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This content is taken from the National STEM Learning Centre's online course, Maths Subject Knowledge: Fractions, Decimals, and Percentages. Join the course to learn more.
4.3

## National STEM Learning Centre

Skip to 0 minutes and 7 seconds PAULA KELLY: OK, so we’re going to have a look now at comparing some decimal numbers but using our knowledge of place value. So, if I had to compare our units, our tenths, hundredths, thousandths, if we had the number 0.36– which we wouldn’t ever say as “null point 36,” obviously– we compare that to 0.312.

Skip to 0 minutes and 32 seconds MICHAEL ANDERSON: Now, my students are probably going to think this one’s bigger, because 312 is bigger than 36.

Skip to 0 minutes and 37 seconds PAULA KELLY: Exactly, it’s a really common misconception. So, to try and break this down, we try to explain as we compare the relative size of the digits but going across their place value.

Skip to 0 minutes and 47 seconds MICHAEL ANDERSON: As we go along?

Skip to 0 minutes and 48 seconds PAULA KELLY: Yeah.

Skip to 0 minutes and 48 seconds MICHAEL ANDERSON: OK.

Skip to 0 minutes and 49 seconds PAULA KELLY: So, we start with our units. They’re both 0, so far equal. We compare our tenths, again equal. When we get to the hundredths, however, we’ve got 6 hundredths but only 1 here. So, instantly, we notice our biggest number. Whatever comes next is irrelevant, because we’ve shown already that’s the larger.

Skip to 1 minute and 10 seconds MICHAEL ANDERSON: So, as soon as there’s a difference, you’d stop comparing and just ignore the rest of the numbers.

Skip to 1 minute and 15 seconds PAULA KELLY: Yeah, you’re all done. OK. Another pair of examples that might also cause some problems– say, if we had 0.301, we’ll compare that to if we had 0.31. So, again, the same methods– we compare our units.

Skip to 1 minute and 35 seconds MICHAEL ANDERSON: Same?

Skip to 1 minute and 35 seconds PAULA KELLY: Same– our tenths–

Skip to 1 minute and 37 seconds MICHAEL ANDERSON: The same?

Skip to 1 minute and 38 seconds PAULA KELLY: Same– when we get to our hundredths, however, we’ve only got 1 hundredth here. There’s no hundredths here.

Skip to 1 minute and 45 seconds MICHAEL ANDERSON: OK, so this one’s larger.

Skip to 1 minute and 47 seconds PAULA KELLY: Yes, exactly.

# Comparisons: decimals

The comparison of decimals requires a good understanding of decimal place value. We introduced this in Week 2.

The table below shows the fraction equivalent for each decimal place:

When comparing decimals a common misconception is to think that 0.312 is larger than 0.36 because ‘312’ is larger than ‘36’. In this video Paula and Michael explain how to compare decimals and avoid making these common mistakes. By placing the numbers in a grid so that digits of the same place value can be easily compared.

## Problem worksheet

Now complete questions 2 and 3 from this week’s worksheet.