One gram is 0.0352739619 ounces, because one avoirdupois ounce is exactly 28.349523125 grams. That long exact figure comes from dividing the pound, 453.59237 g, by sixteen — every digit is definitional rather than measured.
About the units
The gram is a thousandth of a kilogram, and although the kilogram is the SI base unit, the gram is the one people handle. It was originally defined in 1795 as the mass of one cubic centimetre of water at the melting point of ice, which is why a millilitre of water still weighs almost exactly a gram. The ounce is a sixteenth of an avoirdupois pound. Its name comes from the Latin uncia, a twelfth — the same root as the inch — because the Roman ounce was a twelfth of a Roman pound. The shift from twelve to sixteen happened in the medieval avoirdupois system used for bulk goods, and it is the reason the troy ounce, still used for precious metals, is a different and heavier unit at 31.1034768 g.
The exact factor
The exact relationship is 1 oz = 28.349523125 g, derived as 453.59237 ÷ 16. Grams to ounces is therefore 1 ÷ 28.349523125 = 0.0352739619495804..., repeating. A rough mental method: divide grams by 28, or divide by 30 and add about seven per cent. For kitchen work the useful anchors are that 100 g is about 3.5 oz, 250 g is about 8.8 oz, and 500 g is about 17.6 oz — noticeably more than a pound, which is 453.6 g.
Where you meet this conversion
Recipes are the dominant case, and the direction of travel matters: European recipes give dry ingredients in grams while American ones give them in ounces or in cups. Postal and shipping rates are banded by weight, with thresholds in ounces in the United States and grams elsewhere, so a letter that is fine in one system can cross a price band in the other. Nutrition labels use grams worldwide, including on American packaging, which is why a US label often shows serving sizes in ounces and nutrient amounts in grams on the same panel.