Transcript What is Rounding? - Middle School Chaos Mrs. Piper

a quick review of previously learned math
skills
Review Place Value and Conversions
Concept Check
Review Rounding/Estimation and Simplifying Fractions
Concept Check
Review Coordinate Plane
Concept Check
Review Exponents and Integers
Concept Check
• noun: place value; plural noun: place
values
• the numerical value that a digit has by virtue
of its position in a number.
• For example: In the number 352, the “5” is in
the tens place which means the “5” has a
value of 50
Answer these questions in your
Interactive Student Notebook (ISN).
What is the place value of
the digit 7 in the number
6,789?
Which digit is in the
thousands place in the
number 68,521?
What is the place value of the
digit 5 in the number 43.7529?
Which digit is in the tenths place
in the number 12.387?
What is the place value of the
digit 8 in the number
13,470.0628?
Which digit is in the ones place
in the number 14.985?
• noun: a conversion is defined as an
exchange from one unit of measure to
another.
• An example of conversion is exchanging
dollars for euros.
• An example of conversion is figuring out how
many cups are in a liter.
• verb: to convert is to change, to cause
someone or something to change, or to alter
your beliefs.
• An example of convert is when you buy a
single family house and break it up into
apartments.
• An example of convert is when you
exchange dollars into Euros.
Conversions:
Fractions, Decimals, Percents
Rounding
What is Rounding?
Rounding whole numbers to the nearest ten
•
Numbers that look nice in our mind are
numbers that usually end with a zero such as
10, 30, and 200.
•
When rounding to the nearest ten, if the last
digit ends with 1, 2, 3, or 4, round to the next
number that is smaller than the number
given and ending with a zero.
•
When rounding numbers, it usually means
that you are going to try to put zero(s) at the
end.
•
For instance, round 43 to the nearest ten.
The last digit is 3, so the next number
smaller than 43 with an ending of zero is 40.
•
On the other hand, If the last digit is 5, 6, 7,
8, or 9, round to the next number bigger
than the given number and ending with zero.
•
For instance, round 45 to the nearest ten.
The last digit is 5, so the next number bigger
than 45 and ending with zero is 50.
•
•
Numbers can be rounded to the nearest ten,
hundred, thousand, ten-thousand, etc...
Rounded numbers are only approximates;
they never give exact answers.
Examples:
Round these numbers to the nearest ten.
23
36
55
99
Rounding to the nearest 100
•
•
When rounding to the nearest hundred, you
will need to look at the last two digits. If the
last two digits is 49 or less round to the next
number that is smaller than the number given
and ending with two zeros.
For instance, round 549 to the nearest
hundred. The last two digits is 49, so the next
number smaller than 549 with an ending of
two zeros is 500.
•
On the other hand, if the last two digits is 50
or more, round to the next number bigger than
the given number and ending with two zeros.
•
For instance, round 865 to the nearest
hundred. The last two digits is 65 and 65 is
bigger than 50, so the next number bigger
than 865 and ending with two zeros is 900.
Rounding whole numbers to the nearest ten
•
When rounding to the nearest ten, if the last
digit ends with 1, 2, 3, or 4, round to the next
number that is smaller than the number
given and ending with a zero.
•
For instance, round 43 to the nearest ten.
The last digit is 3, so the next number
smaller than 43 with an ending of zero is 40.
•
On the other hand, If the last digit is 5, 6, 7,
8, or 9, round to the next number bigger
than the given number and ending with zero.
•
For instance, round 45 to the nearest ten.
The last digit is 5, so the next number bigger
than 45 and ending with zero is 50.
Examples:
Round these numbers to the nearest hundred.
121
351
648
950
Rounding Decimals
•
Step #1:
•
Example #1: Round 2.1582 to
hundredths.
•
Find the place you are rounding to. Is it
the tenths, the hundredths, or the
thousandths?
•
Step #1: The place you are rounding
to is the place the number 5 holds:
2.1582
•
Step #2: The digit to the right of 5 is 8
and it is at least 5.
•
Therefore, we can add 1 to 5 to make
it 6
•
Step #3: Drop 82 (all digits to the right
of 5)
•
The answer is 2.16
•
•
•
Step #2:
If the digit to the right of the place you
are rounding to is 5 or more, add 1 to
the place you are rounding to. If it is less
than 5, add nothing.
Step #3: drop all the digits to the right of
the place you are rounding to.
Rounding Decimals
•
Example #2: Round 4.241 to tenths
•
Step #1: The place you are rounding to
is the place the number 2 holds: 4.241
•
Step #2: The digit to the right of 2 is 4
and it is less than 5.
• Examples:
• Round 5.18 to tenths
•
Therefore, we add nothing to 2.
• Round 0.498 to
hundredths
•
Step #3: Drop 41 (all digits to the right
of 2)
• Round 0.04 to tenths
•
The answer is 4.2
Estimation
• noun: an approximate or rough calculation
often based on rounding
• An example would be: Jack makes
$4,080.00 per month. How much does he
make in a year?
• $4000.00 x 12 = $48,000.00
Estimate
• verb: to estimate (to make) an
approximate or rough calculation often
based on rounding
• An example would be: Jack makes
$4,080.00 per month. How much does he
make in a year?
• $4000.00 x 12 = $48,000.00
Simplifying Fractions
• https://www.youtube.com/watch?v=hSOP
HZFmz3s
• https://www.youtube.com/watch?v=ggYdP
ef3Nuk
Examples
Complete the attached problems by simplifying the
fractions.
Coordinate Plane
Watch This!
• https://www.youtube.com/watch?v=l9zOi6
KPGD4
Exponents
Exponents
•
Exponents are shorthand for
repeated multiplication of the same
thing by itself. For instance, the
shorthand for multiplying the
number 5 three times is shown on
the right-hand side of the "equals"
sign in (5)(5)(5) = 53. The
"exponent", being 3 in this example,
stands for however many times the
value is being multiplied. The thing
that's being multiplied, being 5 in
this example, is called the "base".
•
•
This process of using exponents is
called "raising to a power", where
the exponent is the "power". The
expression "53" is pronounced as
"five, raised to the third power" or
"five to the third".
There are two specially-named
powers: "to the second power" is
generally pronounced as
"squared", and "to the third power"
is generally pronounced as
"cubed". So "53" is commonly
pronounced as "five cubed".
Exponential vs. Expanded Forms
Exponential Form
55
43
Now, it’s your turn…
Expanded Form
55555
444
Answer these questions in your
Interactive Student Notebook (ISN).
Write these in exponential form.
1. 6  6  6  6  6  6 = _______
2. 3  3  3 = _______
3. 4  4  5  5  5  4 = _______
Answer these questions in your
Interactive Student Notebook (ISN).
Write these in expanded form.
1. 123 = _______
2. 77 = _______
3. 32  54 = _______
Integers
• Integers are the set of whole numbers and their opposites.
• Whole numbers greater than zero are called positive
integers.
• Whole numbers less than zero are called negative integers.
• The integer zero is neither positive nor negative, and has no
sign.
• Two integers are opposites if they are each the same
distance away from zero, but on opposite sides of the
number line.
• Positive integers can be written with or without a sign.
Integers
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BOOTCAMP
(FOR THE FIRST SEMESTER)