I need help with this really fast! I’ve looked online and they both show the same exact things!!! 57*10 to the 3rd power and stuff like that

One thought on “Is scientific notation and exponential notation the same thing?”

jbdeeds

Exponential notation is more fundamental than scientific notion. You know tht 5^3 = 5 * 5 * 5, and this notation generalizes to negative, fractional and real number exponents.

Scientific notation uses exponents, but in a very structured way to display numbers in science, physics and engineering. This notation is very useful in two ways: It handles very large and very small numbers in a brief and consistent way, and it clearly shows the degree of accuracy intended by those numbers.

While any ‘base’ could be used for the notation, 10 is typically employed to carry the exponent. And, the exponent is always an integer — not a fraction or a general real number as described in the first paragraph. So: If we are using S.N. for the number 405,329.71 we write 4.0532971 x 10^5. For
.007712, we would write 7.712 x 10^-3. The first part of an S.N. quantity is always a decimal number between one and ten. The exponent is adjusted to achieve equality with the given quantity.

We can now easily compare the ‘accuracy’ or significant figures in each of these quantities. While the second appears to have more ‘decimal places’ than the first, the implied accuracy of the first is greater — 8 significant figures compared to four significant figures for the second. When numbers written in scientific notation are combined in arithmetic operations, it becomes fairly easy to control the degree of accuracy in the result — and not imply that various measurements have more validity than they should.

Exponential notation is more fundamental than scientific notion. You know tht 5^3 = 5 * 5 * 5, and this notation generalizes to negative, fractional and real number exponents.

Scientific notation uses exponents, but in a very structured way to display numbers in science, physics and engineering. This notation is very useful in two ways: It handles very large and very small numbers in a brief and consistent way, and it clearly shows the degree of accuracy intended by those numbers.

While any ‘base’ could be used for the notation, 10 is typically employed to carry the exponent. And, the exponent is always an integer — not a fraction or a general real number as described in the first paragraph. So: If we are using S.N. for the number 405,329.71 we write 4.0532971 x 10^5. For

.007712, we would write 7.712 x 10^-3. The first part of an S.N. quantity is always a decimal number between one and ten. The exponent is adjusted to achieve equality with the given quantity.

We can now easily compare the ‘accuracy’ or significant figures in each of these quantities. While the second appears to have more ‘decimal places’ than the first, the implied accuracy of the first is greater — 8 significant figures compared to four significant figures for the second. When numbers written in scientific notation are combined in arithmetic operations, it becomes fairly easy to control the degree of accuracy in the result — and not imply that various measurements have more validity than they should.