Main content

## Decimals vs. fractions

Current time:0:00Total duration:3:58

# Rewriting fractions as decimals

CCSS Math: 4.NF.C.6

## Video transcript

- [Voiceover] Let's write
29/100 as a decimal. So we'll start with 29 over 100, and let's start breaking that down till we can get to place values 'cause place values
will help us to convert to write this as a decimal. 29/100 we can break that down into 20/100 plus 9/100. 20/100 plus nine more hundredths is equal to 29/100. So we've just broken it down some here. It's still equivalent to 29/100. We're just taking it apart
trying to get to place values. Going from there, we
can simplify even more. 20/100 can be simplified. We could divide 20 and 100 by 10. So we'll say 2/10 plus 9/100. And now, if you can hear,
the tenths, hundredths, these are place values we
should recognize from decimals. So what we've shown here is that 29/100 is equal to two-tenths plus nine-hundredths. Here we have two-tenths,
which matches 2/10, and nine-hundreths, like
our 9/100 right there. And so we can take those
and think about place value. If we have our decimal,
let's first put our decimal. Over here to the left of the decimal's our ones place value. We don't have any ones
here so we'll put a zero, zero ones, but then next is tenths, then we have our tenths and we have 2/10. And after tenths, the
place value after tenths is hundredths, and here, we
see, we have nine hundredths. So we'll put a nine in
the hundredths place. And so down here, 0.29 or 29 hundredths, is equivalent to the fraction, 29/100. And just listen to how those are said. It's kind of a clue that we did well. 29 hundredths is equivalent to 29/100. Both the fraction and the
decimal are read the same way. So that's a pretty good clue that we probably rewrote these correctly. So 0.29 is equal to 29/100. Let's try one more, let's try something let's say maybe 53/10. So again we're gonna break this down. We'll have 50/10 plus how
many more tenths are left? There's still three more tenths. And again, we can simplify,
we can simplify this. 50/10 can be divided by 10. So instead of 50/10, we'll say 5/1, plus, we still have those 3/10. And now we've got this to place value. Five ones, is 5/1, plus your 3/10 is three-tenths. So thinking, let's put our decimal, over here to the left of
the decimal's our ones, and we have five ones. And to the right of the decimal is tenths, and we have three tenths. So 5.3 or five and three tenths is equal to 53/10. To write 53/10 as a decimal, we will get 5.3 because it was
five ones and three-tenths, which we showed right here,
five and three tenths.