COUNT THE DECIMAL PLACES!

Total decimal places in factors = Decimal places in product

Step 1: Ignore the decimal points and multiply as whole numbers

Step 2: Count total decimal places in BOTH factors

Step 3: Place decimal point in product (count from right)

Step 4: Add zeros to the left if needed

Problem: 3.6 × 4

Problem: 2.5 × 3.4

Problem: 0.05 × 0.4

Steps:

1. Round each decimal to nearest whole number

2. Multiply the rounded numbers

Example: Estimate 4.8 × 6.2

Place decimal point in quotient DIRECTLY ABOVE the decimal in dividend

Step 1: Divide as normal (ignore decimal)

Step 2: When you bring down the digit after the decimal, place decimal in quotient

Step 3: Continue dividing

Step 4: Add zeros to dividend if needed

Example: 47.5 ÷ 5

Make the divisor a WHOLE NUMBER first!

Multiply both by power of 10

Step 1: Move decimal in divisor to the right until it's a whole number

Step 2: Move decimal in dividend the SAME number of places

Step 3: Divide as usual

Example: 15.75 ÷ 3.5

Example 2: 4.68 ÷ 0.6

10¹ = 10 (1 zero)

10² = 100 (2 zeros)

10³ = 1,000 (3 zeros)

10⁴ = 10,000 (4 zeros)

Move decimal point RIGHT

Number of places = Number of zeros

Move decimal point LEFT

Number of places = Number of zeros

Example: Estimate 47.3 ÷ 6.8

Key Rules:

• Multiplying by number > 1: Product is GREATER

• Multiplying by number < 1: Product is SMALLER

Example: Compare 5.2 × 0.8 and 5.2

Key Rules:

• Dividing by number > 1: Quotient is SMALLER

• Dividing by number < 1: Quotient is GREATER

Example: Compare 8.4 ÷ 0.5 and 8.4

Problem: Gas costs $3.45 per gallon. How much does 8.5 gallons cost?

Problem: A 12.6-meter rope is cut into 6 equal pieces. How long is each piece?

Problem: Apples cost $2.40 per pound. Sarah buys 3.5 pounds and pays with a $20 bill. How much change does she receive?

✓ Multiply: Count total decimal places in BOTH numbers

✓ Divide by whole: Decimal goes straight up in quotient

✓ Divide by decimal: Make divisor whole FIRST

✓ Powers of 10: Count zeros to know how far to move

✓ Multiply by 10: Decimal moves RIGHT

✓ Divide by 10: Decimal moves LEFT

✓ Estimate first to check reasonableness

✓ Add zeros as needed (left for multiply, right for divide)

✓ Multiply by < 1: Answer is smaller

✓ Divide by < 1: Answer is larger

Multiply Decimals:

"Count the places, don't forget your traces!"

Divide by Whole:

"Decimal up, straight as can be!"

Divide by Decimal:

"Move the decimal, make it whole, then you're in control!"

Powers of 10:

Multiply: "Multiply means magnify - decimal moves RIGHT!"

Divide: "Divide means reduce - decimal moves LEFT!"

Inequalities:

"Less than 1, smaller you'll find!"

"More than 1, answer bigger in kind!"