Question

question 4 (1 point)
express the following sum with the correct number of significant figures: 1.00 kg + 1531 g + 2.54 × 10^4 mg.
2.56 kg
27.9 kg
2.53 kg
2.79 kg
question 5 (1 point)
what is the difference between 103.5 and 102.24?
1.3
1.26
1.260
1.2600

Explanation:

Step1: Convert all units to kg

• \(1531g = 1531\times10^{- 3}kg=1.531kg\)
• \(2.54\times10^{4}mg=2.54\times10^{4}\times10^{-6}kg = 0.0254kg\)

Step2: Sum the values

\(1.00kg + 1.531kg+0.0254kg=(1.00 + 1.531+0.0254)kg\)
\(1.00+1.531 + 0.0254=2.5564\)

Step3: Round to the correct number of significant figures

The least number of decimal places among the addends is 2 (from \(1.00\)). So, \(2.5564\approx2.56\)

Step1: Calculate the difference

\(103.5-102.24 = 1.26\)

Step2: Consider significant figures

For subtraction, the result should be rounded to the least number of decimal places. \(103.5\) has one decimal place and \(102.24\) has two decimal places. We go with one decimal place. But wait, actually, when subtracting \(103.5-102.24\), we can also think in terms of significant figures rules for subtraction (the number of decimal places). \(103.5-102.24=1.26\), and if we consider the rules (the number with the least number of decimal places in subtraction: \(103.5\) has one decimal place. But actually, the more accurate way is that when subtracting \(a - b\), we look at the decimal places. \(103.5-102.24\):

$$
LATEXBLOCK0
$$

Since \(103.5\) is precise to the tenths place (implied hundredths place as \(0\)), and \(102.24\) is precise to the hundredths place. The result should be precise to the hundredths place.

Answer:

\(2.56\space kg\)