Arrange 35 and 36 hundredths and 35 and seven hundredths and 34 and 189 thousandths and 34 and 197 thousandths in ascending order.
Ascending order means from least to greatest. Let’s line these values up so that their place values are all in a row: 35 and 36 hundredths, 35 and seven hundredths, 34 and 189 thousandths, 34 and 197 thousandths. We have the tens place, the units place, tenths place, hundredths place, and the thousandths place. We wanna to start all the way on the left with the highest place value and compare and then move to the right.
In the tens place, all of these values are the same. So we move our comparison to the units place. We have five, five, four, and four. The two values with the four in the units place are smaller than the two values with the five in the units place. But in order to tell which of these two values are smaller, we need to move to the right again in the tenths place.
Both of these values have a one in the tenths place. So we move to the right again. In the hundredths place, we have an eight and a nine. Remember, we’re working from least to greatest, so we need the smallest number. Eight is smaller than nine. 34 and 189 thousandths is smaller than 34 and 197 thousandths.
Now we need to compare 35 and 36 hundredths and 35 and seven hundredths. Both numbers have threes in the tens place and five in the units place, which means we need to compare the tenths place.
One of the numbers has a three in the tenths place and one has a zero. Again we’re looking for the smallest value. Zero is smaller than three, and that means 35 and seven tenths is smaller than 35 and 36 tenths. In ascending order, we have 34 and 189 thousandths, 34 and 197 thousandths, 35 and seven hundredths, 35 and 36 hundredths.