الأسبوع 1 · قراءة الكسور العشرية ومقارنتها وكتابتها حتى الأجزاء من ألف · 3 دروس
3
Taking decimals apart and comparing them
Discover Mathematics P5: Term 1, Unit 1, Lessons 1–5
GoalWrite a decimal in expanded form and compare two decimals place by place.
New words
expanded form · a number written as the sum of the values of its digitscompare · to decide which number is greater, smaller or equalequivalent decimals · decimals that name the same amount, such as 0.7 and 0.70
Explanation
Expanded form splits a number into the value of each digit: 4.307 = 4 + 0.3 + 0.007. The 0 in the hundredths place adds nothing, so we leave that part out. We can also write 4 × 1 + 3 × 0.1 + 7 × 0.001. To compare two decimals, line up their decimal points and look at the places from the left. The first place where the digits differ decides. Compare 3.405 and 3.45: the ones are equal (3), the tenths are equal (4), and in the hundredths place 0 is less than 5, so 3.405 < 3.45. A decimal with more digits is not always greater. Also, a zero at the end of a decimal changes nothing: 0.7 = 0.70 = 0.700.
Number
Ones
Tenths
Hundredths
Thousandths
3.405
3
4
0
5
3.45
3
4
5
0
Worked examples
Tens
Ones
Tenths
Hundredths
Thousandths
Digit
6
0
0
8
2
Value
60
0
0
0.08
0.002
Write 60.082 in expanded form. The digits are 6 tens, 0 ones, 0 tenths, 8 hundredths and 2 thousandths. So 60.082 = 60 + 0.08 + 0.002. The zeros add nothing, so they do not appear. Check: 60 + 0.08 + 0.002 = 60.082.
Runner
Ones
Tenths
Hundredths
Thousandths
Mina
2
7
5
0
Karim
2
7
0
5
Youssef
2
7
0
0
In a race Mina ran 2.75 km, Karim ran 2.705 km and Youssef ran 2.7 km. The ones and the tenths are equal. In the hundredths place the digits are 7, 0 and 0, so Mina ran farthest. Karim and Youssef: 2.7 = 2.700, and in the thousandths place 5 > 0, so Karim ran farther than Youssef. Order: 2.75 > 2.705 > 2.7.
Is 0.4 greater than 0.39? Some children say no because 39 is bigger than 4. But compare place by place: in the tenths place 4 > 3, so 0.4 > 0.39. Writing 0.4 as 0.40 shows it: 40 hundredths against 39 hundredths. On the number line 0.4 is to the right of 0.39.
Class activity
Decimal duel. Each player draws four number cards from 0 to 9 and makes a decimal with a whole part of one digit and three digits after the point (for example 6.037). Compare the two decimals aloud, place by place, and write the comparison with < or >. The player with the greater decimal scores a point. Play six rounds.
Practice
1
Write 7.049 in expanded form.
7 + 0.04 + 0.009.
2
Put <, > or = in each gap: 0.58 __ 0.508; 1.30 __ 1.3; 4.09 __ 4.1.
