Week 2 · Comparing, ordering and rounding big numbers · 3 lessons
1
Which big number wins?
Discover Mathematics P4: Term 1, Unit 1, Lessons 7–11
GoalCompare big numbers by their digits, places and forms, and write the answer with < , > or =.
New words
compare · to decide which number is greater, smaller or equalgreater than (>) · the open side of the sign faces the bigger numberless than (<) · the pointed end of the sign faces the smaller number
Explanation
To compare two numbers, use two steps. First count the digits. The number with more digits is greater, because its first digit stands in a higher place. If both have the same number of digits, compare from the left, place by place. Stop at the first place where the digits are different: the bigger digit makes the bigger number. If every place matches, the numbers are equal. We write the answer with a sign: 5,000,000 > 900,000, 3,100 < 3,400 and 2,000 = 2,000. If the numbers are written in different forms, first change them all to standard form, then compare.
Number
Digits
Compare
82,450,000
8
8,245,000
7
82,450,000 > 8,245,000
Worked examples
Number
Digits
82,450,000
8
8,245,000
7
Compare 82,450,000 and 8,245,000. The first has 8 digits and the second has 7 digits. The number with more digits is greater, so 82,450,000 > 8,245,000.
Number
Millions
Thousands
Ones
4,572,310
4
572
310
4,572,130
4
572
130
Compare 4,572,310 and 4,572,130. Both have 7 digits. The millions and thousands periods are the same. In the ones period the hundreds digits differ: 3 and 1. Since 3 > 1, we write 4,572,310 > 4,572,130.
Number
Millions
Thousands
Ones
6,400,000
6
400
000
6,040,000
6
040
000
Aya has 6,000,000 + 400,000 LE written in expanded form. Hana has six million, forty thousand LE. Change both to standard form: 6,400,000 and 6,040,000. Both have 7 digits and the millions digits match. The hundred thousands digits are 4 and 0, and 4 > 0, so 6,400,000 > 6,040,000. Aya has more.
Class activity
Number battle with cards. Each player makes a seven-digit numeral from digit cards and writes it down. Players compare their numbers and the one with the greater number scores a point. Then each player writes the sign < , > or = between the two numbers.
Practice
1
Write < , > or = : 5,090,000 __ 5,900,000.
5,090,000 < 5,900,000 (the hundred thousands digits are 0 and 9).
