University:
Felician University
Course:
MATH-002 | Basic Math Skills-Algebra
Academic year:

2019
Views:

272

Pages:

18
Author:

Clint W.

Derived Quantities and Significant Figures What is a derived quantity? • A derived quantity is a number made by combining two or more other values. • A derived unit is a unit which is made by combining two or more units. • A derived quantity is usually found in formulas as a variable. Examples: Density (g/mL), Velocity (m/s) Steps to solve for derived quantities: 1. Rearrange equation as in math. 2. The units that remain in the final answer are combined as the derived unit. 2 Common SI Units Quantity Length Mass Time Amount of substance Volume Written Unit Meter gram, kg Second Mole Unit Symbol m g, kg s mol Liter L Solving for Density The formula for density can be rearranged to solve for for the required unit. Density (g/mL) Mass (g) Volume (mL) D = m/v 4 Practice Problem #1 A rock has a mass of 0.35 kg and a volume of 500 mL. What is its density in g/L? (Show your work) 5 Practice Problem #1 A rock has a mass of 0.35 kg and a volume of 500 mL. What is its density in g/L? (Show your work) 6 Practice Problem #2 Convert 5.00 g/cm3 into kg/m3 7 Practice Problem #2 Convert 5.00 g/cm3 into kg/m3 𝑔 1𝑘𝑔 100𝑐𝑚 100𝑐𝑚 100𝑐𝑚 𝑘𝑔 5.00 × × × × = 5000 3 3 𝑐𝑚 1000𝑔 1𝑚 1𝑚 1𝑚 𝑚 OR 𝑔 1𝑘𝑔 1 × 106 𝑐𝑚3 𝑘𝑔 5.00 × × = 5000 3 3 3 𝑐𝑚 1000𝑔 1𝑚 𝑚 8 Practice Problem #3 Convert a velocity of 40.0 miles per hour to kilometers per hour. (1 mile = 5280 ft, 1 ft = 12 in, 1 in = 2.54 cm) 9 Practice Problem #3 Convert a velocity of 40.0 miles per hour to kilometers per hour. (1 mile = 5280 ft, 1 ft = 12 in, 1 in = 2.54 cm) 𝑚𝑖 5280𝑓𝑡 12 𝑖𝑛 2.54𝑐𝑚 1𝑚 1𝑘𝑚 𝑘𝑚 40.0 × × × × × = 64.37 ℎ𝑟 1𝑚𝑖 1𝑓𝑡 1𝑖𝑛 100𝑐𝑚 1000𝑚 ℎ𝑟 10 How do we write our answers? • We use what is known as significant figures • A significant figure • is a measured or meaningful digit. • is the total number of digits needed to write a given value without losing certainty Purpose of Significant Figures • We need use them because: • Each measurement may have different accuracy • Numbers we record using different measurements have different accuracy Significant Figure Rules Example Number: 0.012304560 Significant Figure Rules Example Number: 0.012304560 Practice Problem #4 • Underline the significant figures in the following examples: • a) 5 600 • • e) 0.002 • • i) 0.00700 b) 8 060 c) 3.090 d) 0.0112 f) 4.007 g) 0.0040 h) 0.0390 j) 8 000 k) 0.06 l) 120.0 15 Practice Problem #4 • Underline the significant figures in the following examples: • a) 5 600 • • e) 0.002 • • i) 0.00700 b) 8 060 c) 3.090 d) 0.0112 f) 4.007 g) 0.0040 h) 0.0390 j) 8 000 k) 0.06 l) 120.0 16 Practice Problem #5 •Round the number 840.556 and write it with… a) five sig figs = ________________ b) four sig figs = ________________ c) two sig figs = ________________ d) one sig fig = _________________ 17 Practice Problem #5 •Round the number 840.556 and write it with… a) five sig figs = 840.56 b) four sig figs = 840.6 c) two sig figs = 840 d) one sig fig = 800 18