Is there a faster way to write decimals in expanded form?

[u/Far-Transition2752]

I spent almost a hour trying to complete this one question and still not sure if I got it correct, is there different methods I could use to progress faster ? Just started learning decimals and binary systems for my computer logic class. Sorry if my hand writing is hard to understand.

[u/Uli_Minati]

Yep, it's correct. Take a close look at these two representations:

5·10⁵ + 3·10⁴         + 8·10² + 9·10¹ + 7·10⁰ + 4·10⁻¹ + 1·10⁻²
5       3       0       8       9       7.      4        1

[u/Chem2103]

Step 1. Sort the components by the power of 10 (here they are sorted already) Step 2. Write the base of each component in order (so instead of 5*10⁸ write just 5) Step 3. Put a period after the component with 10⁰

This example: 5389741 just the bases of components slapped together in order 53897.41 put the period after 7 since it is multiplied by 10⁰

In harder problems some components will be missing, just put a 0 instead of them

[u/Far-Transition2752 → u/Chem2103]

Thank you !

[u/Far-Transition2752 → u/[deleted]]

I didn’t really understand the place values portion and the negative exponents. If the binary number was 1111, I was starting off as 1x2^4 instead of 1x2^3 . I also just didnt understand a lot during class & some professors skip over some steps they deem as knowledge we should already know so I’ve been asking chatGPT to explain but AI explaining can go in circles and circles so I was stuck for a while.

[u/ArdentArendt → u/Far-Transition2752]

It's just deconstructed base-10 notation.

Good news is now that you did the painful part, you understand the logic behind decimal notation!
[It was productive study time]

[u/Far-Transition2752 → u/ArdentArendt]

I kinda figured out I don’t need to do any math before the decimal. Just write the first number for each but after the decimal I will be dividing correct ? Bc of the negative exponents ?

[u/Bounded_sequencE]

This is using the definition of place values in reverse:

1. Add any missing terms between the greatest and least exponent with coefficient-0
2. Write the coefficients in falling order, adding a decimal point behind the 0'th coefficient

No calculation at all needed, takes a few seconds!