Vishal estimated a number as 2000 when he rounded the number to 1, 2 or 3 significant figures. Ethan was shocked by Vishal's answer and he asked Vishal what is the smallest and largest possible number such that the estimated number is 2000. Can you help Vishal answer Ethan?
Step 1: Identify the first non-zero digit from the left.
Step 2: From this digit, start highlighting n significant figures.
Step 3: Look at the digit just after the last highlighted digit. Round up if
this is 5 and above, otherwise do nothing.
Always remember to include the place-holder ‘0’s.
1 950 < x < 2 050, the x cannot be made equal 2 050, this is because it would be rounded to 2 100. A number like 2 049.9999999 (seven ‘9’s after the decimal point) will be rounded down to 2 000. Even if there were one trillion ‘9’s after the decimal point, as long as the number of decimals terminates (i.e. is finite), it will still be rounded down to 2 000.
2 050 is not the largest number, as it is not among the possible numbers, but 1 950 is the lowest number, because it is among all the possible numbers. Because there is actually no largest number, I used the word “largest” in quotation marks. [ Optional: The interested reader may want to check up infimum and supremum ] These are some very fine details that the textbook authors and editors forgot. Even if the editor has a PhD, the PhD could be in “mathematics education” but not “mathematics”, and may have forgotten the rigours of the real numbers system. The answers given at the back of the book are not only wrong, one pair of answers was missing. This caused some confusion among parents and students. I suspect they employed a non-professional part-timer to do up the answers in order to save costs.