is any integer.
2: A number is divisible by 2 if it is
an even number
3: A number is divisible by 3 if the
3 2 1
,
9 8 7
,
Hundreds
Tens
Ones
Hundred Thousands
Ten Thousands
Thousands
last two digits are divisible by 4.
Ex: 516 is divisible by 4
because the last two digits,
16, is divisible by 4
Hundred Millions
Ten Millions
Millions
4: A number is divisible by 4 if the
Standard to Scientific Notation:
Hundred Billions
Ten Billions
Billions
sum (when you add each digit) of its
digits is divisible by 3.
Ex: 27 is divisible by 3, because
2 + 7 = 9, 9 is divisible by 3
6 5 4 2, 3 2 1
5: A number is divisible by 5 if it
ends in either 0 or 5
8
7
6
5
.
Thousandths
Ten Thousandths
Tenths
Ones
Hundreds
,
Hundred Thousandths
last three digits are divisible by 8.
Ex: 1160 is divisible by 8
because the last three digits,
160, is divisible by 8
Hundredths
8: A number is divisible by 8 if the
Thousands
an even number, and the sum of its
digits are divisible by 3.
Ex:
36 is divisible by 6
because it is an even
number and the sum of its
digits, 9, is divisible by 3
Tens
Place Value
Decimals
6: A number is divisible by 6 if it is
4
3
2
1
10: A number is divisible by 10 if it
ends in a zero
To determine the power of 10: Start
by adding a decimal point between
the first and second digit in the
original number (for example, 8539
would become 8.539). Looking at the
original number, count how many
places you would need to move the
decimal point to get back to that
original number (in this instance, you
would need to move 3 places to the
right). Write in scientific form:
8.539 X 103.
Scientific to Standard Notation:
0
Start at the decimal point, and go to
the right, the number of places that
the power indicates. Fill in with zeros
if necessary:
If the number is divisible by 4,
and the result of dividing the number
by 4 is an even number
sum of its digits is divisible by 9.
Ex:
45 is divisible by 9,
because 4 + 5 = 9,
9 is divisible by 9
In scientific notation, there is one
digit to the left of the decimal point,
and the remaining non-zero numbers
“drop” the zeros if they are on the
very end of the number.
6.38 X 107 = 63,800,000
4.91 X 1010 = 49,100,000,000
(or)
9: A number is divisible by 9 if the
75,200,000 = 7.52 X 107
98,700,000,000 = 9.87 X 1010
Standard/Expanded
Notation
Standard Form:
2,537
13,602
Expanded Form:
2,000 + 500 + 30 + 7
10,000 + 3,000 + 600 + 90 + 2
5.2 X 104 = 5 2 0
0
0 .
5.2 X 104 = 52,000
5.2 X 10-4 = 0.00052 (notice in
this case you moved the decimal
place to the left, since the exponent is
negative)
Writing Fractions in
Lowest Terms
Whenever the numerator and
denominator of a fraction can be
divided by the same non-zero whole
number, it can be “reduced” or
written in lower terms. When the
numerator and denominator can no
longer be divided by the same nonzero whole number, it is said to be
written in lowest terms.
EX:
Remember that division is the
multiplication of the inverse.
* Change the operation to
multiplication
* Invert (flip) the numerator
and denominator of the
second fraction.
* Multiply the denominators.
10 ÷ 5 = 2
15 ÷ 5 3
There is not a whole number that
can be evenly divided into 2 and 3,
* Multiply the numerators.
* Multiply the denominators.
* Write the product in lowest terms
(reduce) if necessary.
2
3

3
7
63
2
=
21  3
7
* You can also simplify before
multiplying:
1
2
3
2
•
=
3
7
7
1
* If multiplying a whole number by a
fraction, make the whole number a
fraction by placing it over 1.
3
9 3
27
6
=
•
=
= 3
7
1 7
7
7
Ex:
14
9
=
1
5
9
You can also simplify in
division problems, after you
change the operation to
multiplication and invert the
second fraction:
*
1
3
6
÷
=
8
7
24.70 (annexed zero)
+ 48.92
73.62
Ex:
* If dividing a whole number
by a fraction, or a fraction by a
whole number, make the whole
number a fraction by placing it
over 1. Then follow the above
steps.
3
7
7
•
=
8
6
16
2
24.7 + 48.92 =
1 1
2
7
•
=
3
3
=
2
3
6
•
=
3
7
21
•
* Line up the decimal points.
necessary
* Add or subtract as you would
with whole numbers
* Remember to bring down the
decimal point in the exact
* Write the product in lowest
terms (reduce) if necessary.
2
is in lowest terms.
3
Multiplying Fractions
9
Decimals
* Multiply the numerators.
10
15
Both can be divided evenly by “5”.
so
Dividing Fractions
59.45 - 17.3 =
59.45
- 17.30 (annexed zero)
42.15
```