Measure It

A unit is a “one” that everybody agrees on. Measuring means counting how many of those ones fit.

Long ago, a foot was somebody’s real foot. But everyone’s feet are different, so people agreed on one official foot.

The same ribbon, two ways

Big unit → small number. Small unit → big number.

• 1 m= 100 cm
• 1 ft= 12 in
• 1 hour= 60 minutes

Every conversion in this course comes back to that one idea.

How many units are there?

Over history, thousands. A cubit was your elbow to your fingertip. A stone was 14 pounds.

Today the world uses two families.

• metricalmost every country, and every scientist
• USfeet, pounds, gallons — what you see in American stores

Measures	Metric	US
Length	mm, cm, m, km	in, ft, yd, mi
Weight	mg, g, kg	oz, lb, ton
Liquid	mL, L	cup, pt, qt, gal
Time	seconds, minutes, hours — the same everywhere
Heat	°C	°F

Fun fact: the whole metric system is built from just 7 base units. You already use three of them: the meter, the kilogram and the second.

Pick the right size first

Before you convert anything, ask: is it the size of an ant, a hand, a room, or a road trip?

• antmillimeters
• handcentimeters or inches
• roommeters or feet
• road tripkilometers or miles

In metric, every step is ×10. So converting is just sliding the decimal point.

Fact	Think
1 cm = 10 mm	a fingernail is about 1 cm wide
1 m = 100 cm	one big step
1 m = 1,000 mm	a thousand tiny ticks
1 km = 1,000 m	about a 12-minute walk

The names tell you the size

• kilo-a thousand (1 kilometer = 1,000 meters)
• centi-a hundredth — like a cent is 1/100 of a dollar
• milli-a thousandth (a millipede was named for “a thousand feet”)

King Henry’s staircase

King Henry Died By Drinking Chocolate Milk. Each step is ×10.

Going down the stairs to a smaller unit, the point moves right. One step for each stair.

Good news: weight and liquid use the same prefixes you learned yesterday.

Fact	Think
1 kg = 1,000 g	a bag of sugar
1 g = 1,000 mg	a paperclip is about 1 g
1 L = 1,000 mL	a big water bottle

• gramshow heavy something is
• litershow much space a liquid takes up

The neat part

1 mL of water weighs exactly 1 gram. So 1 liter of water weighs 1 kilogram.

That was on purpose. The people who invented metric built it around water.

US units don’t go by tens. You have to know each step.

Fact	Think
1 ft = 12 in	a school ruler
1 yd = 3 ft	a baseball bat, about
1 yd = 36 in	3 rulers in a row
1 mi = 5,280 ft	about a 20-minute walk
1 mi = 1,760 yd	17½ football fields

Remembering 5,280: say “five tomatoes” — five, two, eight, oh.

The rule is the same as metric

• to smalleryou need more of them → multiply
• to biggeryou need fewer of them → divide

16 ounces make a pound. 2,000 pounds make a ton.

Fact	Think
1 oz	a slice of bread
1 lb = 16 oz	a loaf of bread
1 ton = 2,000 lb	a small car

Quick way to times by 16: double it four times. 3 → 6 → 12 → 24 → 48.

An old saying: “A pint’s a pound the world around.” A pint of water weighs about a pound.

US liquids mostly go up in twos: 2 cups make a pint, 2 pints make a quart.

Then one jump of four: 4 quarts make a gallon.

Kitchen-small

• 1 tbsp= 3 tsp (tablespoon is the big spoon)
• 1 fl oz= 2 tbsp
• 1 cup= 8 fl oz

Time is the same in every country.

• 1 min= 60 seconds
• 1 hour= 60 minutes
• 1 day= 24 hours
• 1 week= 7 days

Mixed units

“5 ft 3 in” means 5 feet and 3 inches.

To make it all inches: turn the feet into inches, then add the extra.

Going back: how many whole 12s fit, and what is left over?

63 ÷ 12	5 twelves is 60	5 ft
63 − 60	left over	3 in

Same thing with time: 135 minutes = 2 hours (120) and 15 minutes left.

Metric and US units don’t line up neatly. So learn a few close friends.

Fact	Think
1 in = 2.54 cm	exact — about 2½ cm
1 m ≈ 1.1 yd	a yard plus a hand-width
1 m ≈ 3.3 ft	a bit more than 3 feet
1 mi ≈ 1.6 km	a mile is the longer one
1 kg ≈ 2.2 lb	a kilo is more than double
1 L ≈ 1.06 qt	a liter is a little more than a quart
1 gal ≈ 3.8 L	almost 4 liters
1 oz ≈ 28 g	a slice of bread

The ≈ sign means “about”. Close answers count today.

Two thermometers, same heat. Learn four anchors first.

A quick guess

Double the °C and add 30. 20°C → 40 + 30 = about 70°F. (Really 68.)

Exactly: °C to °F

Divide by 5, times by 9, add 32.

25 ÷ 5	divide by 5	5
5 × 9	times 9	45
45 + 32	add 32	77°F

Back again: °F to °C

Do it all backwards: take away 32, divide by 9, times by 5.

50 − 32	take away 32	18
18 ÷ 9	divide by 9	2
2 × 5	times 5	10°C

Why the 32? Water freezes at 32 on the °F scale, but at 0 on the °C scale. °F just starts counting lower.

Today anything can come up. Ask these four questions every time.

1	What am I measuring?length, weight, liquid, time or heat	cups → liquid
2	Same family, or crossing the bridge?metric to metric, US to US, or one to the other	gal → qt: both US
3	Getting smaller or bigger?smaller unit → multiply; bigger → divide	qt is smaller: ×4
4	Does it make sense?more of a small unit, fewer of a big one	3 gal = 12 qt ✓

There is no ladder hint today, just like the test. Use the cheat sheet if you get stuck.

Fifteen questions. No ladders, no hints, no second tries.

• 12+you pass, and you get the Graduate badge
• 15Perfect Paper
• againretake it as often as you like — your best score counts

If a question stalls, ask: is the new unit smaller or bigger?