To provide the best experiences, we use technologies like cookies to store and/or access device information. Consenting to these technologies will allow us to process data such as browsing behavior or unique IDs on this site. Not consenting or withdrawing consent, may adversely affect certain features and functions.
The technical storage or access is strictly necessary for the legitimate purpose of enabling the use of a specific service explicitly requested by the subscriber or user, or for the sole purpose of carrying out the transmission of a communication over an electronic communications network.
The technical storage or access is necessary for the legitimate purpose of storing preferences that are not requested by the subscriber or user.
The technical storage or access that is used exclusively for statistical purposes.
The technical storage or access that is used exclusively for anonymous statistical purposes. Without a subpoena, voluntary compliance on the part of your Internet Service Provider, or additional records from a third party, information stored or retrieved for this purpose alone cannot usually be used to identify you.
The technical storage or access is required to create user profiles to send advertising, or to track the user on a website or across several websites for similar marketing purposes.
3 Responses
Here’s the dead-simple rule I tell myself: if the original number is bigger than 1, the exponent is positive; if it’s between 0 and 1, the exponent is negative; and if it’s already between 1 and 10, the exponent is 0. Another way to glue it in your brain: when you slide the decimal left to make that first part land between 1 and 10, the exponent goes up (positive); when you slide it right, the exponent goes down (negative). Quick example: 0.0071 → to get a number between 1 and 10, move the decimal 3 places to the right to make 7.1, and since you moved right, the exponent is negative, so 0.0071 = 7.1 × 10^-3. You can sanity-check by expanding: 10^-3 = 0.001, and 7.1 × 0.001 = 0.0071-ta-da. If you like a mantra: big number, plus sign; tiny number, minus sign.
I used to trip on this too, so here’s the dead-simple rule I keep in my pocket: first make the number look like “something between 1 and 10,” then note which way you slid the decimal. If you moved the decimal to the left (because the original number was big), the exponent is positive; if you moved it to the right (because the original number was tiny), the exponent is negative. Think of the decimal riding an elevator: left means you went “up” in floors, so the exponent goes up (positive); right means you went “down,” so the exponent goes negative. Quick check: 123000 → 1.23 × 10^5 (left 5 places, +5); 0.0045 → 4.5 × 10^-3 (right 3 places, −3). And if the original number is negative, just slap a minus sign in front-this rule for the exponent doesn’t change. A short refresher with examples here if you want a visual: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-scientific-notation/a/scientific-notation-intro.
Quick rule-of-thumb: slide the decimal LEFT to get a number between 1 and 10 → exponent is POSITIVE; slide it RIGHT → exponent is NEGATIVE (like an elevator: up = +, down = −).
Example: 0.0032 → 3.2 × 10^-3 (moved right 3), and 45,000 → 4.5 × 10^4 (moved left 4).