Week 22 · Comparing and adding decimals and fractions · 3 lessons
1
Longer decimals are not always larger
Discover Mathematics P4: Term 2, Unit 10, Lessons 9–12
GoalCompare decimals with different numbers of digits by writing zeros so that they have the same places.
New words
place · the position of a digit, such as ones, tenths or hundredthscompare · to decide which number is greater, which is less, or whether they are equalgreater than (>) · shows that the number on the left is bigger, as in 0.7 > 0.07
Explanation
With whole numbers, a number with more digits is greater. With decimals this is not true. The decimal 0.07 has two digits after the point and 0.7 has only one, but 0.7 is greater. Seven tenths is much more than seven hundredths. To compare, give both decimals the same number of places by adding a zero at the end, which does not change the value: 0.7 = 0.70. Now compare 70 hundredths with 7 hundredths: 0.70 > 0.07. You can also compare place by place from the left: ones first, then tenths, then hundredths. The first place where the digits are different decides which decimal is greater. Do not look at the length of the decimal, look at the places.
Worked examples
Compare 0.7 and 0.07. Write 0.7 as 0.70. Then 70 hundredths is more than 7 hundredths, so 0.7 > 0.07. The bars agree: 7 full tenths is a long bar, but 0.07 is only a small piece of the first tenth.
Decimal
ones
tenths
hundredths
0.40
0
4
0
0.38
0
3
8
Compare 0.4 and 0.38. Write 0.4 as 0.40. The tenths are 4 and 3, so 0.40 is greater than 0.38 and 0.4 > 0.38. The number 0.38 is longer but smaller.
Decimal
0.6
0.06
0.59
0.5
With two places
0.60
0.06
0.59
0.50
Hundredths
60
6
59
50
Put 0.6, 0.06, 0.59 and 0.5 in order from the smallest. Give them all two places: 0.60, 0.06, 0.59, 0.50. Compare the hundredths: 6 < 50 < 59 < 60. So the order is 0.06, 0.5, 0.59, 0.6.
Class activity
Number line race. Draw a number line from 0 to 1 with ten steps. Write these decimals on cards: 0.9, 0.09, 0.45, 0.5 and 0.15. Put each card at about the right place on the line, starting with the one you think is smallest. Then read the cards from left to right and check them with zeros: 0.90, 0.09, 0.45, 0.50, 0.15.
Practice
1
Write <, > or =: 0.3 __ 0.03.
0.3 > 0.03, because 0.30 is 30 hundredths and 0.03 is 3 hundredths.
2
Write <, > or =: 0.5 __ 0.49.
0.5 > 0.49, because 0.50 > 0.49.
3
Write <, > or =: 0.08 __ 0.1.
0.08 < 0.1, because 0.1 = 0.10 and 8 hundredths is less than 10 hundredths.
4
Put 0.9, 0.09 and 0.19 in order from the smallest to the greatest.
0.09, 0.19, 0.9 (that is 0.09, 0.19, 0.90).
5
Mariam says 0.25 > 0.3 because 25 is greater than 3. Is she right?
No. 0.3 = 0.30 and 25 hundredths is less than 30 hundredths, so 0.25 < 0.3. The length of the decimal does not decide.
