Question

question 5 (1 point) which of the following is the correct answer for the following calculation, reported to the correct number of significant figures? 25.64 - 19.202 a) 6.438 b) 6.43 c) 6.44

Explanation:

Step1: Perform the subtraction

First, we calculate \( 25.64 - 19.202 \).
\( 25.64 - 19.202 = 6.438 \)

Step2: Determine significant figures for subtraction

In subtraction, the result should have the same number of decimal places as the number with the least number of decimal places.

• \( 25.64 \) has two decimal places.
• \( 19.202 \) has three decimal places.

So we round \( 6.438 \) to two decimal places. Looking at the third decimal place (8), which is greater than 5, we round up the second decimal place.
\( 6.438 \approx 6.44 \) when rounded to two decimal places? Wait, no, wait: Wait, \( 25.64 \) has two decimal places, so the result should have two decimal places. Wait, \( 6.438 \) rounded to two decimal places: the third digit is 8, so we round the second decimal place (3) up by 1, making it 4. Wait, but wait, \( 25.64 \) is to the hundredth place (two decimal places), \( 19.202 \) is to the thousandth. So the result should be to the hundredth place.

Wait, let's recalculate the subtraction:

\( 25.640 - 19.202 = 6.438 \) (we can add a zero to \( 25.64 \) to make it \( 25.640 \) for subtraction). Now, \( 25.64 \) has two decimal places, so the result should be rounded to two decimal places.

\( 6.438 \) rounded to two decimal places: look at the third decimal place, which is 8. Since 8 ≥ 5, we round the second decimal place (3) up to 4. So \( 6.438 \approx 6.44 \)? Wait, but wait, no: Wait, \( 25.64 \) is precise to the hundredth, \( 19.202 \) to the thousandth. The rule for addition/subtraction is that the result has the same number of decimal places as the term with the least number of decimal places. So \( 25.64 \) has two decimal places, so the result should have two decimal places.

Wait, \( 6.438 \) to two decimal places: the first decimal is 4, second is 3, third is 8. Rounding 3 up by 1 (because 8 ≥ 5) gives 4. So \( 6.438 \approx 6.44 \)? Wait, but let's check the options. Option c is 6.44, option b is 6.43, option a is 6.438.

Wait, maybe I made a mistake. Let's re-express the numbers:

\( 25.64 \) has two decimal places (the 4 is in the hundredth place). \( 19.202 \) has three decimal places (the 2 is in the thousandth place). When subtracting, the number of decimal places in the result is determined by the least precise measurement, which is \( 25.64 \) with two decimal places. So we need to round the result to two decimal places.

Calculating \( 25.64 - 19.202 = 6.438 \). Now, rounding 6.438 to two decimal places: look at the third decimal digit, which is 8. Since 8 > 5, we round the second decimal digit (3) up by 1, making it 4. So \( 6.438 \approx 6.44 \). So the correct answer is option c.

Answer:

c) 6.44