Comparing, using place value
When we compare, or order whole numbers up to thousands, we know that thousands are bigger than hundreds, hundreds are bigger than tens, and tens are bigger than units. If we think of numbers in a place value table, we see that as we move to the left, the value of the number gets bigger. Or, you might think of it as moving to the right means the value of our number is smaller.
What about decimals?
With decimals, the same rules apply. The value of our number becomes smaller as we move to the right. So, a $3$3 in the hundredths place is smaller than a $3$3 in the tenths place.
We can also think of $300$300 thousandths as $30$30 hundredths, or $30$30 tenths. Let's explore this in the video below. You might also want to check out comparing hundredths, before watching this video.
Using numbers only
Sometimes we don't have a shaded pictures to help us. In that case, we can look at which place value columns our numbers are in, to compare the numbers. If we have $0.342$0.342, and we are comparing it to $0.458$0.458, we know that $342$342 is smaller than $458$458, so $342$342 thousandths is smaller than $458$458 thousandths.
But what do we do if it's not as clear? In Video 2, we work through some examples, and see how we can compare decimals to thousandths, using only numbers.
- > means 'greater than' and < means 'less than'
- We can start at the place value column furthest to the left and work to the right, comparing the values in each column to work out the bigger/ smaller number.
- Or, we can add zeros at the end of a decimal so we can compare the same number of place value columns. For example, if we wanted to compare $0.45$0.45 and $0.672$0.672, we could write $0.45$0.45 as $0.450$0.450. This means we can compare thousandths to thousandths.