One gram per millilitre is exactly one kilogram per litre. They are the same density with two names, and the identity is not a coincidence — it is the metric system doing exactly what it was designed to do.
About the units
The equality follows from two facts that hold exactly: a kilogram is a thousand grams, and a litre is a thousand millilitres. Divide one by the other and the thousands cancel. That cancellation was designed in. When the metric system was created in the 1790s, the gram was defined as the mass of one cubic centimetre of water at the ice point, which made water's density exactly 1 g/cm³ by construction. The modern definitions run through the kilogram and the Planck constant instead, so the correspondence is no longer exact — water at 4 °C is 0.999972 g/cm³ — but it is close enough that the design intent survives intact.
The exact factor
The factor is exactly 1, so no arithmetic is needed. What the page is useful for is the family of identities around it: 1 g/ml = 1 kg/l = 1 g/cm³ = 1,000 kg/m³ = 1,000 g/l. All five describe the density of water, and being able to move between them without thinking is what makes metric density calculations quick. The corresponding relationship in imperial units does not exist — a pound per gallon and an ounce per cubic inch have no such tidy correspondence, which is precisely the advantage the metric system was built for.
Where you meet this conversion
Laboratory work and food production, where the two labels appear on facing pages of the same document. Reagent bottles state density in g/ml, bulk tank specifications in kg/l, and both are the same number. Fuel, oil and chemical shipping documents use kg/l while the laboratory certificate uses g/ml. Recognising the identity saves a conversion that would otherwise be attempted and occasionally got wrong.