Digital SAT Math: Decimals & Fractions

Part 1: Decimals & Another Way to Write the Same Number

Can you answer these mentally?[cite: 1]

• Write 1/2 as a decimal.[cite: 1]
• Write 0.75 as a fraction.[cite: 1]
• Which is greater? 0.8 or 0.78[cite: 1]
• Round 6.47 to the nearest tenth.[cite: 1]
• Which is greater? 0.49 or 1/2[cite: 1]

If these feel easy, skim this spread and spend more time on the SAT Practice section.[cite: 1]

📋 Essential Rules

Decimals are simply another way to write fractions. Nothing new. Nothing scary[cite: 1].

For example: $1/2 = 0.5$, $3/4 = 0.75$, $1/5 = 0.2$. The number hasn’t changed. Only the notation has[cite: 1].

📊 Common Decimal Equivalents

These values appear so often that recognizing them instantly can save valuable time[cite: 1].

Part 2: Converting Fractions and Decimals

📋 Essential Rules

There are only two methods to learn[cite: 1]:

• Method 1 — Fraction $\rightarrow$ Decimal: Divide. That’s all. Example: $3/4 = 3 \div 4$[cite: 1].
• Method 2 — Decimal $\rightarrow$ Fraction: Read the decimal using its place value. Example: 0.25 means 25 hundredths, so write 25/100 and simplify to 1/4[cite: 1].

⚡ Speed Boost

Additional frequent values: $1/8 = 0.125$, $3/8 = 0.375$, $5/8 = 0.625$, $7/8 = 0.875$[cite: 1].

Part 3: Decimal Operations

📋 Essential Rules

Working with decimals is almost the same as working with whole numbers. The only extra step is keeping track of the decimal point[cite: 1].

• Addition & Subtraction: Line up the decimal points. Adding trailing zeros often makes your work clearer[cite: 1].
• Multiplication: Multiply as if the numbers were whole numbers, then place the decimal point in the answer[cite: 1].
• Division: On the SAT, many decimal division questions appear in the calculator section, or are designed for mental math/simple rewrites[cite: 1].

🟡 SAT-Style Practice & Solutions

Selected Practice Highlights

• Question: A student answered 18 out of 20 questions correctly. Write as a fraction, decimal, and percent[cite: 1].
  Answer: 9/10, 0.9, 90%[cite: 1]
• Question: Which number is greatest? A) 0.62, B) 3/5, C) 61%, D) 0.605[cite: 1]
  Answer: A[cite: 1]
• Question: A bottle contains 0.75 L of water. Emma drinks 0.25 L. How much remains?[cite: 1]
  Answer: 0.50 L[cite: 1]

⭐ Checkpoint Challenge

Without a calculator, order these numbers from least to greatest: $0.8, 3/4, 75\%, 0.78, 4/5$[cite: 1].

Solution: Notice that several numbers are already equivalent ($3/4 = 75\% = 0.75$ and $4/5 = 0.8$). Since $0.75 < 0.78 < 0.80$, the complete order is:[cite: 1]

$$3/4 = 75\% < 0.78 < 0.8 = 4/5$$[cite: 1]