Transcript UNDERSTANDING NUMBERS BETTER

UNDERSTANDING
NUMBERS
BETTER
Period
BILLIONS
HUNDRED
BILLIONS
TEN
BILLIONS
MILLIONS
BILLIONS
HUNDRED
MILLIONS
Place Value
TEN
MILLIONS
THOUSANDS
MILLIONS
HUNDRED
TEN
THOUSANDS HUNDREDS
THOUSANDS THOUSANDS
UNITS
TENS
ONES
BILLIONS
HUNDRED
BILLIONS
TEN
BILLIONS
MILLIONS
BILLIONS
HUNDRED
MILLIONS
TEN
MILLIONS
THOUSANDS
MILLIONS
HUNDRED
TEN
THOUSANDS HUNDREDS
THOUSANDS THOUSANDS
3 8 6
In 3 861 254:
UNITS
TENS
ONES
1 2 5
4
the digit 3 stands for 3 000 000
the value of the digit 3 is 3 000 000
the digit 6 stands for 60 000
the value of the digit 6 is 60 000
the digit 5 stands for 50
the value of the digit 5 is 50
BILLIONS
HUNDRED
BILLIONS
TEN
BILLIONS
MILLIONS
BILLIONS
HUNDRED
MILLIONS
TEN
MILLIONS
THOUSANDS
MILLIONS
HUNDRED
TEN
THOUSANDS HUNDREDS
THOUSANDS THOUSANDS
3 8 6
In 3 861 254:
UNITS
TENS
ONES
1 2 5
4
the digit 3 is in the millions place
the digit 8 is in the hundred thousands place
the digit 6 is in the ten thousands place
the digit 1 is in the thousands place
the digit 2 is in the hundreds place
Nineteen million
three hundred fifty four thousand
eight hundred sixty two
1 9, 3 5 4, 8 6 2
10, 000, 000
10, 000, 000
1 9, 3 5 4, 8 6 2
9, 000, 000
1, 000, 000
2 5 4. 8 6 2
2 5 4. 8 6 2
2 5 4. 8 6 2
2 5 4. 8 6 2
Look at the values of the digit in 3 861 254. We can add
the values of the digits to get the number.
3 861 254 = 3 000 000 + 800 000 + 60 000 + 1 000 + 200 + 50 + 4
3861254
Sum
4
50
200
1 000
60 000
800 000
3 000 000
3 861 254
3 861 254 = 3 000 000 + 800 000 + 60 000
+ 1 000 + 200 + 50 + 4
3 861 254 = 3 x 106 + 8 x 105 + 6 x 104
+ 1 x 103 + 2 x 102 + 5 x 10 + 4
Write in standard notation.
Write in expanded notation.
A. How many times as great as the underlined
5 than the 5 that is not underlined?
Dividing 50, 000 by 50
50, 000 ÷ 50
=
The underlined 5 is 1, 000 times
as great as the not underlined 5.
Exercises:
1. In 670 932 the value of the digit 6 is _____.
2. What is the value of the digit 2 in each of the
following 6-digit numbers?
a. 812 679
c. 3 652 249
b. 260 358
d. 2 915 365
3. What is the place value of the digit 6 in #2.
4. In 937 416 the digit ___ is in the
hundreds place.
5. In 6 825 371, the digit in the
hundred thousands place is____.
Put On Your Thinking Caps!
The Mystery of Two Numbers
You are a Number Investigator
and have just received two
cases for investigation. Find
out the numbers using the
following clues.
CASE 1
It is a 7-digit even number. There is no repetition of
digits.
The digit 5 is in the thousands place.
The greatest digit is in the millions place.
The digit in the hundred thousands place is twice
the digit in the hundreds place.
The digit in the hundreds place is twice the
digit in the ones place.
The digit in the tens place is 2 less than the
digit in the millions place.
9835472
9865472
9815472
CASE 2
It is a 6-digit number. There is no repetition of digits.
It is divisible by 5 and more than 300 000.
The digit in the hundreds place is 3 more than the digit in
the ones place.
The digit in the ten thousands place is 3 times the digit in
the hundred thousands place.
The digit in the thousands place is half the
value of the digit in the hundreds place.
The difference of the digits in the tens
place and in the thousands place is 2.
394825
394865
Comparing Numbers
Which number is smaller, 3 805 216 or 5 608 317?
BILLIONS
HUNDRED
BILLIONS
TEN
BILLIONS
MILLIONS
BILLIONS
HUNDRED
MILLIONS
TEN
MILLIONS
THOUSANDS
MILLIONS
HUNDRED
TEN
THOUSANDS HUNDREDS
THOUSANDS THOUSANDS
UNITS
TENS
ONES
3 8 0 5 2 1
5 6 0 8 3 1
6
7
Compare the values of the digits starting from the left.
3 millions is smaller than 5 millions.
So, 3 805 216 is smaller than 5 608 317.
Which number is greater, 8 370 589 or 8 305 938?
8 370 589
8 305 938
Compare the values of the digits starting from the
left. Here the values of the digits in the ten
thousands place are different.
Compare the values of the digits in the ten
thousands place.
Compare the values of the digits in the ten
thousands place. 7 is greater than 0, so 8 370 589
is greater than 8 305 938.
Rounding Numbers
We will use the term rounding digit - which
means: When asked to round to the
closest tens - our rounding digit is the
second number to the left (ten's place)
when working with whole numbers. When
asked to round to the nearest
hundreds, the third place from
the left is the rounding digit
(hundreds place).
Rule One. Determine your rounding digit and look to
the right side of it. If the digit is 0, 1, 2, 3, or 4 do not
change the rounding digit. All digits that are on the right
side of the requested rounding digit will become 0.
Round 5648 to the nearest hundred.
5600
Rule Two. Determine your rounding digit and look to
the right side of it. If the digit is 5, 6, 7, 8, or 9, your
rounding digit rounds up by one number.
All digits that are on the right side of
the requested rounding digit will become 0.
Round 7864 to nearest hundred
7900
Roman Numerals
I
V
Roman
numerals are X
expressed by L
letters of the C
alphabet:
D
M
= 1
= 5
= 10
= 50
= 100
= 500
= 1000
c. Do not subtract a number from one that
is more than
10 times greater (that is, you can subtract
1 from 10
[IX] but not 1 from 20—there is no such
number as IXX.)
For 99, do NOT write IC (C – I or 100 1).
DO write XCIX (XC + IX or 90 + 9)
You can keep the values in your mind as
follows.
V is the upper half of X
C stands for centum=100, known from
centimeter = cm
L is the lower half of C, if you have some
imagination
M stands for mille=1000, known from
millimeter=mm
D is the right half of (I), an old
writing of 1000
One
I
Eleven
XI
Thirty
XXX
Two
II
Twelve
XII
Forty
XL
Three
III
Thirteen
XIII
Fifty
L
Four
IV
Fourteen XIV
Sixty
LX
Five
V
Fifteen
XV
Seventy
LXX
Six
VI
Sixteen
XVI
Eighty
LXXX
Seven
VII
Seventeen XVII
Ninety
XC
Eight
VIII
Eighteen XVIII
One
hundred
C
Nine
IX
Nineteen XIX
Five
hundred
D
Ten
X
Twenty
One
M
thousand
XX