The Metric System Jumps
Converting between metric units is all about multiplying or dividing by powers of 10. Remember the mnemonic: King Henry Died By Drinking Chocolate Milk.
Metric Conversion Ladder
Example: Large to Small
Convert $4.5$ kilometers (km) to centimeters (cm).
Step 1: Locate 'kilo' and 'centi' on the ladder.
Step 2: Count the jumps moving from km to cm.
5 jumps to the RIGHT → Multiply by $10$, $5$ times (or $\times 100,000$).
Calculation:
$$ 4.5 \times 10 \times 10 \times 10 \times 10 \times 10 $$ $$ = 4.5 \times 10^5 $$ $$ = 4.5 \times 100,000 $$ $$ = 450,000 \text{ cm} $$Example: Small to Large
Convert $350$ milliliters (mL) to Liters (L).
Step 1: Locate 'milli' and 'Base (L)' on the ladder.
Step 2: Count the jumps moving from mL to L.
3 jumps to the LEFT → Divide by $10$, $3$ times (or $\div 1,000$).
Calculation:
$$ 350 \div 10 \div 10 \div 10 $$ $$ = 350 \div 10^3 $$ $$ = 350 \div 1,000 $$ $$ = 0.35 \text{ L} $$Knowledge Check 1
Marking Schedule:
Q1 (Large to Small): kg to g is 3 jumps RIGHT ($\times 1000$).
$$ 3.2 \times 1000 = 3200 \text{ g} $$Q2 (Small to Large): mm to m (Base) is 3 jumps LEFT ($\div 1000$).
$$ 450 \div 1000 = 0.45 \text{ m} $$Navigating Time Units
Time units do not follow the metric base-10 rule. You must know the specific constraints: $60$ seconds in a minute, $60$ minutes in an hour, and $24$ hours in a day.
Example: Large to Small
Convert exactly 1 week into seconds.
Moving from larger units (weeks) to smaller units (seconds), we multiply at each step.
- 1 week = $7$ days
- $7 \times 24 = 168$ hours
- $168 \times 60 = 10,080$ minutes
- $10,080 \times 60 = 604,800$ seconds
Example: Small to Large
Convert $540$ minutes into hours.
Moving from smaller units (minutes) to larger units (hours), we divide by the conversion factor ($60$).
Calculation:
$$ 540 \div 60 $$ $$ = 9 \text{ hours} $$Knowledge Check 2
Marking Schedule:
Q1 (Large to Small): hr → min ($\times 60$) → sec ($\times 60$).
$$ 2.5 \times 60 \times 60 = 9000 \text{ s} $$Q2 (Small to Large): sec → min ($\div 60$) → hr ($\div 60$).
$$ 43,200 \div 60 \div 60 = 12 \text{ hours} $$Derived Rates (Mass per Volume / Distance per Time)
Derived rates are composed of two distinct units. To convert them, you must logically analyze how the numerator and denominator change.
Example: Large Rate to Small Rate
"Convert a density of $14.5 \text{ kg}/m^3$ to $\text{g}/cm^3$."
Since $1 \text{ kg} = 1000 \text{ g}$, the top value must be multiplied by $1000$. $$ 14.5 \times 1000 = 14,500 \text{ g per cubic meter} $$
$1 \text{ meter} = 100 \text{ cm}$. Therefore, $1 \text{ m}^3 = (100 \text{ cm})^3 = 1,000,000 \text{ cm}^3$. Since cubic meters are in the denominator, the overall value must be divided by $1,000,000$. $$ 14,500 \div 1,000,000 = 0.0145 \text{ g/cm}^3 $$
Example: Speed L$\to$S and S$\to$L
"Convert $90 \text{ km/h}$ into $\text{m/s}$."
$1 \text{ km} = 1000 \text{ m}$. We must multiply by $1000$. $$ 90 \times 1000 = 90,000 \text{ m per hour} $$
$1 \text{ hour} = 3600 \text{ seconds}$. We must divide by $3600$. $$ 90,000 \div 3600 = 25 \text{ m/s} $$
*Shortcut check: to go m/s to km/h, multiply by 3.6. To go km/h to m/s, divide by 3.6.
Knowledge Check 3
Marking Schedule:
Q1 (Large Rate to Small Rate): km→m ($\times 1000$), hr→s ($\div 3600$ overall).
$$ 72 \times 1000 = 72,000 \text{ m/h} $$ $$ 72,000 \div 3600 = 20 \text{ m/s} $$Q2 (Small Rate to Large Rate): m→km ($\div 1000$), s→hr ($\times 3600$ overall).
$$ 10 \div 1000 = 0.01 \text{ km/s} $$ $$ 0.01 \times 3600 = 36 \text{ km/h} $$Synthesis Task
Combine all skills. Complete 18 mixed-context questions. You have 2 attempts.
Section A: Basic Length and Mass Jumps
Section B: Time Conversions
Section C: Derived Rate Conversions
Section D: Rich Context and Harder Multi-Step Tasks
Student Mastery Report
Take a screenshot of this report to submit to Mr. Shen.