Question

Write 6789 correct to 3 significant figures.

Answer 1

Hint:- We had to use the statement that the first non-zero digit, reading from left to right in a number, is the first significant figure. And this goes on to second, third significant figures till the number ends.

Complete step-by-step solution -
As we know that if we are asked to write a number up to n significant figures then we start from the leftmost digit of the number and then round off till the \[{n^{th}}\] digit of the number.
So, let us take an example to understand the significant figures
The accuracy of the answer will depend on the number of significant figures. The answer will be more accurate, if it is given to a higher number of significant figures.
Like if 64,492 be the number than when we write it up to,
1 significant figure it will be 60,000
2 significant figures it will be 64,000
3 significant figures it will be 64,500
4 significant figures it will be 64,490
5 significant figures it will be 64,492
So, the most accurate answer will be when we write it up to 5 significant figures.
Now we are asked to write 6789 correct to 3 significant figures.
So, it can be written as 6790.
Hence, 6789 correct to 3 significant figures will be 6790.

Note:- Whenever we come up with this type of problem then another way to write the given number correct to n significant digits will be if the \[{\left( {n +1} \right)^{th}}\] digit from the left most of the number is greater than 5 then increase the \[{\left( n \right)^{th}}\] by 1 and replace all the digits to the right of \[{\left( n \right)^{th}}\] digit by 0 (Like 3rd significant figure in 64,492 will be 64,500). And if the \[{\left( {n + 1} \right)^{th}}\] digit from the left most of the number is less than 5 then decrease the \[{\left( n \right)^{th}}\] by 1 and replace all the digits to the right of \[{\left( n \right)^{th}}\] digit by 0 (Like 4th significant figure in 64,492 2ill be 64,490).