Alisa says it is easier to compare the numbers in set a (45,000, 1,025,680) instead of set b (492,111, 409,867). 1. What is one way you could construct an argument justifying whether Alissa conjecture is true? 2. Is Alisa's conjecture true? Justify your answer. 3. Alisa wrote a comparison for Set B using ten thousand place. Explain what strategy she could have used.

1. Set a has two numbers with different number of digits and set b has two number with same number of digits

2. Alissa conjecture is true

3. Her strategy is the number which has the greatest ten thousand place is the greatest number because hundred thousand place has same digit in both numbers

Step-by-step explanation:

* Lets explain how we can solve the problem

- Alisa says it is easier to compare the numbers in set

a (45,000, 1,025,680) instead of set b (492,111, 409,867)

∵ Set a has two numbers one of them 5-digit and the other is 7-digit

∵ Set b has two numbers both of them 6-digit

∴ We can decide whether Alissa conjecture is true or not

1. Set a has two numbers with different number of digits and set b

has two number with same number of digits

- Lets look to set a there are two numbers

45,000 and 1,025,680

∵ The first number formed fro 5 digits and the greatest place value

is ten thousands

∵ The second number formed from 7 digits and the greatest place

value is million

∴ The second number is greatest then the first number

- She did that without looking to the digits and compare them

- Lets look to set b there are two numbers

492,111 and 409,867

∵ The first number formed from six digits and the greatest place

value is hundred thousands

∵ The second number formed from six digits and the greatest place

value is hundred thousands

∴ The two numbers have same number of digits

∴ We must start to compare the digits from greatest place value

- She must compare the corresponding digits to find the greatest one

2. Alissa conjecture is true because she can compare the number in

set a by counting the number of digits but in set b she must

compare the corresponding digits

∵ The greatest place value is hundred thousands and the two

numbers have the same digit 4 in this place, so she must look

to the ten thousand place

∵ The ten thousands digit in the first number is 9

∵ The ten thousands digit in the second number is 0

∵ 9 > 0

∴ The first number is greater than the second number

3. Her strategy is the number which has the greatest ten thousand

place is the greatest number because hundred thousand place

has same digit in both numbers