Chemistry · Some Basic Concepts Of Chemistry · NEET
You ADD the powers. This confuses many students because the word is 'multiply', so they think everything gets multiplied. But the power of 10 is an exponent, and the rule for exponents is 10^a x 10^b = 10^(a+b). So you multiply the front digit terms, but you ADD the exponents. Example: (2 x 10^3) x (3 x 10^4) = (2 x 3) x 10^(3+4) = 6 x 10^7.
Just add the exponents, keeping their signs: (-3) + (5) = +2. So 10^-3 x 10^5 = 10^2. Adding a negative power is like subtracting. Be careful with signs on the number line: (-3) + 5 = 2, not 8. A full example: (4 x 10^-3) x (2 x 10^5) = 8 x 10^2 = 800.
Yes. For division you divide the front digit terms and SUBTRACT the exponents: 10^a / 10^b = 10^(a-b). Example: (6 x 10^8) / (2 x 10^3) = (6/2) x 10^(8-3) = 3 x 10^5. Watch the order: top exponent minus bottom exponent.
Subtracting a negative power flips it to a plus. Example: (9 x 10^4) / (3 x 10^-2) = (9/3) x 10^(4-(-2)) = 3 x 10^(4+2) = 3 x 10^6. So a negative power in the denominator makes the final power larger. Rule: minus a minus becomes plus.
It is not wrong, but it is not proper scientific notation yet. The front number N must be between 1 and just under 10. Fix 12 x 10^5: move the decimal one place left, add 1 to the power -> 1.2 x 10^6. Fix 0.6 x 10^3: move the decimal one place right, subtract 1 from the power -> 6 x 10^2. Always tidy the final answer.
NEET chemistry numericals (mole concept, Avogadro number 6.022 x 10^23, wavelengths, tiny masses) are full of very large and very small numbers. If you cannot quickly combine powers of 10, you lose easy marks and waste time. Getting the exponent sign wrong is one of the most common silent errors in Physical Chemistry calculations.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Multiply the digit terms (front numbers) and add the exponents of 10. Then adjust the answer so the front number is between 1 and 10. Example: (3 x 10^5)(2 x 10^2) = 6 x 10^7.
Divide the digit terms and subtract the bottom exponent from the top exponent. Example: (8 x 10^6)/(4 x 10^2) = 2 x 10^4.
Yes. NCERT states these two operations follow the same rules as exponential numbers: 10^a x 10^b = 10^(a+b) and 10^a / 10^b = 10^(a-b). The digit terms are simply multiplied or divided.
The digit term N must satisfy 1 <= N < 10. If N is 10 or more, move the decimal left and add 1 to the power. If N is less than 1, move the decimal right and subtract 1 from the power.
No. For addition and subtraction you must first make the exponents equal, then add or subtract only the digit terms (the power stays the same). That is a separate rule covered on the next page.
