Convert A Number To Scientific Notation

Very large or very small numbers are usually written in scientific notation :

A × 10ⁿ where and n is an integer.

Example:

2 350 000 = 2.35 × 10⁶

0.000 875 4 = 8.754 × 10^–4

To convert a number into scientific notation:

Method 1

Rewrite the number as a product of a number A such that and a power of 10.

Example:

64 000 = 6.4 × 10 000

= 6.4 × 10⁴

Method 2

Step 1 : Shift the decimal point of the number A to the left or to the right until

Step 2 : Count the number of places that the decimal point has moved. The count would be the index n. If the decimal point was moved to the left then n is positive. If the decimal point was moved to the right then n is negative.

Example:

Example:

Write each of the following numbers in scientific notation:

a) 734 000         b) 0.00685

Solution:

a) 734 000 = 7.34 × 10 000 = 7.34 × 10 5

or

b) 0.00685 = 6.85 × = 6.85 × 10 -3

or

The following video shows more examples of converting numbers to scientific notation.

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