Scientific notation writes a number as a coefficient from 1 up to 10 multiplied by a power of ten. The value 4,500,000 is 4.5 × 10⁶, while 0.00045 is 4.5 × 10⁻⁴. A positive exponent moves the decimal right when expanding; a negative exponent moves it left. The exponent changes magnitude, not the decimal digits.
How do I convert to scientific notation?
To write 0.000672, move the decimal four places right to obtain 6.72, so the exponent is −4: 6.72 × 10⁻⁴. Expand 3.04 × 10⁵ by moving the decimal five places right: 304,000. The zero in 3.04 matters; writing 3.4 × 10⁵ would instead mean 340,000 and loses the stated precision.
Which direction does a scientific-notation exponent move the decimal?
Move the decimal until one non-zero digit sits to its left. Count places moved: moving left in the original large number gives a positive exponent; moving right in the original small decimal gives a negative exponent. The scientific-notation calculator can check an entry, but count the movement yourself as a sign check.
How do I write a small number with a negative exponent?
The coefficient must be at least 1 and less than 10 in normalized decimal scientific notation. Multiplying by 10³ moves a decimal three places right; multiplying by 10⁻³ moves it three places left. Keep significant figures in the coefficient: 1.200 × 10³ communicates four significant digits, whereas 1.2 × 10³ communicates two.
Why do zeros matter in scientific notation?
Do not reverse the sign because the decimal moved right while normalizing a small number. Do not read 10⁻⁴ as a negative number; it is a positive factor of 0.0001. Do not drop zeros that are significant. Do not add exponents when adding ordinary decimal quantities; exponent rules differ between multiplication and addition.
When does scientific notation need a unit and uncertainty?
Scientific notation expresses magnitude and stated precision; it does not validate a measurement, select significant-figure rules for a discipline, or replace units. Keep the physical unit attached, such as 6.72 × 10⁻⁴ m. Laboratory reports and regulated calculations can impose their own rounding and uncertainty conventions.
Source for the external fact
NIST explains that 3.3 × 10⁷ Hz and 9.52 × 10⁻³ g are valid scientific expressions and discusses significant zeros in its SI style guide.
Related calculators
Check a coefficient and exponent with the scientific-notation tool, convert a measurement unit in the length converter, and retain percent scale with the percentage calculator.