Three spellings

Express 65 percent as a decimal. Here's one whole, with nothing cut off it yet. Cut it into one hundred equal parts. Percent means out of one hundred, so 65 percent is 65 of those parts. 65 shaded parts out of one hundred parts is the fraction 65 over one hundred. It's the same shading. Only the way it's written has changed. Look at one row. 10 parts out of one hundred is one tenth of the whole. The 65 shaded parts fill 6 whole rows, and 5 parts of the next one. That's 6 tenths and 5 hundredths. The first place after the point counts tenths and the second counts hundredths, so 65 over one hundred is written zero point six five. That's how the square reads it. Here's how it's written in school. One hundred has two zeros. One. Two. Two zeros, so the point hops twice. It starts behind the 5. One hop, over the 5, and 65 is 6 point 5. Two hops, over the 6, and the point is in front of the 6. Write a 0 in front of the point, and there's zero point six five. Two hops for the two zeros, and it's the same 6 tenths and 5 hundredths on the square. So one shading, and three ways to write it. 65 percent. 65 over one hundred. Zero point six five. The fraction over one hundred is the middle one, and all three are the same 65 parts.

Your turn. Express zero point four as a percentage. Here's the same whole again, cut into one hundred, with nothing shaded on it yet. How much of it is zero point four, and what percentage is that? Try it first. Pause if you like. Zero point four is 4 tenths, and one tenth is one whole row. So 4 whole rows are shaded. Each row is 10 of the one hundred parts, so 4 rows is 40 of them. And 40 out of one hundred is 40 percent. One shading, and three ways to write it. Zero point four. 40 over one hundred. 40 percent. The fraction over one hundred is the middle one, and it's the same number as the other two. So whichever one you're given, write it over one hundred first. The percentage and the decimal are both in that one line.