Unit 5 · Topic 07 · Fractions and Decimals
Kabir wrote 3/4 on one side of the board and 0.75 on the other, insisting they were two totally different numbers.
Anaya divided 3 by 4 on paper and got exactly 0.75, no remainder, no argument.
Fractions and decimals turned out to be two different costumes for the exact same number.
"A fraction is really just a division waiting to happen," said Ms. Rao. "3/4 means 3 divided by 4. Do that division, and you get its decimal form." Kabir did the long division: 3.00 ÷ 4 = 0.75. "So 3/4 = 0.75, exactly."
"Fractions with denominators that are powers of 10 convert instantly," she added. "7/10 = 0.7. 23/100 = 0.23. 9/1000 = 0.009 — the denominator literally tells you which decimal place to stop at." Anaya noticed a shortcut: if a fraction's denominator isn't already a power of 10, she could sometimes convert it into an EQUIVALENT fraction that is. 3/4 x 25/25 = 75/100 = 0.75 — matching the division answer exactly.
"Can we go the other way, decimal to fraction?" asked Kabir. Ms. Rao wrote 0.6. "Read it as 'six tenths' — that's 6/10, which simplifies to 3/5." She tried 0.25: "twenty-five hundredths" = 25/100 = 1/4 simplified. "The number of decimal digits tells you the denominator: one digit means tenths, two digits means hundredths."
"Some fractions," Ms. Rao warned, "like 1/3, don't convert to a neat, finishing decimal at all — 1÷3 = 0.333... repeating forever. Those are called recurring decimals, and you'll study them more later. For now, focus on fractions whose denominators are, or can become, powers of 10 — those always convert cleanly both ways."
A fraction converts to a decimal by dividing the numerator by the denominator.
Fractions with denominator 10, 100, 1000 (powers of 10) convert instantly: the number of zeros tells you the decimal place.
A decimal converts to a fraction by reading its last digit's place value as the denominator, then simplifying.
Some fractions (like 1/3) produce repeating decimals that never terminate — a topic for later study.
Convert 7/20 to a decimal by first finding an equivalent fraction with denominator 100.
Convert 0.45 to a fraction in simplest form.
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