Fractions and decimals are two notations for the same idea. Any fraction with a denominator of 10 or 100 converts directly to a decimal: 7/10 = 0.7 and 23/100 = 0.23. Other fractions can be converted by finding an equivalent fraction with a denominator of 10 or 100 (1/4 = 25/100 = 0.25) or by dividing the numerator by the denominator. Conversely, 0.6 = 6/10 = 3/5. Understanding this equivalence lets students move flexibly between representations, choosing whichever is more convenient for a given problem. Common benchmarks (1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2) should become automatic.
Use 10x10 grids: shading 25 of 100 squares shows both 25/100 and 0.25 simultaneously. Practice converting fractions with denominators of 2, 4, 5, 10, 20, 25, and 100. Place both fractions and decimals on the same number line to reinforce that they name the same points.
You already know how to work with fractions, and you've been introduced to decimals like 0.7 and 0.25. The big idea here is that these are not two different kinds of numbers — they are two different notations for the same quantities. Just as "a dozen" and "12" name the same amount, ½ and 0.5 name the same point on the number line. Switching fluently between the two representations is a skill you'll use constantly.
The bridge between the notations is our decimal system, which is built on powers of 10. The first decimal place is tenths, the second is hundredths. So any fraction with denominator 10 converts directly: 7/10 = 0.7, 3/10 = 0.3. Any fraction with denominator 100 also converts directly: 47/100 = 0.47, 8/100 = 0.08. You can read the decimal aloud as the fraction: 0.47 says "47 hundredths," which writes as 47/100. The decimal notation is just a shorthand for fractions with powers-of-ten denominators.
Fractions with other denominators require a conversion step — and this is where your knowledge of equivalent fractions comes in. To convert ¼ to a decimal, ask: what can I multiply 4 by to get 10 or 100? Since 4 × 25 = 100, multiply both numerator and denominator by 25: 1/4 = 25/100 = 0.25. To convert ⅕, note 5 × 2 = 10, so 1/5 = 2/10 = 0.2. The strategy is always to find a multiplier that turns the denominator into 10 or 100, then read off the decimal. Not every fraction has a nice denominator — 1/3 cannot be written as a fraction with denominator 10 or 100 exactly, which is why it produces a repeating decimal (0.333...) rather than a clean one.
The benchmark conversions — ½ = 0.5, ¼ = 0.25, ¾ = 0.75, ⅕ = 0.2, 1/10 = 0.1 — appear so often in everyday contexts (prices, measurements, percentages) that they're worth making automatic. When a store advertises 25% off, that's ¼ off. When a recipe calls for ¾ cup, you can also measure 0.75 cups. The ability to move fluently between fractions and decimals is not just a school skill — it's the numerical literacy that underlies how quantities are communicated in the real world.