Question

A piece of length 3.532 m is cut from a rod of length 43.4 m. The length of the remaining rod in metre is (up to correct significant figures)

• A. 39.9
• B. 39.8
• C. 39.868
• D. 39.87

Hint:

For addition and subtraction with significant figures, the result's precision is limited by the least precise measurement. The rule is to round the final answer to the same number of decimal places as the input number with the fewest decimal places.

Answer 1

The Correct Option is A

First, perform the subtraction to find the raw length of the remaining rod.
Remaining length = Initial length - Length of piece cut.
Remaining length = $43.4$ m - $3.532$ m = $39.868$ m.
Now, we must apply the rules for significant figures in addition and subtraction.
The rule states that the result should have the same number of decimal places as the measurement with the fewest decimal places.
The initial length, $43.4$ m, has one decimal place.
The length of the piece cut, $3.532$ m, has three decimal places.
The number with the fewest decimal places is $43.4$ (one decimal place).
Therefore, the final answer must be rounded to one decimal place.
Rounding $39.868$ m to one decimal place: The digit after the first decimal place is 6, which is 5 or greater, so we round up the first decimal digit.
Rounded length = $39.9$ m.