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➗ Math · Numbers and Algebra · Lesson 1 of 8 · 5 min

Converting fractions, decimals and percents

🔄 Three-quarters, 0.75 and 75% are the same amount wearing different clothes. The TEAS expects you to switch outfits fast.

💡 Key idea

Divide to get a decimal, then move the decimal point two places right to get a percent (or two places left to go back).

🧠 The idea

A FRACTION, a DECIMAL and a PERCENT are three ways to write one quantity. To turn a fraction into a decimal, divide the top (numerator) by the bottom (denominator): 3/8 = 3 ÷ 8 = 0.375. To turn a decimal into a percent, multiply by 100, which moves the decimal point two places right: 0.375 = 37.5%. Going back, a percent becomes a decimal by dividing by 100 (moving the point two places left): 6% = 0.06, not 0.6. A decimal becomes a fraction by reading its place value: 0.45 is forty-five hundredths, 45/100, which SIMPLIFIES to 9/20 when you divide top and bottom by their greatest common factor, 5. Memorize the common pairs: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 1/5 = 0.2 = 20%, 1/8 = 0.125 = 12.5%, 1/3 = 0.333… = 33 1/3%.

✏️ Worked example

A patient drank 7/20 of a water pitcher. Write that as a decimal and a percent.
Step 1: Fraction to decimal: 7 ÷ 20 = 0.35.
Step 2: Decimal to percent: 0.35 × 100 = 35%.
Step 3: Check by going back: 35% = 35/100; divide top and bottom by 5 to get 7/20. ✓
Answer: 7/20 = 0.35 = 35%.

📌 Takeaways

  • Fraction to decimal: divide numerator by denominator.
  • Decimal to percent: move the point two places right; percent to decimal: two places left.
  • Write a decimal over its place value (10, 100, 1,000), then simplify.

📖 Terms in this lesson

Numerator and denominator: The numerator is the top number of a fraction (parts taken) and the denominator is the bottom number (equal parts in the whole); for example, in 3/4, 3 is the numerator and 4 is the denominator.

Percent: A part per hundred; for example, 25% = 25/100 = 0.25.

✅ Check yourself

Question 1 of 3

What is 5/8 written as a decimal?

  1. 0.0625
  2. 1.6
  3. 0.58
  4. 0.625
Show the answer and rationale

Answer: D

Divide 5 ÷ 8 = 0.625. Writing 0.58 just places the digits side by side, 1.6 comes from dividing 8 ÷ 5 (the fraction upside down), and 0.0625 puts the decimal point one place too far left.

Question 2 of 3

Which decimal is equal to 4%?

  1. 0.4
  2. 4.0
  3. 0.04
  4. 0.004
Show the answer and rationale

Answer: C

Percent to decimal means dividing by 100, moving the point two places left: 4% = 0.04. The value 0.4 moves the point only one place (that is 40%), and 0.004 moves it three places (0.4%).

Question 3 of 3

What is 0.65 written as a fraction in lowest terms?

  1. 13/200
  2. 65/10
  3. 13/20
  4. 13/25
Show the answer and rationale

Answer: C

0.65 is sixty-five hundredths, 65/100. Dividing top and bottom by 5 gives 13/20. The fraction 13/25 divides the top by 5 but the bottom by 4, 65/10 uses tenths instead of hundredths (that is 6.5), and 13/200 uses thousandths (that is 0.065).

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