Place value of decimals

In forty-six point three seven two, what is the value of the digit seven? Try it first. Pause if you like. Start at the decimal point. What is the second place to its right? This rectangle represents one whole. Its size will stay fixed. Divide that same whole into ten equal parts. Each part is one tenth. Divide each tenth into ten equal parts. Each small rectangle is one hundredth of the same whole. Now divide just one hundredth into ten equal parts. Each tiny rectangle is one thousandth. The whole has not changed. After ones come tenths, hundredths, then thousandths. Each place is one tenth of the place before it. Forty-six point three seven two is forty, plus six, plus zero point three, plus zero point zero seven, plus zero point zero zero two. Four tens, six ones, three tenths, seven hundredths and two thousandths make the number in the question. The seven is in the hundredths place. It is the second digit after the decimal point. Seven hundredths have a value of zero point zero seven. That is the value of the digit seven in forty-six point three seven two. The blue region covers seven hundredths of our fixed whole. Seven is the digit; zero point zero seven is its value. Name the place before reading the value. The decimal point tells us where to start.

A decimal has two ones, four tenths and zero hundredths. It also has a digit nine whose value is zero point zero zero nine. Write the decimal. Try it first. Pause if you like. Where must the nine go? What keeps the empty hundredths place open? The value of the digit nine is zero point zero zero nine. This is given in the question. Keep the same whole. Divide one hundredth into ten equal thousandths. Zero point zero zero nine is nine thousandths, so the nine is in the thousandths place. The question gives zero hundredths. We must keep that place between the tenths and the thousandths. The decimal is two, plus zero point four, plus zero point zero zero nine, which is two point four zero nine. Read the places: two ones, four tenths, zero hundredths, nine thousandths. The zero keeps the nine in the correct place. A digit gets its value from its place. Keep the decimal point and every needed zero.