Scientific Notation

Front

What is scientific notation?

Back

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is typically in the form of a x 10^n, where 1 ≤ a < 10 and n is an integer.

Front

How do you convert a number from scientific notation to standard form?

Back

To convert from scientific notation to standard form, multiply the coefficient (a) by 10 raised to the power of the exponent (n). For example, 6.79 x 10^4 = 6.79 * 10,000 = 67,900.

Front

How do you convert a number from standard form to scientific notation?

Back

To convert from standard form to scientific notation, move the decimal point in the number until only one non-zero digit remains to its left. Count the number of places the decimal point is moved; this will be the exponent (n) of 10. For example, 0.004078 becomes 4.078 x 10^-3.

Front

What does a negative exponent in scientific notation indicate?

Back

A negative exponent in scientific notation indicates that the number is a fraction or a very small number. For example, 7.82 x 10^-6 represents 0.00000782.

Front

What does a positive exponent in scientific notation indicate?

Back

A positive exponent in scientific notation indicates that the number is large. For example, 1.25678 x 10^8 represents 125,678,000.

Front

What is the standard form of 3.98 x 10^-4?

Back

The standard form of 3.98 x 10^-4 is 0.000398.

Front

What is the scientific notation for the number 67,900?

Back

The scientific notation for 67,900 is 6.79 x 10^4.

Front

How do you determine the exponent when converting to scientific notation?

Back

The exponent is determined by how many places the decimal point is moved to convert the number to a value between 1 and 10. If you move the decimal to the left, the exponent is positive; if you move it to the right, the exponent is negative.

Front

What is the scientific notation for the number 0.000398?

Back

The scientific notation for 0.000398 is 3.98 x 10^-4.

Front

What is the standard form of 1.25678 x 10^8?

Back

The standard form of 1.25678 x 10^8 is 125,678,000.