How Accurate Are These Sig Fig Calculations and Unit Conversions?

[cbrowne]

Hey I don't want to loose points for this primary question, could someone please go over my answers. Thanks!

Homework Statement

1. Perform the following operations and write your answers with appropriate
number of significant figures: (a) 589.01−89.020 (b) 1.0×9.00 (c) 180 /pi
(d) 180.0 /pi (e)3.901x10^-5+ 1.0x10^-7

2. Perform the following unit conversions and express the answer in scientific
notation: (a) 0.510 kg to g (b) 92 mi to km (c) 3 0.50 m to 3 cm (d) 15 μs to ms
(e) 60.0 km/h to m/s

The Attempt at a Solution

a) 589.01-89.020 = 499.99
b) 1.0 x 9.00 = 9.0
c) 180/ Π = 57
d) 180.0/Π = 57.30
e) 3.901 x 10^-5 + 1.0 x 10^-7 = 0.00004


2. a) 0.510kg x 1000g/1kg= 5.1 x 10²g

b) 92 mi x 1.609344km/1mi= 1.48059 x 10² km

c) 0.50m³ x 1 000 000cm³/ 1m³ = 5 x 10⁵ cm³

d) 15μs x 1ms/0.001 μs = 1.5 x 10^-2ms

e) 60.0km/1hour = 65000m/3600 sec = 1.805556 x 10¹ m/s

 

[Joskoplas]

1e looks reeaall suspicious.

If I multiplied both numbers by 10^7 (for my convenience), I'd see 390.1 + 1.0

I don't have to convert it back to the proper decimal place to see there's a problem with saying 400

 

[thomate1]

As a scientist, it is important to understand the concept of significant figures and proper unit conversions. In order to accurately represent and communicate scientific data, we must use the appropriate number of significant figures. In the first question, the answers provided are correct based on the given numbers and their corresponding significant figures. However, it is important to note that in scientific calculations, we typically carry out the calculations with more significant figures and then round off the final answer to the appropriate number of significant figures.

In the second question, the conversions are also correct. It is important to use the correct conversion factors and units in order to accurately convert between different units. Additionally, expressing the final answer in scientific notation allows for easier comparison and understanding of the magnitude of the quantities.

In conclusion, understanding significant figures and unit conversions is crucial for accurate and precise scientific calculations and communication of data. It is important to pay attention to the given numbers and their corresponding significant figures as well as the appropriate conversion factors and units.