Extreme Units & Standard Form
Standard units are great for everyday objects, but they break down when measuring the distance to stars or the size of a virus. We use Prefixes combined with Scientific Notation (Standard Form) to scale units up or down efficiently.
Instead of writing millions of zeros, link the metric prefix directly to its power of 10:
- Tera (T) $10^{12}$
- Giga (G) $10^9$
- Mega (M) $10^6$
- Kilo (k) $10^3$
- Base Unit $10^0$
- Milli (m) $10^{-3}$
- Micro ($\mu$) $10^{-6}$
- Nano (n) $10^{-9}$
Standard Form requires a number between 1 and 10, multiplied by a power of 10 ($A \times 10^n$).
Example: Convert $45 \text{ MW}$ to watts in standard form.
1. Mega (M) means $10^6$. So, $45 \times 10^6$ W.
2. $45$ is not between 1 and 10! Move the decimal left: $4.5 \times 10^1$.
3. Combine: $(4.5 \times 10^1) \times 10^6 = \mathbf{4.5 \times 10^7 \text{ W}}$.
Quiz 1: Prefix to Exponent Translation
Find the missing exponent or numerical value. Pay close attention to standard form requirements!
Answers:
Fundamentals of Speed & Conversions
Kinematics is the mathematics of motion. At its core, it relies on the relationship between Distance ($d$), Speed ($v$), and Time ($t$).
Cover the letter you want to find with your finger. What is left shows you the formula!
- Want Speed ($v$)? → $d \div t$
- Want Time ($t$)? → $d \div v$
- Want Distance ($d$)? → $v \times t$
To convert between standard speed units, use the magic number 3.6 (because there are 3600 seconds in an hour and 1000 meters in a km).
• km/h to m/s: Divide ($\div$) by 3.6
• m/s to km/h: Multiply ($\times$) by 3.6
Quiz 2: Kinematics & Conversions
Calculate the missing variable. Watch out for mixed units!
Answers:
The Average Speed Trap
When a journey has multiple parts (e.g., driving fast on a highway, then slow in the city), finding the overall average speed is not as simple as finding the middle of the two speeds.
You must strictly use this formula:
Trip: Drive $120 \text{ km}$ at $60 \text{ km/h}$. Then drive $120 \text{ km}$ at $40 \text{ km/h}$. What is the average speed?
Wrong Way: $(60+40) \div 2 = 50 \text{ km/h}$. (NO!)
Right Way:
Total Dist = $120 + 120 = \mathbf{240 \text{ km}}$.
Total Time = $(120\div60) + (120\div40) = 2\text{h} + 3\text{h} = \mathbf{5 \text{ hours}}$.
Avg Speed = $240 \div 5 = \mathbf{48 \text{ km/h}}$.
Quiz 3: Multi-Part Journeys
Calculate carefully. Find total distance and total time first.
Answers:
Relative Kinematics (Meet & Chase)
When two objects are moving at the same time, we calculate their Relative Speed. We pretend one object is completely stationary, and the other is doing all the moving.
Meeting (Opposite Directions)
Rule: ADD the speeds.
Chasing (Same Direction)
Rule: SUBTRACT the speeds.
Quiz 4: Meet & Chase Logistics
Find the relative speed first, then calculate time or distance.
Answers:
Unit Complete!
You have completed all modules for Measurement Week 2. Please copy your final report and submit it to your teacher.