Firstly the question and the correct solution is

https://preview.redd.it/yp53qu0z190h1.png?width=1122&format=png&auto=webp&s=02eff4df938d87a94672aba03efd3b796052ae67

Some common arguments put forward by 7.6 supporters are -

1) The 4 after 5 means nothing, it will be anyways be dropped and and answer will come out to 7.65~7.6

https://preview.redd.it/atkz9tyx190h1.png?width=700&format=png&auto=webp&s=2c0c8219f632572a2bcd087590667bad3671c34f

Many here take refuge of the incomplete NCERT rule stating

"if preceding digit is raised by 1 if the insignificant digit to be dropped (the underlined digit in this case) is more than 5, and is left unchanged if the latter is less than 5"

This statement is incomplete in the NCERT ❗❗

According to Indian standard rules for rounding off numerical value

https://preview.redd.it/lt529qoh590h1.png?width=531&format=png&auto=webp&s=0be72f54c8fc696adcc6341eb9a0723c7d566eaa

Rule II- When the figure next beyond the last figure or place to be retained is more than 5 or is 5 followed by any figures other than zeros, the figure in the last place retained shall be increased by 1. SOURCE

This is the correct rule that NCERT does not mention ✅✅

so, the 4 following 5 does hold its value

2) The side of the cube is given in 2 significant figures, so the volume that comes to be 729 has to be rounded off to 2 SF i.e. 730, which will land you to 7.64~7.6

https://preview.redd.it/9v1l96lb790h1.png?width=692&format=png&auto=webp&s=7f5fad739732c16e255ea3d647e812a14bca94d6

This can be answered by NCERT itself

https://preview.redd.it/a7p7bi5p790h1.png?width=336&format=png&auto=webp&s=7e7dde8a92749c692fd94ae853798ae80262a185

Source: NCERT Reprint 2026-27 (Pg. no. 6)

Here we are calculating for density, the volume here is our intermediate result, hence we have to keep volume with one more than the least number of SF that is 3, hence volume will remain 729

Also, according to the Indian Standard Rules for Rounding Off Numerical Values Clause 4.2.2, it is the final answer where rules of rounding off to required number of SF is applied to maintain accuracy.

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Now some people say,

Since, it isn't given in NCERT, 7.6 is to be assumed correct

Let's take an incident from NEET 2024, there was a similar controversy. After all court filings and considerations, finally the actual correct answer was given to correct (Which was incorrect according to the NCERT)

Taking all this into consideration

7.7 is the CORRECT answer ✅✅

7.6 is INCORRECT ❌❌

if you want, I can provide you with similar questions, solutions and explanations from Cengage, SL Arora and HC Verma

if you still are not satisfied, you can watch this video by Shashi Bhushan Tiwari sir

https://youtu.be/kZ1ZJP9cWUg

if you still have any arguments, u/fuck-dignity u/A_Lazy_Genius u/Excellent_Radish8361 will counter them