One number, three ways to write it

Express sixty five percent as a decimal. This square is one whole. Divide the whole into one hundred equal parts. The same square becomes a counting board. Each cell is still one of the hundred equal parts. Percent means out of one hundred. Sixty five percent is sixty five of these parts. Sixty five shaded parts out of one hundred is sixty five over one hundred. One row has ten of the hundred parts. That is one tenth of the whole. The shading fills six whole rows. That is six tenths. Five more cells make five hundredths. Six tenths and five hundredths is written zero point six five. To divide sixty five by one hundred, keep the decimal point fixed. One hundred has two zeros. One. Two. Keep the decimal point fixed. The digits move. Move both digits one place to the right. Sixty five becomes six point five. Move both digits one more place to the right. That makes zero point six five. Write a zero in the ones place. Zero point six five. Sixty five percent. Sixty five over one hundred. Zero point six five. Three ways to write the same shaded quantity.

Your turn. Express zero point four as a percentage. The same whole has one hundred equal cells, with nothing shaded yet. Try it first. Pause if you like. Zero point four is four tenths. One tenth is one whole row. So four whole rows are shaded. Each row has ten parts, so four rows are forty of the hundred parts. Forty out of one hundred is forty percent. Zero point four. Forty over one hundred. Forty percent. The same quantity, written three ways. The fraction over one hundred links the decimal and the percentage.