What is standard form?

Answer 1

Standard form (also known as "standard index form" or "scientific notation") is a method of writing very big, or very small, numbers in a compact way. It is written with a single non-zero digit before a decimal point and then the rest of the number, followed by multiplying it by a power of 10 which gets the decimal point back to where it was in the original number. To calculated the power of the ten count how many digits the decimal point needs to move; if it needs to move to the left make it negative.

Examples (writing normal form in standard form):

1234 = 1.234 × 10^3

123.4 = 1.234 × 10^2

0.01234 = 1.234 × 10^-2

With a scientific calculator the power of 10 is called the exponent and is access by the [exp] button.

To convert a number in standard form to normal form multiply it out; the easiest way to do this is to jump the decimal point the same number of digits as the power of the ten: if the power is positive to the right, if negative to the left; if there are not enough digits to complete the number of jumps required, insert zeros.

Examples:

1.234 × 10^3 = 1234

1.2 × 10^3 = 1200

1.2 × 10^-1 = 0.12

1.2 × 10^-3 = 0.0012

Americans use "Standard form" to mean something different: they pair Standard form with "Expanded form", where standard form is the number written normally (or in normal form), and expanded form is a number is written as the sum of its individual digits multiplied by their place value column value.

Examples (writing normal form in expanded form):

1234 = 1000 + 200 + 30 + 4

120.4 = 100 + 20 + 0.4

0.012 = 0.01 + 0.002

Sometimes a large number can be written using words (eg 1.6 million) and normal form can be achieved by multiplying it out.

example 1.6 million:

1 million is 1,000,000, so 1.6 million = 1.6 × 1 million = 1.6 × 1,000,000 = 1,600,000.