Unit 2 –
Operations with Whole Numbers
and Decimals
Name: ___________________
Lesson 2.1 - Large Numbers
Standard Notation
 Each place is 10 times the place to its right
 Each period, or group, is divided into ones, tens, hundreds
 Each period is separated by a comma
Expanded Notation
 A number is written as the sum of the values of its digits
345 = 300 + 40 + 5
or
345 = (3 * 100) + (4 * 10) + (5 * 1)
Number-and-Word Notation
 Significant digits followed by a word for the place value of the largest period
63,800,000 = 63,800,000 = 63.8 million
 Process
1. Choose the largest period group
2. Replace the comma with a decimal
3. Write down any other digits to the right of the decimal
4. Write the word for the largest period
Lesson 2.2 - Small Numbers
Small numbers:
 Each place is 1/10 of the place to its left
 Each place is 10 times the place to its right
 The decimal divides between the parts and whole
Reading Small Numbers
1. Identify the place value of the smallest digit.
2. Read the number (ignore the decimal and zeros) and
say the smallest digit’s place value
Ex.: 0.0134 = 134 ten-thousandths
Writing Small Numbers
1. Draw a decimal point and enough spaces for the smallest digit
2. Write the number in the spaces so the smallest digit is on the last space
3. Fill the blanks with zeros
Ex. 345 thousandths =
___ . ___ ___ ___
Lesson 2.3 - Decimals: Add and Subtract
Decimal computation:
1. Line up the decimals
2. Estimate whole numbers
3. Add or Subtract
4. Verify answer with estimate
Example:
34.9+ 3.25
Lesson 2.4 - Powers of 10
Powers of 10
 Numbers such as 0.1, 1,10, 100, 0.01
Exponential Notation
 numbers written with an exponent
Lesson 2.5- Multiplying Decimals
Estimating Products with Decimals
 Round each factor to its greatest place value
(5.3 * 0.64 = 5 * 0.6 = 3)
 Remember, if one factor is less than 1, the product
will be less than the other factor.
 For numbers less than one, use a fraction for a more accurate estimate
Lesson 2.6 - Divisibility Rules
Divisible
by
My Hypothesis
I think….
Rule
I learned…
2
All even numbers
(end in 0, 2, 4, 6, 8)
3
Find sum of all digits (add
them up)… the sum is
divisible by 3.
Underline last two digits of
number…they are
divisible by 4.
4
5
Ends in a 0 or 5
6
Is divisible by both 2 and 3
7




Take the last digit in a number.
Double and subtract the last digit from the
rest of the digits.
Is it divisible by 7? If so, the number is.
Example: 357 (Double the 7 to get 14.
Subtract 14 from 35 to get 21 which is
divisible by 7
8
The last 3 digits are divisible
by 8
9
Add up all digits. If the sum
is divisible by 9, so is the
number.
10
Ends in a zero
Lesson 2.7 - Rounding
Rounding Rules

Underline the place that you are rounding to

Look at the number to the right of the place
0,1,2,3,4 – Ignore the number and leave the rounding number as it is
5,6,7,8,9 – Round up to the next number you are rounding too
Lesson 2.9 - Scientific Notation
Powers of 10
Scientific Notation
 Used for large and small numbers:
 First part: a number between one and nine
 Second part: a positive or negative power of ten that
was used to get the first part
4
Ex:
5.3 * 10
-4
1.05 * 10
Exponents
 Negative Exponents = Divide by 10 (decimal to the left)
 Positive Exponents = Multiply by 10 (decimal to the right)
Unit 2 Study Zone
Test Date: ___________________
Parent’s Signature: ____________________
My plan to prepare for this test is:
Skill
Vocabulary/Process
Write and compare
Define the words:
numbers written in
Scientific Notation
different notation types Standard Notation
Repeated Factors
Word and Number Notation
Exponential Notation
Write exponents
Exponents
Add decimals
Subtract decimals
Multiply decimals
Divide Decimals
Divide Decimals to two
decimal places
Process:
1. Line up decimals in problem
2. Add; carry if needed
3. Copy correctly
Process:
1. Line up decimals in problem
2. Subtract; borrow if needed
3. Copy with decimal
How to Study
Study each notation type in your notes.
Test yourself and check by looking up the definitions in
the glossary
Create a number; then translate it in each notation form
Make 5 numbers in different notation forms, convert
each to standard form to order (compare) them
Practice writing numbers with
 positive exponents and create large numbers
 negative exponents and create small numbers
Ideas to practice computation:
 Review your quizzes for types of mistakes
that you made so that you will know what
to watch out for
 Create a problem, solve it, then check
answer on a calculator
 Copy problems that you feel more practice
is need on out of the journal. Then go back
and solve them.
 Look over your quizzes and redo any
problems that were missed.
Process:
1. Copy problem & estimate
2. Multiply by ones in bottom
number. Remember to carry.
3. Add a space-keeper, then
multiply by tens
Process:
Basic Facts:
1. Copy carefully
 www.Xtramath.com
2. Remove decimal in divisor;
 www.emgames.com
same process in dividend
3. Place decimal in answer
4. Divide
Set up the problem…
1. Remove decimal in factor and then do the same thing to the product.
2. Find where the decimal is in the product and move it into the answer
3. Make the product have two decimal places to the right of the decimal point
4. Divide and write the remainder as a fraction
5. Determine whether to round up or ignore the fraction