How to multiply scientific notation by a whole number

Multiplication and Division

Quantities with exponents can be multiplied and divided easily if they have the same base. Since all number in scientific notation have base 10, we can always multiply them and divide them.

To multiply two numbers in scientific notation, multiply their coefficients and add their exponents. To divide two numbers in scientific notation, divide their coefficients and subtract their exponents. In either case, the answer must be converted to scientific notation.

Here are the steps to multiply two numbers in scientific notation:

Multiply the coefficients--round to the number of significant figures in the coefficient with the smallest number of significant figures.
Add the exponents.
Convert the result to scientific notation.

Here are the steps to divide two numbers in scientific notation:

Divide the coefficients--round to the number of significant figures in the coefficient with the smallest number of significant figures.
Subtract the exponents.
Convert the result to scientific notation.

Example 1: (5.60×1012)×(7.102×104) = ?

5.6×7.102 = 39.8
1012×104 = 1012+4 = 1016
(5.60×1012)×(7.102×104) = 39.8×1016
39.8×1016 = 3.98×1017

Thus, (5.6×1012)×(7.102×104) = 3.98×1017.

Example 2: (3.04×105)÷(9.89×102) = ?

= 0.307
= 105-2 = 103
(3.04×105)÷(9.89×102) = 0.307×103
0.307×103 = 3.07×102

Thus, (3.04×105)÷(9.89×102) = 3.07×102.

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Calculator Use

Use this calculator to add, subtract, multiply and divide numbers in scientific notation, E notation or engineering notation. Answers are provided in three formats: scientific notation, E notation and engineering notation. You can also do operations on whole numbers, integers, and decimal numbers and get answers in scientific notation.

If you mark the check box the calculator automatically determines the number of significant figures in the answer. If you do not mark the check box, answers may contain more digits than are signficant.

Caution: See note regarding significant figures calculations.

Example Calculations

Use the links below to load a sample calculation into the calculator. In each example the input forms are different, but they all produce the same answers in scientific notation and E notation.

Standard Notation

Standard notation is the usual way to write numbers, with or without commas and decimals. This example calculation solves the addition problem 122500 + 3655. Click on the link and then refer to the calculator above. Note that the inputs are standard notation numbers. The answers are formatted in scientific notation and E notation.

122500 + 3655 = 1.26155 x 105

Scientific Notation

In scientific notation a large number is converted to an equivalent decimal number between 1 and 10, multiplied by 10 raised to some power. Very small numbers are converted to an equivalent decimal number between 1 and 10, multiplied by 10 raised to some negative power. In this example scientific notation calculation we're solving 1.225 × 105 + 3.655 × 103:

1.225 × 105 + 3.655 × 103 = 1.26155 x 105

E Notation

E notation is also known as exponential notation. E notation is the same as scientific notation where a decimal number between 1 and 10 is multiplied by 10 raised to some power. In E notation the "times 10 raised to a power" is replaced with the letter e in either uppercase or lowercase. The number after the "e" indicates how many powers of 10. In this example calculation we're adding 1.225e5 and 3.655e3:

1.225e5 + 3.655e3 = 1.26155e5

Note: Doing Math With Significant Figures

There are some cases where you would not want to auto-calculate significant figures. If your calculation involves a constant or an exact value as you might find in a formula, do not check the "auto-calculate" box.

For example, consider the formula for diameter of a circle, d = 2r, where diameter is twice the length of the radius. If you measure a radius of 2.35, multiply by 2 to find the diameter of the circle: 2 * 2.35 = 4.70

If you use this calculator for the calculation and you mark the "auto-calculate" box, the calculator will read the 2 as one significant figure. Your resulting calculation will be rounded from 4.70 to 5, which is clearly not the correct answer to the diameter calculation d=2r.

You can think of constants or exact values as having infinitely many significant figures, or at least as many significant figures as the least precise number in your calculation. Use the appropriate number of significant figures when you input exact values in this calculator. In this example you would want to enter 2.00 for the constant value so that it has the same number of significant figures as the radius entry. The resulting answer would be 4.70 which has 3 significant figures.

Additional Resources

See our Rounding Significant Figures Calculator for more information on significant figures.

See the Scientific Notation Converter to convert a number into scientific notation or E notation.

If you need a scientific calculator see our resources on scientific calculators.

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How do you multiply scientific notation numbers?

How do you multiply scientific notation with positive and negative exponents?

To multiply numbers in scientific notation when the exponents are negative, follow the same rules as simple multiplication. First, multiply the coefficients and then add the exponents. When adding the exponents, use the rules of addition for negative numbers. For example, (3 x 10^-4) (3 x 10-3) = 9.0 x 10-7.

How do you write 1000000000 in scientific notation?

Scientific notation is essentially moving the decimal point from the end of the number to just before the first non-zero number. The number is then shown to be multiplied by an exponent of ten that accomplishes this manipulation. So, the scientific notation for 1,000,000,000 is 1 x 10 9.