 ## Friday, July 31, 2015

### Converting from Base 6 to Base 10 Problems, 2

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 4520136 into Base 10.

Solution:

The given number which is
4520136 is written in Base 6. Base 6 number is also called heximal system. The digits of Base 6 number are 0, 1, 2, 3, 4, and 5.

On the other hand, Base 10 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. If you don't see any subscript at the given number, then that number is written in Base 10. Base 10 number is also called decimal system. Base 10 number is a common number that we are using right now in everyday life.

Now, let's convert
4520136 into Base 10. How? Let's multiply each digits by the powers of 6 as follows:

Base 6 Digits:        4      5      2
0      1      3
Multiply by:
6⁵     6⁴     6³
6²     6¹     6⁰

Add all the digits, we have

(4 x
6⁵) + (5 x 6⁴) + (2 x ) + (0 x ) + (1 x ) + (3 x 6⁰) = 31104 + 6480 + 432 + 0 + 6 + 3 = 38025

Therefore,
4520136 = 38025

## Thursday, July 30, 2015

### Converting from Base 6 to Base 10 Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 2456 into Base 10.

Solution:

The given number which is
2456 is written in Base 6. Base 6 number is also called heximal system. The digits of Base 6 number are 0, 1, 2, 3, 4, and 5.

On the other hand, Base 10 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. If you don't see any subscript at the given number, then that number is written in Base 10. Base 10 number is also called decimal system. Base 10 number is a common number that we are using right now in everyday life.

Now, let's convert
2456 into Base 10. How? Let's multiply each digits by the powers of 6 as follows:

Base 6 Digits:        2      4      5

Multiply by:
6²     6¹     6⁰

Add all the digits, we have

(2 x ) + (4 x ) + (5 x 6⁰) = 72 + 24 + 5 = 101

Therefore,
2456 = 101

## Wednesday, July 29, 2015

### Converting from Base 10 to Base 6 Problems, 2

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 148506 into Base 6.

Solution:

The given number which is
148506 is written in Base 10. 148506 can also be written as 14850610. If you don't see any subscript at the given number, then that number is written in Base 10. Base 10 number is also called decimal system.  The digits of Base 10 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Base 10 number is a common number that we are using right now in everyday life.

On the other hand, Base 6 number is a number whose digits are 0, 1, 2, 3, 4, and 5. If you see a subscript of 6 at the given number, then that number is written in Base 6. Base 6 number is also called heximal system.

Now, let's convert
148506 into Base 6. How? Let's divide 148506 by 6 as follows:

148506 ÷ 6 = 24751 + R(0)

Next, let's divide the quotient, which is 24751, as follows:

148506
÷ 6 = 24751 + R(0)
24751 ÷ 6 =   4125 + R(1)

Do the same thing with 4125 until the quotient is 0 as follows:

148506 ÷ 6 = 24751 + R(0)
24751 ÷ 6 =   4125 + R(1)

4125 ÷ 6 =     687 + R(3)
687 ÷ 6 =     114 + R(3)
114 ÷ 6 =       19 + R(0)
19 ÷ 6 =         3 + R(1)
3 ÷ 6 =         0 + R(3)

The remainders will be the digits of Base 6 number. Use the digits of the remainders from bottom to top. Therefore,

148506 = 31033106

## Tuesday, July 28, 2015

### Converting from Base 10 to Base 6 Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 699 into Base 6.

Solution:

The given number which is
699 is written in Base 10. 699 can also be written as 69910. If you don't see any subscript at the given number, then that number is written in Base 10. Base 10 number is also called decimal system.  The digits of Base 10 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Base 10 number is a common number that we are using right now in everyday life.

On the other hand, Base 6 number is a number whose digits are 0, 1, 2, 3, 4, and 5. If you see a subscript of 6 at the given number, then that number is written in Base 6. Base 6 number is also called heximal system.

Now, let's convert
699 into Base 6. How? Let's divide 699 by 6 as follows:

699 ÷ 6 = 116 + R(3)

Next, let's divide the quotient, which is 116, as follows:

699
÷ 6 = 116 + R(3)
116 ÷ 6 =   19 + R(2)

Do the same thing with 19 until the quotient is 0 as follows:

699 ÷ 6 = 116 + R(3)
116 ÷ 6 =   19 + R(2)

19 ÷ 6 =     3 + R(1)
3 ÷ 6 =     0 + R(3)

The remainders will be the digits of Base 6 number. Use the digits of the remainders from bottom to top. Therefore,

699
= 31236

## Monday, July 27, 2015

### Converting from Base 5 to Base 10 Problems, 2

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 3344215 into Base 10.

Solution:

The given number which is
3344215 is written in Base 5. Base 5 number is also called quinary system. The digits of Base 5 number are 0, 1, 2, 3, and 4.

On the other hand, Base 10 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. If you don't see any subscript at the given number, then that number is written in Base 10. Base 10 number is also called decimal system. Base 10 number is a common number that we are using right now in everyday life.

Now, let's convert
3344215 into Base 10. How? Let's multiply each digits by the powers of 5 as follows:

Base 5 Digits:        3      3      4      4
2      1
Multiply by:            5⁵     5⁴     5³
5²     5¹     5⁰

Add all the digits, we have

(3 x
5⁵) + (3 x 5⁴) + (4 x ) + (4 x ) + (2 x ) + (1 x 5⁰) = 9375 + 1875 + 500 + 100 + 10 + 1 = 11861

Therefore,
3344215 = 11861