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Work with radicals and integer exponents.
Work with radicals and integer exponents.
Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.
Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.
The Breakdown
The Breakdown
Scientific notation is a way to express very large and very small numbers. It is always written as a product of two factors: the first factor called the coefficient, is less than ten, but greater than or equal to one; the second factor is a power of ten (base of ten and integer exponent).
To convert a number from standard form into scientific notation, first move the decimal point to form the coefficient (and count the spaces moved). Then multiply it by ten with an exponent (number of spaces the decimal was moved).
The exponent is positive if the decimal is moved right. The exponent is negative if the decimal is moved left.
To compare numbers in scientific notation, simply look at the exponent on the power of ten. If exponents are the same, use the coefficient to compare the two numbers.
To compare numbers in scientific notation and figure out how many times larger one number is, divide the two.
- Divide the coefficients.
- Divide the powers of ten by subtracting the exponents
- Rewrite as the new coefficient times the new power of ten.
- Be sure the new number is properly written in scientific notation.
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