Standard form of a decimal

Standard form is a term used to describe the typical form of a number of different objects (numbers, equations, etc). The standard form of a whole number involves separating each 3 digits with a comma, like in the number 1,000. The number can also be written as 1 000 with a shorter space between each 3 digits. Having a "standard form" makes it easier for us to communicate what we mean.

The standard form of a decimal number is also known as scientific notation. It involves expressing a given decimal number by its first digit followed by a decimal point and its remaining digits, multiplied by a power of 10 such that it is equivalent to the original value. For example, the number 4359.892 written in the standard form of a decimal would be:

4.359892 × 103


How to write decimals in standard form


Converting a decimal number into standard form mostly just requires an understanding of the decimal number system. We just need to multiply by the correct power of 10. Use the following steps to accomplish this:

  1. Note where the decimal point in the number is. If it is a whole number, add the decimal point after the last digit. If it is a number smaller than 0, the decimal point will need to be shifted right.
  2. Shift the decimal point; rewrite it immediately after the first digit in the number if it is a number larger than 0, or after the first non-zero digit if the number is smaller than 0. Write all non-zero digits after the decimal point (include 0s between non-zero digits).
  3. Count the number of decimal places you had to shift the decimal point.
  4. Write the result from step 2 multiplied by 10 to the power of n, where n is the number of decimal places you had to shift the decimal point. If the number was smaller than 0, raise 10 to the power of -n.

Example

1. Write 100 000 000 000 in standard form:

  1. This is a whole number, so the decimal point is after the last 0: 100 000 000 000.
  2. Next we write the decimal point after the 1.
  3. Then we count the number of decimal places we moved the decimal point:

  4. 1 × 1011

In this example, one of the benefits of standard form is clear. For very large or small numbers with many trailing or leading zeros (respectively), standard form is a more efficient way to write the number, and makes the number easier for someone else to read since they don't have to count the number of zeros.


2. Write 0.00001467 in standard form:

  1. This is a number smaller than 0, so we will need to shift the decimal point right
  2. We write the decimal point after the first non-zero number, followed by the rest of the non-zero digits: 1.467
  3. Next we count how many decimal places we shifted the decimal point:

  4. Since the number is smaller than 0, we know that the power needs to be negative:
    1.467 × 10-5

Did you know??

In some countries, the decimal component of a number is separated with a comma (,) rather than a period (.), and each 3 digits is separated by a period rather than a comma. For example,

100.563,757

in some countries is the same as:

100,563.757

In both cases, the number reads as "one hundred thousand five hundred sixty-three point seven five seven."