Writing Each Number In Standard Form

Standard Form Calculator

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Calculator Use

Find standard form of a positive or negative number with the standard form calculator. Convert from number format to standard form as a decimal multiplied by a power of 10.

What is Standard Form

Standard form is a way of writing a number so it is easier to read. It is often used for very large or very small numbers. Standard form is like scientific notation and is typically used in science and engineering.

A number is written in standard form when it is represented as a decimal number times a power of 10.

As an example, consider the speed of light which travels at about 671,000,000 miles per hour. Written in standard form this number is equivalent to 6.71 x 10⁸.

How to Convert to Standard Form

Standard form is like scientific notation where a number is represented as a decimal number times a power of 10. Standard form format is:

\[ a \times 10^{b} \]

Where

a is a number whose absolute value is a decimal number greater than or equal to 1, and less than 10: \[ 1 \le \left\lvert a \right\rvert \lt 10 \]
b is an integer and is the power of 10 required so that the product of the multiplication in standard form equals the original number

How to Convert a Number to Standard Form

Standard form of a number is a x 10 ^b where a is a number, 1 ≤ |a| < 10. b is the power of 10 required so that the standard form is mathematically equivalent to the original number.

Move the decimal point in your number until there is only one non-zero digit to the left of the decimal point. The resulting decimal number is a.
Count how many places you moved the decimal point. This number is b.
- If you moved the decimal to the left b is positive.
- If you moved the decimal to the right b is negative.
- If you did not need to move the decimal b = 0.
Write your scientific notation number as a x 10 ^b and read it as "a times 10 to the power of b."
Remove trailing 0's only if they were to the left of the decimal point.

Example: Convert 459,608 to Standard Form

Move the decimal 5 places to the left to get 4.59608
a = 4.59608
We moved the decimal to the left so b is positive
b = 5
The number 459,608 converted to standard form is 4.59608 x 10⁵

Example: Convert 0.000380 to Standard Form

Move the decimal 4 places to the right and remove leading zeros to get 3.80
a = 3.80
We moved the decimal to the right so b is negative
b = -4
The number 0.000380 converted to standard form is 3.80 x 10^-4
Note that we do not remove the trailing 0 because it was originally to the right of the decimal and is therefore a significant figure.