Scientific notation and significant figures

Writing large and small numbers in scientific notation, converting back to decimal form, rounding to significant figures and calculating with scientific notation.

Scientific notation

$3\,450\,000 = 3.45 \times 10^6$ (decimal point moved $6$ places left). $0.00072 = 7.2 \times 10^{-4}$ (moved $4$ places right, so the power is negative).

Example 1●●

Calculate $(3 \times 10^4) \times (2 \times 10^5)$.

$3 \times 2 = 6$ and $10^4 \times 10^5 = 10^9$

$6 \times 10^9$

Significant figures

Count from the first non-zero digit. $0.004572$ to $2$ significant figures is $0.0046$; $38\,615$ to $3$ significant figures is $38\,600$.

Flashcards

Big number

Positive power of $10$

Small number (less than 1)

Negative power of $10$

$0.004572$ to 2 s.f.

$0.0046$

Practice

Write $3\,450\,000$ in scientific notation.
Write $0.00072$ in scientific notation.
Calculate $(3 \times 10^4)(2 \times 10^5)$.
Write $4.8 \times 10^{-3}$ as a decimal.
Round $0.004572$ to $2$ significant figures.
Round $38\,615$ to $3$ significant figures.
Calculate $(8 \times 10^7) \div (2 \times 10^4)$.
Write $150\,000\,000\,000$ in scientific notation.