What is scientific notation?
Scientific notation is a compact way of writing very big or very small numbers using a power of 10. A number in scientific notation looks like a × 10ⁿ, where a is between 1 and 10 (not including 10) and n is an integer that tells you how many places the decimal point moves.
Why it matters
Scientific notation is how scientists and calculators write distances to stars, sizes of viruses, file sizes, and anything else with lots of zeros. It also turns multiplying and dividing huge numbers into a simple "add the exponents" move, which is why every Grade 8 science and math course uses it.
Worked example
Write 47,000 in scientific notation.
- 1
Put a decimal point AFTER the first non-zero digit so the result is between 1 and 10. 47,000 becomes 4.7000.
In scientific notation, the leading number (called the coefficient) must be at least 1 and less than 10.
- 2
Count how many places the decimal point moved. In 47000., the decimal was implicitly at the far right; in 4.7, it’s after the 4. That’s 4 places to the LEFT.
Moving the decimal LEFT means the exponent on 10 will be POSITIVE — because you’re writing a big number compactly.
- 3
Drop the trailing zeros from 4.7000 (they don’t change the value): the coefficient is 4.7.
The coefficient should be written as compactly as possible — keep only meaningful digits.
- 4
Write the answer as 4.7 × 10⁴.
10⁴ = 10,000, and 4.7 × 10,000 = 47,000. ✓ The exponent 4 matches the number of decimal moves.
Answer
4.7 × 10⁴
Common mistakes
- •Writing a coefficient that’s NOT between 1 and 10 — e.g. writing 47 × 10³ instead of 4.7 × 10⁴. Same value, but not in proper scientific notation.
- •Getting the sign of the exponent backwards. Numbers BIGGER than 1 use a positive exponent; numbers SMALLER than 1 (like 0.00047) use a negative exponent.
- •Counting decimal places wrong — losing track of where the decimal started, especially for numbers with no explicit decimal point.
- •When multiplying numbers in scientific notation: forgetting to ADD the exponents (and to renormalize the coefficient if it ends up ≥ 10).
How Briveli teaches scientific notation
Briveli teaches scientific notation in Grade 8 alongside exponent rules and powers of 10, then applies it in operations (multiplying, dividing, comparing) — the way 8th-grade state tests bundle the topic with the rest of the exponents unit.
Practice Grade 8 math on Briveli