Count the number of hundreds:
6 hundreds
Add up Hundred-Groups
Hundred-Groups = 100 + 100 + 100 + 100 + 100 + 100
Hundred-Groups = 600
Count the number of tens:
7 tens
Add up Ten-Groups
Ten-Groups = 10 + 10 + 10 + 10 + 10 + 10 + 10
Ten-Groups = 70
Count the number of ones:
5 ones
Add this to the ones for our total:
675 = 600 Hundreds + 70 Tens + 5 ones
675 = 600 + 70 + 5
Show numerical properties of 675
675
Draw this point on a number line:
Word Notation for 675
six hundred seventy five
Write the number 675 in expanded notation form:
Decompose 675
Express in powers of 10
Each digit in the whole number represents a power of 10:
Take the whole number portion on the left side of the decimal
Build Expanded Notation with powers of 10
Expanded Notation of 675 = (6 x 102) + (7 x 101) + (5 x 100)
Expanded Notation of 675 = (6 x 100) + (7 x 10) + (5 x 1)
Prove this is the correct notation:
675 = 600 + 70 + 5
675 = 675 <---- Correct!
Tally Marks for 675
Make blocks of 5
Tally Marks Definition:
1 tally mark = |
2 tally marks = ||
3 tally marks = |||
4 tally marks = ||||
5 tally marks = | | | |
135 blocks of 5 and 0 left over
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Tallies for 675
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Ordinal for 675
Define an ordinal number
A position in a list
675th
Digit and Reduced Digit Sum for 675
Calculate the digit sum of 675
Calculate the reduced digit sum of 675
Add up 3 digits of 675:
Digit Sum → 6 + 7 + 5 = 18
Since our digit sum > 9:
repeat this process to get the reduced digit sum:
Our new number to evaluate is 18
Add up 2 digits of 18:
Digit Sum → 1 + 8 = 9
Since our digit sum ≤ 9:
we have our reduced digit sum
Digit Sum → 1 + 8 = 9
Digit Product for 675:
Calculate the digit product of 675
Digit Product = Value when you multiply
all the digits of a number together.
We multiply the 3 digits of 675 together
Digit product of 675 = 6 * 7 * 5
Digit product of 675 = 210
Opposite of 675
Opposite of 675 = -(675)
Opposite of = -675
Place Value for 675
Place value describes each digit
Whole Number Position 3: 675
6 is our hundreds digit
This means we have 6 sets of hundreds
Whole Number Position 2: 675
7 is our tens digit
This means we have 7 sets of tens
Whole Number Position 1: 675
5 is our ones digit
This means we have 5 sets of ones
6 is our hundreds digit
7 is our tens digit
5 is our ones digit
Natural Logarithm of 675
When ey = x and e = 2.718281828459
We have Ln(x) = loge(x) = y
Evaluate x = 675
Ln(675) = loge(675) = 6.5147126908725
Is 675 divisible by:
2,3,4,5,6,7,8,9,10,11
Divisibililty Check for 2
Last digit ends in 0,2,4,6,8
The last digit of 675 is 5
Since 5 is not equal to 0,2,4,6,8:
then 675 is not divisible by 2
Divisibililty Check for 3
Sum of the digits is divisible by 3
The sum of the digits for 675 is 6 + 7 + 5 = 18
Since 18 is divisible by 3:
Then 675 is divisible by 3
Divisibililty Check for 4
Take the last two digits
Are they divisible by 4?
The last 2 digits of 675 are 75
Since 75 is not divisible by 4:
Then 675 is not divisible by 4
Divisibililty Check for 5
Number ends with a 0 or 5
The last digit of 675 is 5
Since 5 is equal to 0 or 5:
Then 675 is divisible by 5
Divisibililty Check for 6
Divisible by both 2 and 3
Since 675 is not divisible by 2 and 3:
Then 675 is not divisible by 6
Divisibililty Check for 7
Multiply each respective digit by 1,3,2,6,4,5
Work backwards
Repeat as necessary
5(1) + 7(3) + 6(2) = 39
Since 39 is not divisible by 7:
Then 675 is not divisible by 7
Divisibililty Check for 8
Take the last three digits
Are they divisible by 8
The last 3 digits of 675 are 675
Since 675 is not divisible by 8:
Then 675 is not divisible by 8
Divisibililty Check for 9
Sum of digits divisible by 9
The sum of the digits for 675 is 6 + 7 + 5 = 18
Since 18 is divisible by 9:
Then 675 is divisible by 9
Divisibililty Check for 10
Ends with a 0
The last digit of 675 is 5
Since 5 is not equal to 0:
Then 675 is not divisible by 10
Divisibililty Check for 11
Σ odd digits - Σ even digits = 0
or 675 is a multiple of 11
Sum the odd digits:
675
6 + 5
Odd Sum = 11
Sum the even digits:
675
7
Even Sum = 7
Take the difference:
Δ = Odd Sum - Even Sum
Δ = 11 - 7
Δ = 4
Divisibility Check:
Because Δ / 11 = 61.363636363636:
Then 675 is NOT divisible by 11
Divisibility Final Answer
675 is divisible by
(3,5,9)
Final Answer
7 is our tens digit
5 is our ones digit
Ln(675) = loge(675) = 6.5147126908725
675 is divisible by
(3,5,9)
Keep Practicing
Common Core State Standards In This Lesson
What is the Answer?
7 is our tens digit
5 is our ones digit
Ln(675) = loge(675) = 6.5147126908725
675 is divisible by
(3,5,9)
How does the Number Information Calculator work?
This calculator has 1 input.
What 4 concepts are covered in the Number Information Calculator?
- integer
- a whole number; a number that is not a fraction
...,-5,-4,-3,-2,-1,0,1,2,3,4,5,... - number
- an arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity and used in counting and making calculations and for showing order in a series or for identification. A quantity or amount.
- property
- an attribute, quality, or characteristic of something
- tally
- a vertical line used to record counting
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