Convert between scientific notation and standard form

Scientific notation represents a nonzero number as $a \times 10^n$ , where $1 \leq a < 10$ and $n$ is an integer; converting to standard decimal form uses the exponent to determine the place-value scale, with positive exponents producing large numbers and negative exponents producing numbers between zero and one. This understanding connects powers of ten to place value and does not include generalized bases, irrational exponents, or advanced computations with scientific notation.

Detailed Explanation: Convert between scientific notation and standard form

Scientific notation has the form

a \times 10^n,

where $a$ is at least $1$ but less than $10$ . The exponent $n$ tells you how many places to move the decimal point:

A positive exponent means move the decimal point to the right.
A negative exponent means move the decimal point to the left.
Add zeros when there are not enough digits.

Example

Convert $3.2 \times 10^4$ to standard form.

Start with the number $3.2$ .
The exponent is $4$ , so move the decimal point $4$ places to the right:

3.2 \longrightarrow 32 \longrightarrow 320 \longrightarrow 3{,}200 \longrightarrow 32{,}000

Therefore,

3.2 \times 10^4 = 32{,}000.

To convert back, start with $32{,}000$ and move the decimal point $4$ places left:

32{,}000 \longrightarrow 3.2.

So,

32{,}000 = 3.2 \times 10^4.

Learn by doing: Convert between scientific notation and standard form

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Scientific Notation - Convert to Scientific Notation - 2 Decimal Places

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