Question

Owain thinks of a number, t.

He rounds t to 1 d.p.
He then rounds the result to the nearest intege
His final number is 37.
What is the smallest value that t could have?

Answer 1

The smallest value of t that Owain could have thought of is 36.95, because this number rounds up to 37.0 at the first stage (1 decimal place) and then remains 37 when rounded to the nearest integer.

Step-by-step explanation:

Owain thinks of a number, t. He first rounds t to 1 decimal place (d.p.), and then rounds that result to the nearest integer. His final number is 37. To determine the smallest value that t could have been, we need to consider the rounding rules:

• If a number ends in 5 and is to be rounded to one fewer decimal place, the number rounds up if a nonzero digit follows the 5 or if the last digit before the 5 is odd.
• If the last digit before the 5 is even and no nonzero digit follows the 5, the number rounds down.

For t to round to 37 at both stages, t could have been 36.95 at least, because:

1. 36.95 rounds up to 37.0 when rounded to 1 d.p. (because the dropping digit is 5).
2. 37.0 then rounds to 37 when rounded to the nearest integer (it is already an integer).

Thus, the smallest value for t that Owain could have thought of is 36.95.