Question Details

Subtract 2.5 x 10⁴ from 3.9 x 10⁵ with due regard to significant figures.

Options

A

4.7 x 10⁵

B

6.7 x 10⁵

C

2.7 x 10⁵

D

3.7 x 10⁵

Correct Answer :

3.7 x 10⁵

Solution :

The correct option is 3.7 x 10���.

To subtract the given numbers, we must first express both numbers with the same power of 10. Let us convert them so that they both have an exponent of 5:

3.9×105

and

2.5×104=0.25×105

Now, perform the subtraction:

(3.9-0.25)×105=3.65×105

According to the rules for significant figures in subtraction, the final result must be rounded to the same number of decimal places as the term with the fewest decimal places (when both terms share the same exponent).

Looking at our terms:
- 3.9×105 has 1 decimal place.
- 0.25×105 has 2 decimal places.

Since the minimum number of decimal places is 1, the result must be rounded to 1 decimal place (the tenths place). Rounding 3.65 to one decimal place yields 3.7.

Therefore, the final answer with due regard to significant figures is:

3.7×105

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