Write the following in standard form: a) 0,032 b) 67000. 2. Simplify the following: a) 2,6x104 + 1,3x103 b) 6,4x10⁻² + 5,5x10⁻² c) 7,52x10⁻³ - 2,5x10⁻³

It moved 2 places to the right, so the exponent of 10 is $-2$.

$$0.032 = \boxed{3.2 \times 10^{-2}}$$

b) 67000

It moved 4 places to the left, so the exponent of 10 is 4.

$$67000 = \boxed{6.7 \times 10^{4}}$$

2) Simplify the following, leaving your answers in standard form:

a) $2.6 \times 10^4 + 1.3 \times 10^3$

Convert $1.3 \times 10^3$ to a term with $10^4$.

$$1.3 \times 10^3 = 0.13 \times 10^4$$

$$2.6 \times 10^4 + 0.13 \times 10^4 = (2.6 + 0.13) \times 10^4$$ $$= 2.73 \times 10^4$$

2.73 is between 1 and 10, so it is in standard form.

$$\boxed{2.73 \times 10^{4}}$$

b) $6.4 \times 10^{-2} + 5.5 \times 10^{-2}$

Add the coefficients.

$$(6.4 + 5.5) \times 10^{-2} = 11.9 \times 10^{-2}$$

11.9 is not between 1 and 10.

$$11.9 \times 10^{-2} = (1.19 \times 10^1) \times 10^{-2}$$ $$= 1.19 \times 10^{1-2}$$ $$= 1.19 \times 10^{-1}$$ $$\boxed{1.19 \times 10^{-1}}$$

c) $7.52 \times 10^{-3} - 2.5 \times 10^{-3}$

Subtract the coefficients.

$$(7.52 - 2.5) \times 10^{-3} = 5.02 \times 10^{-3}$$

5.02 is between 1 and 10, so it is in standard form.

$$\boxed{5.02 \times 10^{-3}}$$