Scientific Notation - Pre-Algebra Step by Step

Convert between standard form and scientific notation m × 10^n, where 1 ≤ m < 10.

scientific-notation To write a number in scientific notation: - Move the decimal so 1 ≤ m < 10. - Count moves: right → positive exp, left → negative exp. - Verify: m × 10^n equals the original.

Example

Move the decimal point and record the matching power of ten.

highlighted = computed this step

Step 1 — Large number

Set up the expression.

3400

Step 2 — Move decimal left

Move the decimal left 3 places: 3400 = 3.4 x 10^3.

3400 = \hl{3.4} \times \hlmath{10^{3}}

Step 3 — Check expanded value

Check by expanding: 3.4 x 10^3 = 3400.

3.4 \times 10^{3} = \hl{3400}

Step 4 — Small number

Set up the expression.

0.0072

Step 5 — Move decimal right

Move right 3 places: 0.0072 = 7.2 x 10^-3.

0.0072 = \hl{7.2} \times 10 ^{ \hl{-3} }

Step 6 — Check expanded value

Check by expanding: 7.2 x 10^-3 = 0.0072.

7.2 \times 10 ^{ -3 }= \hl{0.0072}

Step 7 — Result

Read the final result.

3.4 \times 10^{3} \quad 7.2 \times 10 ^{ -3 }