Converting Measurement Units Within a System

Lesson 1 of 1: Measurement and Data

In this lesson:

• Convert metric units using powers of 10
• Convert customary units using reference charts
• Solve real-world problems that require unit conversion

What You Will Learn Today

By the end of this lesson, you should be able to:

1. Convert metric units by multiplying or dividing by powers of 10
2. Convert customary units using non-base-10 factors
3. Decide whether to multiply or divide based on unit size
4. Solve multi-step real-world problems requiring conversions

Same Length Described With Different Units

A table measured as 1.5 m is also 150 cm — same length, different description.

Smaller Units Always Give Bigger Numbers

• Smaller unit → number gets bigger (more units needed)
• Bigger unit → number gets smaller (fewer units needed)
• The quantity stays the same — only the description changes

Multiply or Divide Based on Direction

• Larger unit → smaller unit: multiply (number gets bigger)
• Smaller unit → larger unit: divide (number gets smaller)

Predict the Direction Before You Compute

Which direction does the answer go?

• 4 km to meters → bigger or smaller?
• 500 g to kilograms → bigger or smaller?
• 3 feet to inches → bigger or smaller?

Answers: bigger, smaller, bigger

Metric Conversions Use Powers of Ten

The metric system makes converting straightforward.

• Every metric factor is 10, 100, or 1,000
• This connects directly to digit shifting from place value

Multiplying by 100 shifts digits two places to the left.

Metric Units and Their Conversion Factors

Keep this chart handy for every metric conversion.

Converting Metric Length With Digit Shifting

Example 1: Convert 3 km to meters

Example 2: Convert 4.5 m to centimeters

Larger → smaller = multiply. The decimal shifts right.

Converting Five Centimeters to Meters

Convert 5 cm to meters

• Centimeters → meters is smaller → larger, so divide
• The factor is 100

Yes, 0.05 m is a real measurement — it equals 5 cm!

Converting Metric Mass and Capacity Units

Example 3: Convert 0.8 kg to grams

Example 4: Convert 2,500 mL to liters

Same rule, same digit shifting — different units.

Your Turn to Try Metric Conversions

Try these conversions:

1. Convert 6.2 m to centimeters

2. Convert 4,000 g to kilograms

Decide the direction and factor, then compute.

Four More Metric Conversions to Practice

Convert each measurement:

1. 7.5 km = ? m
2. 350 cm = ? m
3. 2.4 L = ? mL
4. 6,500 g = ? kg

Pause and try all four before advancing.

Answers for the Metric Practice Problems

1. 7.5 km = 7,500 m (× 1,000)
2. 350 cm = 3.5 m (÷ 100)
3. 2.4 L = 2,400 mL (× 1,000)
4. 6,500 g = 6.5 kg (÷ 1,000)

Check: did each answer go the right direction?

Customary Units Have Non-Base-Ten Factors

The customary system uses factors like 12, 16, and 5,280.

• The logic is identical: multiply for smaller, divide for larger
• The arithmetic is harder: use reference charts to look up factors

You do not need to memorize every factor!

Customary Conversion Factors by Measurement Type

• Length: 1 ft = 12 in, 1 yd = 3 ft
• Mass: 1 lb = 16 oz, 1 T = 2,000 lb
• Capacity: 1 c = 8 fl oz, 1 pt = 2 c, 1 gal = 4 qt

Examples of Converting Customary Units

Example 1: Convert 4 feet to inches

Example 2: Convert 10 quarts to gallons

Look up the factor, decide the direction, then compute.

Two Steps to Convert Yards to Inches

Convert 3 yards to inches

Step 1: Yards to feet

Step 2: Feet to inches

Or directly: inches.

Your Turn to Try Customary Conversions

Try these using the reference chart:

1. Convert 7 pounds to ounces

2. Convert 6 gallons to quarts

Look up the factor, decide multiply or divide, then compute.

Why Metric Conversion Is So Much Easier

• Metric: 4.5 m × 100 = 450 cm (just shift the decimal)
• Customary: 4 ft × 12 = 48 in (multiply by 12)

The metric system was designed for easy conversion using powers of 10.

Conversions Are a Tool for Solving Problems

Conversion is a tool, not the final answer:

1. Read the problem and identify the units
2. Check — are the units the same?
3. If not, convert first, then compute
4. Check — does the answer make sense?

Solving the Hiking Trail Distance Problem

A trail is 3 km long. Jaylen walked 1,800 m. How far to go?

Step 1: Convert 3 km to meters

Step 2: Subtract

Checking if Marcus Can Ride the Coaster

Marcus is 4 ft 8 in tall. The ride needs 54 inches minimum.

Step 1: Convert feet to inches: in

Step 2: Add extra inches: in

Step 3: Compare: 56 > 54 — Yes, Marcus can ride!

Your Turn to Solve the Beaker Problem

An experiment needs 1.5 L of water. The beaker holds 400 mL.

How many full beakers are needed?

Hint: convert first, then divide, then think about rounding.

Three Real-World Problems to Practice Solving

1. A recipe needs 2 cups of milk. You have 1 pint. Enough?
2. A ribbon is 3 m. You cut 85 cm. How many cm remain?
3. A box weighs 5 lb. Limit is 72 oz. Under the limit?

Pause and try all three before advancing.

Answers for the Real-World Practice Problems

1. 1 pint = 2 cups — Yes, exactly enough
2. 3 m = 300 cm; 300 − 85 = 215 cm remain
3. 5 lb = 80 oz; 80 > 72 — No, over the limit

Did you convert before computing each time?

Key Takeaways and Common Mistake Warnings

✓ Conversion changes the description, not the quantity
✓ Smaller unit → bigger number; bigger unit → smaller number
✓ Metric uses powers of 10; customary uses reference charts

Watch out: Always predict the direction before computing
Watch out: Convert to the same unit before adding or comparing

Preparing for Ratios and Unit Rates

• Practice converting with mixed metric and customary problems
• Apply conversions in science experiments and recipe scaling
• Build toward ratios and unit rates in Grade 6

Keep your reference charts handy — the skill is in the reasoning!