Write eighty-three and three hundred six thousandths in expanded form.
So we’ve got effectively two parts of the number here: we’ve got eighty-three and three hundred six thousandths or some of you might say three hundred and six thousandths. And this is the whole number. And this part is going to be the fractional or decimal part of the number and effectively we’re adding them together. Now we can work out this number as a decimal by just doing three hundred and six or three hundred six divided by a thousand.
Now the number three hundred six has a three in the hundreds column and a six in the one or the units column. Every time I divide by ten, I’m reducing the value of each of those digits by ten. So I’m moving them one place to the right. Now to divide by a thousand, that’s the same as dividing by ten three times: so ten, a hundred, a thousand. So let’s divide by ten. And each digit moves one place to the right. Obviously the decimal point stays where it was. So three o six and then the o moves to the right.
Now the value of those decimal columns, the first column is tenths and the second column is hundredths. So having divided by ten once, we’ve now got thirty point six or thirty and six-tenths. So let’s divide by ten again. And that gives us three point o six o. Well in fact we’re gonna ignore the-the zero on the end now because it’s not really contributing anything to this number. So if we divide by ten again, so in total we’ve now divided by ten three times; we’ve divided by a thousand. We’ve got zero point three zero six. So eighty-three plus zero point three zero six is eighty-three point three zero six.
Now that’s not expanded form; that’s just a normal standard form: eight three point three zero six. Now let’s put in the place value of each of those columns. We can write out each digit in turn combined with the place value of its position in order to write this number in its expanded form. So the first digit represents eight times ten, the second digit represents three times one, the third digit is three times a tenth, the fourth digit is zero times a hundredth, and the fifth digit is six times a thousandth. And just converting all of those fractions: a tenth, a hundredth, a thousandth into their decimal version: nought point one, nought point nought one, and nought point nought nought one. That is the number in its expanded form.