Question

How do you round each of the given numbers to four significant figures? \[0 \cdot 004384010\] and \[431801kg\].

Answer 1

Hint:The given question asks to round off the given numbers to four significant figures. Significant figures are the digits that gives some information about the accuracy of the number. We round off a number in order to keep the value of the number intact.

Complete step by step answer:
Before rounding off the given numbers, let us first understand what significant figures are and what is rounding off.
Rounding off a number: Rounding off numbers is a numerical approach used to adjust the digits of the number to make it easier to use it during calculations. The numbers are rounded to a certain degree of accuracy to make the calculations simpler and the results simpler to comprehend.Significant figures are non-zero digits that convey about the accuracy of a number.Example: 73 has two significant digits. Likewise, 0.00234 has three significant figures. They are, 2,3 and 4 and zeroes tell us about the place values.

Now, given numbers are: \[0 \cdot 004384010\] Here we have to round off up to four significant digits. Therefore, we start counting four non-zero digits from the left. Therefore, we get \[0 \cdot 004384\] which is our required rounded off digit.Secondly we are given, \[431801kg\] has six significant figures. The number is about four hundred thousand in size. Despite any rounding, it still has to be about four hundred thousand.

Therefore, our answer for this number becomes, \[431800kg\] which has four significant digits.

Note:It is important to note here that each of the non-zero digits are significant. The zeroes to the right of decimal after all significant digits are always non-significant. The zeroes to the left of the decimal between the non-zero digits are significant.