Summary: Scientific Notation
Key Concepts
- Summary of Exponent Properties
- If a,b are real numbers and m,n are integers, then
Product PropertyPower PropertyProduct to a Power PropertyQuotient PropertyZero Exponent PropertyQuotient to a Power PropertyDefinition of Negative Exponentam⋅an=am+n(am)n=am⋅n(ab)m=ambmanam=am−n,a=0a0=1,a=0(ba)m=bmam,b=0a−n=an1
- Convert from Decimal Notation to Scientific Notation: To convert a decimal to scientific notation:
- Move the decimal point so that the first factor is greater than or equal to 1 but less than 10.
- Count the number of decimal places, n , that the decimal point was moved.
- Write the number as a product with a power of 10.
- If the original number is greater than 1, the power of 10 will be 10n .
- If the original number is between 0 and 1, the power of 10 will be 10n .
- Check.
- Convert Scientific Notation to Decimal Form: To convert scientific notation to decimal form:
- Determine the exponent, n , on the factor 10.
- Move the decimal n places, adding zeros if needed.
- If the exponent is positive, move the decimal point n places to the right.
- If the exponent is negative, move the decimal point ∣n∣ places to the left.
- Check.
Glossary
- negative exponent
- If n is a positive integer and a=0 , then a−n=an1 .
- scientific notation
- A number expressed in the form a×10n, where a≥1 and a<10, and n is an integer.
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