Discover Mathematics P4: Term 2, Unit 10, Lessons 5–8
GoalCompare decimals with models, and see that adding a zero at the end does not change a decimal.
New words
compare · to decide which number is greater, which is less, or whether they are equalmodel · a picture, such as a grid or a bar, that shows a numberequivalent decimals · different ways to write the same value, such as 0.5 and 0.50
Explanation
To compare two decimals, show each one on a model of the same size and see which has more shaded. A bar cut into 10 parts shows tenths, and a grid of 100 squares shows hundredths. The decimals 0.5 and 0.50 are equal: 5 tenths is 5 full columns, and 50 hundredths is the same 50 squares. So a zero added at the end of a decimal does not change its value. Be careful: a zero between the point and the digit does change it, because 0.05 is not 0.5. To compare decimals with the same number of digits, compare the digits from the left. 0.46 and 0.38 have 4 tenths and 3 tenths, so 0.46 > 0.38. If the tenths are equal, compare the hundredths.
Worked examples
Compare 0.3 and 0.6 with bars. Both bars are cut into 10 equal parts. The first has 3 parts shaded and the second has 6 parts shaded. Six tenths is more than three tenths, so 0.3 < 0.6.
Decimal
0.46
0.38
Tenths
4
3
Hundredths
6
8
Squares of 100
46
38
Compare 0.46 and 0.38. On a hundred grid, 0.46 is 46 squares and 0.38 is 38 squares. Comparing the digits from the left: 4 tenths is more than 3 tenths. So 0.46 > 0.38.
Show that 0.7 = 0.70. Seven tenths is 7 full columns of 10 squares, which is 70 squares of 100. So 7/10 = 70/100 and 0.7 = 0.70.
Class activity
Equal or not? Draw three hundred grids on squared paper. Colour 0.3 on the first, 0.30 on the second and 0.03 on the third. Which two grids look the same? Say why, using columns and squares.
Practice
1
Write <, > or =: 0.8 __ 0.5.
0.8 > 0.5, because 8 tenths is more than 5 tenths.
2
Write <, > or =: 0.20 __ 0.2.
0.20 = 0.2: 20 hundredths is 2 full columns, the same as 2 tenths.
3
Write a decimal with two places that is equal to 0.9.
0.90.
4
Put 0.52, 0.25 and 0.55 in order from the smallest to the greatest.
0.25, 0.52, 0.55. The tenths are 2, 5 and 5; then compare 2 and 5 hundredths.
5
Aya says 0.4 < 0.40 because 0.40 has more digits. Is she right?
No. 0.4 = 0.40: 4 columns are 40 squares. A zero at the end does not change the value.
