How do you convert a number to standard form?

First, move the decimal point so the new number a is between 1 and 10 in absolute value. Count how many places you moved the decimal; that count is the power n of ten. If you moved the decimal to the left, n is positive; if you moved it to the right, n is negative. Then write the number as a × 10ⁿ.

How is scientific notation related to standard form?

In many UK and GCSE contexts, 'standard form' and 'scientific notation' mean the same thing: writing numbers as a × 10ⁿ, with 1 ≤ |a| < 10 and integer n. In some other countries, 'standard form' can mean something else, such as the expanded form of a polynomial or linear equation, so always check the context.

What about zero in standard form?

Strictly speaking, zero does not have a unique standard form a × 10ⁿ because any choice of n gives 0 × 10ⁿ = 0. In practice, we just write 0 rather than trying to force it into a × 10ⁿ.

How many significant figures should I use?

The number of significant figures depends on the problem: exam questions usually specify 2 or 3 significant figures, while scientific work often uses more. The calculator lets you choose the number of significant figures so you can match the precision you need.

Standard Form Calculator – Convert to & from Scientific Notation

Q: What is standard form in maths?

In GCSE and A-level maths, standard form (also called scientific notation) means writing a number as a × 10ⁿ, where 1 ≤ |a| < 10 and n is an integer. For example, 350000 is 3.5 × 10⁵ and 0.0042 is 4.2 × 10⁻³.

Q: What about zero in standard form?

Strictly speaking, zero does not have a unique standard form a × 10ⁿ because any choice of n gives 0 × 10ⁿ = 0. In practice, we just write 0 rather than trying to force it into a × 10ⁿ.

Q: How many significant figures should I use?

The number of significant figures depends on the problem: exam questions usually specify 2 or 3 significant figures, while scientific work often uses more. The calculator lets you choose the number of significant figures so you can match the precision you need.

Convert numbers to and from standard form (scientific notation) \(a \times 10^n\) with full control over significant figures. Perfect for GCSE, A-level, and scientific work with very large or very small numbers.

What is standard form in maths?

In many GCSE/A-level and science contexts, standard form means scientific notation:

\[ \text{number} = a \times 10^n, \]

where:

\(1 \le |a| < 10\) (the coefficient or mantissa),
\(n\) is an integer (the power of ten).

Examples:

\(350000 = 3.5 \times 10^5\)
\(0.0042 = 4.2 \times 10^{-3}\)
\(-1200000 = -1.2 \times 10^6\)

Standard form vs other meanings

In the UK, “standard form” almost always means scientific notation. In other contexts, “standard form” can mean:

the expanded decimal form of a number (e.g. 300 + 40 + 5),
the standard form of a linear equation (e.g. \(ax + by = c\)),
the standard form of a polynomial (terms in descending powers).

This calculator focuses on the scientific notation meaning (numbers written as \(a \times 10^n\)).

How to convert a number to standard form

To convert a decimal number into standard form:

Move the decimal point so the new number \(a\) is between 1 and 10 in absolute value.
Count how many places you moved the decimal; this gives the exponent \(n\).
If you moved the decimal to the left, \(n\) is positive; if you moved it to the right, \(n\) is negative.
Write the result as \(a \times 10^n\) and round \(a\) to the required significant figures.

Example 1 – large number

Convert \(350000\) to standard form, to 3 significant figures.

Write 350000 as 3.50000 × 10⁵ (we moved the decimal 5 places left).
Coefficient \(a = 3.50000\), exponent \(n = 5\).
Round \(a\) to 3 significant figures → \(a = 3.50\).
Standard form: \(350000 = 3.50 \times 10^5\).

Example 2 – small number

Convert \(0.0042\) to standard form, to 2 significant figures.

Move the decimal 3 places to the right: 0.0042 → 4.2 × 10⁻³.
Coefficient \(a = 4.2\), exponent \(n = -3\).
\(a\) already has 2 significant figures.
So \(0.0042 = 4.2 \times 10^{-3}\).

How to convert from standard form to a normal number

Suppose a number is written as \(a \times 10^n\). To convert back:

Write down \(a\).
If \(n > 0\), move the decimal point \(n\) places to the right.
If \(n < 0\), move the decimal point \(|n|\) places to the left.

Example 3 – 3.5 × 10⁵

\[ 3.5 \times 10^5 = 350000. \]

Move the decimal point 5 places to the right: 3.5 → 350000.

Example 4 – 7.2 × 10⁻³

\[ 7.2 \times 10^{-3} = 0.0072. \]

Move the decimal point 3 places to the left: 7.2 → 0.0072.

Zero and special cases

Zero: zero does not have a unique standard form, since \(0 = 0 \times 10^n\) for any \(n\). We simply write 0.
Negative numbers: the sign is carried by the coefficient \(a\), e.g. \(-1200000 = -1.2 \times 10^6\).
Very large/small values: calculators often show them using E-notation, e.g. \(3.5 \times 10^5\) as 3.5E5.

Standard form, significant figures, and rounding

Standard form is closely linked to significant figures. Once a number is written as \(a \times 10^n\), rounding to a given number of significant figures is simply rounding the coefficient \(a\) to that many digits.

Rounding in standard form

If \(x = a \times 10^n\) and you want \(x\) to 3 significant figures, you:

Round \(a\) to 3 significant figures → \(\tilde{a}\).
Write \(x \approx \tilde{a} \times 10^n\).

Our calculator does this automatically when you choose the number of significant figures in the drop-down.

Standard Form Calculator

Convert numbers to and from standard form

Number in standard form

Standard form as a normal number