# Decimal to negadecimal converter

## World's simplest number tool

Quickly convert a decimal number to a negadecimal number in your browser. To get your number in the base minus ten, just enter it in the input field, and this utility will print it as a negadecimal. Created by developers from team Browserling.

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Decimal to negadecimal converter tool
What is a decimal to negadecimal converter?

This is an online browser-based utility for converting decimals to negadecimals (also called base -10 numbers). All decimal number can be decomposed into a sum of powers of ten. For example, the integer 125 can be written as 1×100 + 2×10 + 5 and this can be rewritten as a sum of powers of ten: 1×10

^{2}+ 2×10^{1}+ 5×10^{0}. If we look at the coefficients before powers of ten we see 1, 2, 5, which makes up our number. In the same way, we can write any number in the base -10. Odd powers of this negative base create negative numbers, but even powers produce positive ones. By combining these negative and positive powers, we can construct any number. Thus, the number 125 in base -10 can be decomposed as follows: 125_{10}= 2×(-10)^{2}+ 8×(-10)^{1}+ 5×(-10)^{0}= 285_{-10}. So we find that 125 is 285 in base -10. An interesting fact is that in the base -10 we don't need the sign symbol as all negative numbers are always represented as positive numbers. For example, -125_{10}= 1×(-10)^{3}+ 9×(-10)^{2}+ 3×(-10)^{1}+ 5×(-10)^{0}= 1935_{-10}. With this tool, you can convert positive numbers, negative numbers, or both at the same time, simply by entering each of them on a new line. If you are interested in the power series that create the number, use the "Show Representation Sum" option, which will print your number "x" in the form x = a_{0}(-10)^{n}+ … + a_{n-1}(-10)^{1}+ a_{n}(-10)^{0}. The coefficients a_{0}a_{1}…a_{n-2}a_{n-1}a_{n}create the number in this interesting base. That's numberwang!
Decimal to negadecimal converter examples
Click to use

Five Numbers to Base -10

In this example, we convert five whole numbers to the base -10. Each number x decomposes as a sum of powers of minus ten in the form x = ∑a

_{n}(-10)^{n}. The power coefficients a_{n}…a_{1}a_{0}create the number in the new base. For example the number 25 in base 10 is 1×(-10)^{2}+ 8×(-10)^{1}+ 5×(-10)^{0}or 185 in base -10.
1
10
25
456
1024

1
190
185
556
19184

**Required options**

Write the full series of
powers of -10.

Show Full Sum

In this example, we wanted to see a detailed decomposition of the base change formula for numbers 148 and -148. We activated the option "Show Representation Sum" and as you can see, the number 148 is created from three terms – two even powers and one odd power. The negative number -148 needs for addends because to get a negative value, it needs a large odd power. Thus, -148

_{10}is 1×(-10)³ + 9×(-10)² + 5×(-10)¹ + 2×(-10)⁰ = -1000 + 900 - 50 + 2, or 1952_{-10}.
148
-148

2×(-10)² + 6×(-10)¹ + 8×(-10)⁰
1×(-10)³ + 9×(-10)² + 5×(-10)¹ + 2×(-10)⁰

**Required options**

Write the full series of
powers of -10.

Pro tips
Master online number tools

You can pass input to this tool via

__?input__query argument and it will automatically compute output. Here's how to type it in your browser's address bar. Click to try!
https://onlinenumbertools.com/convert-number-to-negadecimal

__?input__=1%0A10%0A25%0A456%0A1024&show-representation-sum=false
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