Question

using significant figures, which of the following students wrote a calculation that could have a sum or difference of 51.9?

student	calculation
lori	48.22 + 3.76
nobu	48.2222 + 3.7
jerome	48.2 + 3.769

select choice

Explanation:

Step1: Analyze Juliana's Calculation

Juliana's calculation: \(48.2222 + 3.769\)
First, add the two numbers: \(48.2222+3.769 = 51.9912\)
Now, consider significant figures. The least number of decimal places in the numbers being added: \(48.2222\) has 4 decimal places, \(3.769\) has 3 decimal places. When adding, we go by the least number of decimal places for precision, but here we are looking at the sum's possible value with significant figures. The sum is approximately \(52.0\) (if we consider significant figures), but wait, no—wait, the target is \(51.9\). Wait, maybe I made a mistake. Let's check each student:

Step2: Analyze Lori's Calculation

Lori's calculation: \(48.22 + 3.76\)
Add them: \(48.22 + 3.76 = 51.98\)
Now, with significant figures, \(48.22\) has two decimal places, \(3.76\) has two decimal places. The sum is \(51.98\), which rounds to \(52.0\) (four significant figures) or \(52\) (two significant figures)? Wait, no, the question is which calculation could have a sum of \(51.9\) (assuming maybe a typo, or maybe \(51.9\) as in three significant figures? Wait, \(51.9\) has three significant figures.

Wait, let's check Jerome: \(48.2 + 3.769\)
\(48.2 + 3.769 = 51.969\), which is approximately \(52.0\) (three significant figures? No, \(51.969\) rounded to three significant figures is \(52.0\)? Wait, no, \(51.969\) to three significant figures: the third is 9, next digit 6, so round up: \(52.0\)? Wait, maybe I messed up.

Wait, Nobu: \(48.222 + 3.7\)
\(48.222 + 3.7 = 51.922\)
Now, \(51.922\) rounded to three significant figures is \(51.9\) (since the fourth digit is 2, which is less than 5, so we keep the third digit as 9). Ah! So Nobu's calculation: \(48.222 + 3.7 = 51.922\), which when considering significant figures (since \(3.7\) has two significant figures? Wait, no, \(3.7\) has two decimal places? No, \(3.7\) has one decimal place. Wait, \(48.222\) has three decimal places, \(3.7\) has one. When adding, the result should have one decimal place (because of \(3.7\)). So \(51.922\) rounded to one decimal place is \(51.9\) (since the second decimal is 2, which is less than 5, so we keep the first decimal as 9). Yes! So Nobu's calculation, when rounded to one decimal place (due to \(3.7\) having one decimal place), gives \(51.9\).

Wait, let's recheck:

• Juliana: \(48.2222 + 3.769 = 51.9912\) → rounds to \(52.0\) (if one decimal place: \(52.0\))
• Lori: \(48.22 + 3.76 = 51.98\) → rounds to \(52.0\) (one decimal place)
• Nobu: \(48.222 + 3.7 = 51.922\) → rounds to \(51.9\) (one decimal place, because \(3.7\) has one decimal place, so the sum should have one decimal place. The first decimal is 9, the next digit is 2, so we don't round up. So \(51.9\))
• Jerome: \(48.2 + 3.769 = 51.969\) → rounds to \(52.0\) (one decimal place, since \(48.2\) has one decimal place)

So Nobu's calculation, when considering significant figures (specifically decimal places from the least precise measurement, \(3.7\) with one decimal place), gives \(51.9\).

Step3: Confirm the Correct Student

So the student whose calculation could result in \(51.9\) (with significant figures) is Nobu.

Answer:

Nobu (with calculation \(48.222 + 3.7\))