3 hundreds
Hundred-Groups = 100 + 100 + 100
Hundred-Groups = 300
6 tens
Ten-Groups = 10 + 10 + 10 + 10 + 10 + 10
Ten-Groups = 60
5 ones
365 = 300 Hundreds + 60 Tens + 5 ones
365 = 300 + 60 + 5
Show numerical properties of 365
365
three hundred sixty five
Decompose 365
Each digit in the whole number represents a power of 10:
Take the whole number portion on the left side of the decimal
Expanded Notation of 365 = (3 x 102) + (6 x 101) + (5 x 100)
Expanded Notation of 365 = (3 x 100) + (6 x 10) + (5 x 1)
365 = 300 + 60 + 5
365 = 365 <---- Correct!
Make blocks of 5
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Define an ordinal number
A position in a list
365th
Calculate the digit sum of 365
Calculate the reduced digit sum of 365
Digit Sum → 3 + 6 + 5 = 14
Since our digit sum > 9:
repeat this process to get the reduced digit sum:
Our new number to evaluate is 14
Digit Sum → 1 + 4 = 5
Since our digit sum ≤ 9:
we have our reduced digit sum
Digit Sum → 1 + 4 = 5
Calculate the digit product of 365
Digit Product = Value when you multiply
all the digits of a number together.
We multiply the 3 digits of 365 together
Digit product of 365 = 3 * 6 * 5
Digit product of 365 = 90
Opposite of 365 = -(365)
Opposite of = -365
Place value describes each digit
3 is our hundreds digit
This means we have 3 sets of hundreds
6 is our tens digit
This means we have 6 sets of tens
5 is our ones digit
This means we have 5 sets of ones
3 is our hundreds digit
6 is our tens digit
5 is our ones digit
When ey = x and e = 2.718281828459
We have Ln(x) = loge(x) = y
Ln(365) = loge(365) = 5.8998973535825
Is 365 divisible by:
2,3,4,5,6,7,8,9,10,11
Last digit ends in 0,2,4,6,8
The last digit of 365 is 5
Since 5 is not equal to 0,2,4,6,8:
then 365 is not divisible by 2
Sum of the digits is divisible by 3
The sum of the digits for 365 is 3 + 6 + 5 = 14
Since 14 is not divisible by 3:
Then 365 is not divisible by 3
Take the last two digits
Are they divisible by 4?
The last 2 digits of 365 are 65
Since 65 is not divisible by 4:
Then 365 is not divisible by 4
Number ends with a 0 or 5
The last digit of 365 is 5
Since 5 is equal to 0 or 5:
Then 365 is divisible by 5
Divisible by both 2 and 3
Since 365 is not divisible by 2 and 3:
Then 365 is not divisible by 6
Multiply each respective digit by 1,3,2,6,4,5
Work backwards
Repeat as necessary
5(1) + 6(3) + 3(2) = 30
Since 30 is not divisible by 7:
Then 365 is not divisible by 7
Take the last three digits
Are they divisible by 8
The last 3 digits of 365 are 365
Since 365 is not divisible by 8:
Then 365 is not divisible by 8
Sum of digits divisible by 9
The sum of the digits for 365 is 3 + 6 + 5 = 14
Since 14 is not divisible by 9:
Then 365 is not divisible by 9
Ends with a 0
The last digit of 365 is 5
Since 5 is not equal to 0:
Then 365 is not divisible by 10
Σ odd digits - Σ even digits = 0
or 365 is a multiple of 11
365
3 + 5
Odd Sum = 8
365
6
Even Sum = 6
Δ = Odd Sum - Even Sum
Δ = 8 - 6
Δ = 2
Because Δ / 11 = 33.181818181818:
Then 365 is NOT divisible by 11
365 is divisible by
(5)