Express nine and thirty-nine hundredths in standard form.
In this question, you can see we’re given a number. It’s written in words, nine and thirty-nine hundredths. If we wrote this number exactly as it’s written, we might write nine and then a fraction, thirty-nine hundredths. We’d call this a mixed number. It’s a mixture of a whole number part and a fraction part. And we can see that writing this value as a mixed number exactly mirrors the way that it’s been written in words. We’ve got nine and thirty-nine hundredths. Now, the question doesn’t ask us to write it as a mixed number. It asks to express the amount in standard form, in other words, the usual way that we’d write a number that’s made up of a whole number and a part, as a regular decimal number.
To do this, we’re going to have to think about place value. So let’s draw a place value grid to begin with. Our number contains nine, which we can say is worth nine ones. And also thirty-nine hundredths. Is this how we’d write the value as a decimal? Well, it doesn’t look quite right, does it? Because we’re trying to squash two digits into a column that should only have one. We know that every column only has one digit in it. And the highest we go up to is nine. So how can we express thirty-nine hundredths without writing two digits in one column? To help us with this, we need to understand the relationship between tenth and hundredths.
Let’s imagine that this square is worth one whole. Now, it’s been split into tenths. And now each of these small squares is worth one hundredth. So what does thirty-nine hundredths look like? There we are, thirty-nine hundredths. Now, if we look closely at this number and think back to what we originally said about tenths, we can see either is made up of three tenths and nine hundredths. This part here is worth three tenths and these nine individual squares are worth nine hundredths.
So we can say and we can see that thirty-nine hundredths are worth three tenths and nine hundredths. We can now use this to help express thirty-nine hundredths in standard form. Thirty-nine hundredths is the same as we just said as three tenths and nine hundredths. Nine and thirty-nine hundredths is exactly the same as nine, three tenths, and nine hundredths. And so we can express nine and thirty-nine hundredths as a standard decimal by writing 9.39.