Visual Models:

• Area Model: A square or rectangle divided into equal parts (shaded parts show the fraction/decimal)
• Number Line: Points between 0 and 1 represent fractions and decimals
• Base-10 Blocks: Flats, rods, and units represent ones, tenths, and hundredths

Example:

A grid with 100 squares where 25 are shaded shows:

$\frac{25}{100}$ = 0.25 = twenty-five hundredths

When to use: When the denominator is 10, 100, or 1000

1Look at the denominator

• If denominator = 10 → tenths place → 1 decimal digit
• If denominator = 100 → hundredths place → 2 decimal digits
• If denominator = 1000 → thousandths place → 3 decimal digits

2Write the numerator with the decimal point in the correct place

Examples:

$\frac{7}{10}$ = 0.7 (seven tenths)

$\frac{37}{100}$ = 0.37 (thirty-seven hundredths)

$\frac{5}{1000}$ = 0.005 (five thousandths)

$\frac{603}{1000}$ = 0.603 (six hundred three thousandths)

When to use: When the denominator is NOT 10, 100, or 1000

1Divide the numerator by the denominator

Example 1: Convert $\frac{3}{4}$ to a decimal

$3 ÷ 4 = 0.75$

Example 2: Convert $\frac{1}{2}$ to a decimal

$1 ÷ 2 = 0.5$

Example 3: Convert $\frac{5}{8}$ to a decimal

$5 ÷ 8 = 0.625$

When to use: When you can easily convert the denominator to 10, 100, or 1000

1Find what to multiply the denominator by to get 10, 100, or 1000

2Multiply both numerator and denominator by that number

3Write as a decimal using Method 1

Example 1: Convert $\frac{1}{5}$ to a decimal

$\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10} = 0.2$

Example 2: Convert $\frac{3}{20}$ to a decimal

$\frac{3}{20} = \frac{3 \times 5}{20 \times 5} = \frac{15}{100} = 0.15$

Step-by-Step Process:

1Write down the whole number

2Convert the fraction part to a decimal (use methods from Topic 2)

3Add the whole number and the decimal together

Example 1: Convert $1\frac{88}{100}$ to a decimal

Step 1: Whole number = 1
Step 2: $\frac{88}{100} = 0.88$
Step 3: $1 + 0.88 = 1.88$

Example 2: Convert $3\frac{1}{4}$ to a decimal

Step 1: Whole number = 3
Step 2: $\frac{1}{4} = 1 ÷ 4 = 0.25$
Step 3: $3 + 0.25 = 3.25$

Example 3: Convert $9\frac{5}{10}$ to a decimal

Step 1: Whole number = 9
Step 2: $\frac{5}{10} = 0.5$
Step 3: $9 + 0.5 = 9.5$

Example 4: Convert $5\frac{3}{8}$ to a decimal

Step 1: Whole number = 5
Step 2: $\frac{3}{8} = 3 ÷ 8 = 0.375$
Step 3: $5 + 0.375 = 5.375$

The numbers after the decimal = Numerator (top)

The place value = Denominator (bottom)

Example 1: Convert 0.7 to a fraction

Read: "seven tenths"
Write: $\frac{7}{10}$
✅ Already simplified!

Example 2: Convert 0.45 to a fraction

Read: "forty-five hundredths"
Write: $\frac{45}{100}$
Simplify: $\frac{45 ÷ 5}{100 ÷ 5} = \frac{9}{20}$

Example 3: Convert 0.125 to a fraction

Read: "one hundred twenty-five thousandths"
Write: $\frac{125}{1000}$
Simplify: $\frac{125 ÷ 125}{1000 ÷ 125} = \frac{1}{8}$

Example 4: Convert 0.04 to a fraction

Read: "four hundredths"
Write: $\frac{4}{100}$
Simplify: $\frac{4 ÷ 4}{100 ÷ 4} = \frac{1}{25}$

Step-by-Step Process:

1The whole number part stays the same

Everything before the decimal point = whole number

2Convert the decimal part to a fraction

Use the same method as Topic 4

3Simplify the fraction (if possible)

Example 1: Convert 1.37 to a mixed number

Step 1: Whole number = 1
Step 2: 0.37 = "thirty-seven hundredths" = $\frac{37}{100}$
Step 3: Cannot simplify
Answer: $1\frac{37}{100}$

Example 2: Convert 3.5 to a mixed number

Step 1: Whole number = 3
Step 2: 0.5 = "five tenths" = $\frac{5}{10}$
Step 3: Simplify: $\frac{5}{10} = \frac{1}{2}$
Answer: $3\frac{1}{2}$

Example 3: Convert 2.75 to a mixed number

Step 1: Whole number = 2
Step 2: 0.75 = "seventy-five hundredths" = $\frac{75}{100}$
Step 3: Simplify: $\frac{75}{100} = \frac{3}{4}$ (divide by 25)
Answer: $2\frac{3}{4}$

Example 4: Convert 5.008 to a mixed number

Step 1: Whole number = 5
Step 2: 0.008 = "eight thousandths" = $\frac{8}{1000}$
Step 3: Simplify: $\frac{8}{1000} = \frac{1}{125}$ (divide by 8)
Answer: $5\frac{1}{125}$