**High School Number Sense Lesson 35: Converting from Base 10 to Base N**

Last week we learned how to go from some other base to base 10 (

**BaseNtoBase10**). Today we will go the other direction. This showed up

**6 times**this year, with a median placement at

**question # 35**.

**Number Dojo Level: 178**

I was about to teach you the "old way" to convert to another base. But I'd rather not confuse the issue, because this way will save lots of time. I think I learned this way as the "remainder" method.

**How to Solve:**

- Divide the base 10 number by the base; think of the quotient and the remainder.
- Write down the
**remainder**from Step 1. Divide the quotient from Step 1 by the base. - Write down the
**remainder**from Step 2 in front of the number you wrote down in Step 2. Divide the quotient from Step 2 by the base. - Continue this process until you run out of numbers.

**Example 1: 144 base 10 in base 5 is ___**

- Divide 144 by the base (5). 144 ÷ 5 =
**28 remainder 4**. - Write down the remainder:
**4**. Divide the quotient (**28**) by the base (**5**). 28 ÷ 5 =**5 remainder 3**. - Write the remainder in front:
**3**. Divide the quotient (**5**) by the base (**5**). 5 ÷ 5 =**1 remainder 0**. - Write the remainder in front:
**0**. Divide the quotient (**1**) by the base (**5**). 1 ÷ 5 =**0 remainder 1**. - Write the remainder in front:
**1**. Your answer is**1034**.**Notice that once your quotient is < the base, you can simply write it in front of your last remainder.**

**Example 2: 118 base 10 in base 6 is ___**

- Divide 118 by the base (6). 118 ÷ 6 =
**19 remainder 4**. - Write down the remainder:
**4**. Divide the quotient (**19**) by the base (**6**). 19 ÷ 6 =**3 remainder 1**. - Write the remainder in front:
**1**. The quotient is < the base; write it in front:**3**. - Your answer is
**314**.

**Example 3: 88 base 10 in base 3 is ___**

- Divide 88 by the base (3). 88 ÷ 3 =
**29 remainder 1**. - Write down the remainder:
**1**. Divide the quotient (**29**) by the base (**3**). 29 ÷ 3 =**9 remainder 2**. - Write the remainder in front:
**2**. Divide the quotient (**9**) by the base (**3**). 9 ÷ 3 =**3 remainder 0**. - Write the remainder in front:
**0**. Divide the quotient (**3**) by the base (**3**). 3 ÷ 3 =**1 remainder 0**. - Write the remainder in front:
**0**. The quotient is < the base; write it in front:**1**. - Your answer is
**10021**.

**Example 4: 314 base 10 in base 7 is ___**

- Divide 314 by the base (7). 314 ÷ 7 =
**44 remainder 6**. - Write down the remainder:
**6**. Divide the quotient (**44**) by the base (**7**). 44 ÷ 7 =**6 remainder 2**. - Write the remainder in front:
**2**. The quotient is < the base; write it in front:**6**. - Your answer is
**626**.

**Example 5: 777 base 10 in base 9 is ___**

- Divide 777 by the base (9). 777 ÷ 9 =
**86 remainder 3**. - Write down the remainder:
**3**. Divide the quotient (**86**) by the base (**9**). 86 ÷ 9 =**9 remainder 5**. - Write the remainder in front:
**5**. Divide the quotient (**9**) by the base (**9**). 9 ÷ 9 =**1 remainder 0**. - Write the remainder in front:
**0**. The quotient is < the base; write it in front:**1**. - Your answer is
**1053**.

**Here's a free worksheet to help you practice Base10toBaseN:**

base10tobasen.pdf |

**Up Next for High School: DivMix**