Question

what are the base seven counting numbers just before and after 16 base seven ?

Answer 1

just before is 15
just after is 20

In base 7 we have only the following digits: 0,1,2,3,4,5,6
where the 6 in base 7 is like the 9 in base 10.

Answer 2

that's why in base 7, 20 comes after 16.

Answer 3

THANKS FIDDLE

Answer 4

SO 17 IS 7 AND 20 IS 14 ?

Answer 5

I MEAN SO 10 IS 7 AND 20 IS 14

Answer 6

yes,
10 (base 7) is 7 (base 10)
20 (base 7) is 14 (base 10)

Answer 7

and 123 (base 7) = 1*7^2 + 2*7^1 + 3*7^0 = 49 + 14 + 3 = 66 (base 10)

Answer 8

WHAT ARE THE LEAST AND GREATEST FOUR DIGIT NUMBERS AND THEIR DECIMAL EQUIVALENTS IN BASE 5?

Answer 9

base 5 means we have the digits 0,1,2,3,4

Answer 10

ONLY 0 1 2 3 4 R USED RIGHT?

Answer 11

what would you say is the least one ?

Answer 12

I WOULD SAY THE LEAST IS 0, BUT THAT IS NOT FOUR DIGITS.

Answer 13

so, if you're not allowed to have leading zeros in the number - what would you pick as the smallest leading digit ?

Answer 14

1

Answer 15

and the entire number would be ?

Answer 16

1000

Answer 17

yep

Answer 18

now the largest 4 digit number ?

Answer 19

IN BASE 5 WOULD BE 4444

Answer 20

yep. now we need the decimal equivalents of the base 5 numbers 1000 and 4444 .

Answer 21

???

Answer 22

isn't that part of the question - to find the decimal equivalents of these two base 5 numbers ?
do you know how to do it ?

Answer 23

YES, BUT I DONT KNOW HOW?

Answer 24

1000 (base 5) = 1 * 5^3 + 0 *5^2 + 0 *5^1 + 0 *5^0
= 1*125 + 0*25 + 0*5 + 0*1 = 125 (decimal)

Answer 25

is what I did above clear ?

Answer 26

I THINK SO, LET ME TRY TO FIGURE OUT THE GREATEST DECIMAL. GIVE ME A MIN

Answer 27

624?

Answer 28

can you post how you got that ?

Answer 29

it's correct :)

Answer 30

I DID WHAT U DID TO GET THE LEST DECIMAL. 4 * 5^3 + 4 * 5^2 + 4 *5^1 + 4 *5^0

Answer 31

it's correct .

Answer 32

WOULD I USE THE SAME FORMULA TO FIND THE DECIMAL EQUIVALNT FOR 65 BASE 9

Answer 33

It's the same idea, just use 9^.. instead of 5^..

Answer 34

9 * 6^2 + 9 * 5^1 ?

Answer 35

6*9^1 + 5*9^0

Answer 36

BUT 6 IS IN THE TENS PLACE, AND 5 IS IN THE ONES PLACE. WHY USE THE ZERO POWER IF IN THE ONES PLACE?

Answer 37

9^0 = 1 so this represents the ones place.
9^1 = 9 which represents the "tens" place in base 9

Answer 38

just like in base 10 (decimal)
10^0 = 1 represents the one's place
10^1 = 10 represents the tens place

Answer 39

SO 65 BASE NINE IS DECIMAL # 59?

Answer 40

yep that's right

Answer 41

IF I USE ^1 FOR THE TENS AND 0^ FOR THE ONES......WHAT DO U USE FOR 0?

Answer 42

to represent the number 0 ?

Answer 43

THE ZERO PLACE IN A NUMBER.....LIKE 400?

Answer 44

you are referring the the values of the digits being zero , not their place.
In 400 , one zero is placed in the "ones" place and the other is placed in the "tens" place.

Answer 45

OIC

Answer 46

don't forget to click "good answer" :)

Answer 47

SORRY

Answer 48

np

Answer 49

SO HOW WOULD IT WORK THE OTHER WAY AROUND, HOW DO I CONVERT 98 TO BASE FIVE?

Answer 50

First you would write out the powers of the base you want to convert to (five).
5^0=1
5^1=5
5^2=25
5^3=125
And I'm stopping here, coz 125 is bigger than 98.

Now, I start with 5^2 , and check how many times it goes into 98.
98 / 25 = 3 with remainder of 23 ( coz 98 - 3*25 = 23)
This means, my answer will have 3 in the base 5 hundreds place (5^2).

Next, I go to 5^1 , and check how many times it goes into 23 (remainder from above)
23/5 = 4 with remainder of 3 (coz 23 - 4*5 = 3)
This means, my answer will have 4 in the base 5 tens place (5^1)

Now, I am at 5^0 (the base 5 ones place).
It will contain 3 (the remainder from the previous step).

So, 98 (decimal) is 343 (base 5)

To check if I got it right, I'll convert 343 ( base 5) back to decimal:

3*5^2 + 4*5^1 + 3 = 3*25 + 4*5 + 3 = 75 + 20 + 3 = 98 (decimal)

Answer 51

it's a bit more annoying :)

Answer 52

4479 TO BASE SIXTEEN. ?

Answer 53

Start by listing base 16 powers:
16^0=0
16^1=16
16^2=256
16^3=4096
16^4=65536 <--- larger than 4479 so stopping here.

The base 16 number will have 4 digits.

We start with 16^3 .
How many times does it go into 4479 , and what is the remainder ?

Answer 54

1 R =383

Answer 55

yes. that means that in the base 16 thousands position we will have a 1.
Now we move to the base 16 hundreds place , with that remainder of 383 ,
and do the same thing.

Answer 56

how many times does 16^2 go into 383 , and what is the remainder ?

Answer 57

1 R 127

Answer 58

so, we will have a 1 in the base 16 hundreds place.
now take the remainder of 127 - and proceed with it to the base 16 tens place.

Answer 59

how many times does 16^1 go into 127, and what is the remainder ?

Answer 60

7

Answer 61

and remainder ?

Answer 62

15

Answer 63

yes. so the 7 will go in the base 16 tens place .
And the remainder 15 will go to the ones place.

Answer 64

In base 16 we have the following digits:
0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F
So our remainder of 15 (decimal) is represented by the digit F in base 16.

Answer 65

117F

Answer 66

So what would be our entire base 16 number ?

Answer 67

yep. that's it.

Answer 68

you can try converting it back to decimal to check it.

Answer 69

A BOOKSTORE ORDERED 2 GROSS, 11 DOZEN, AND 7 PENCILS. EXPRESS IN BASE 12 AND BASE 10?????????