Writing in Scientific Notation

Algebra 1 · Axiom Academy

LESSON Writing in Scientific Notation Move the decimal, count the hops — and watch that hop-count become the power of 10. A number is in scientific notation when it is written as a coefficient times a power of 10 . The catch is the coefficient: it must land in a strict window — at least 1, but below 10 — so there is exactly one non-zero digit in front of the decimal point. The coefficient a sits in the window 1 |a| < 10 The exponent n is an integer (the magnitude) Is the coefficient in the window? 2. Large Numbers → Positive Exponent For a big number, picture the decimal point at the far right. Hop it to the left until only one non-zero digit remains in front of it. The number of hops is your exponent — and because the number was big, that exponent is positive . Step 1. Put the decimal at the end: 45000. Step 2. Hop it left until one digit remains in front: 4.5000 — that took 4 hops. Step 3. Drop the trailing zeros; the 4 hops become the exponent. 3. Small Numbers → Negative Exponent For a tiny decimal, start at the decimal point and hop it to the right , past the leading zeros, until it sits just after the first non-zero digit. The number of hops is the magnitude of the exponent — and because the number was small, that exponent is negative . Step 1. The decimal starts here: 0.00067. Step 2. Hop it right until it sits after the first non-zero digit: 6.7 — that took 4 hops. Step 3. The 4 hops to the right become the negative exponent.

This is the written version of the interactive lesson above. See the full Algebra 1 course.