The question
Question: which is bigger, 0.7 or 0.65?
0.7 or 0.65
1 Same number of digits
Zeros at the end of a decimal do not change it: 0.7 is the same as 0.70.
So we give every number 2 digits after the point.
= 0.70, 0.65
2 Compare
Now both have 2 digits after the point.
So we can forget the point and compare them like whole numbers: 65 < 70.
= 0.65 < 0.70
65 < 70
Careful!
More digits does not mean bigger.
Compare 0.65 with 0.70.
Careful: not 0.65 > 0.7 ✗
3 Write the answer
Now with the numbers as they were given: 0.65 < 0.7.
So 0.7 is bigger.
= 0.65 < 0.7
4 Check
Let's check on a number line.
Smaller numbers are further to the left.
We put a dot for each number.
From left to right: 0.65, 0.7.
The same order.
So the answer is right!
left to right: same order
Let's look back.
First: same number of digits.
Then: compare.
Then: write the answer.
Last: check.
▶ Watch it solved
The question
Question: compare −0.4 and −0.35.
−0.4 and −0.35
1 Same number of digits
Zeros at the end of a decimal do not change it: −0.4 is the same as −0.40.
So we give every number 2 digits after the point.
= −0.40, −0.35
2 Compare
Negative numbers are below 0.
40 > 35, so −0.40 is further below 0.
Further below 0 means smaller.
= −0.40 < −0.35
40 > 35: further below 0
Careful!
0.4 is more than 0.35.
But −0.4 is further below 0, so it is smaller.
Careful: not −0.4 > −0.35 ✗
3 Write the answer
Now with the numbers as they were given: −0.4 < −0.35.
−0.4 is less than −0.35.
= −0.4 < −0.35
4 Check
Let's check on a number line.
Smaller numbers are further to the left.
We put a dot for each number.
From left to right: −0.4, −0.35.
The same order.
So the answer is right!
left to right: same order
Let's look back.
First: same number of digits.
Then: compare.
Then: write the answer.
Last: check.
▶ Watch it solved
The question
Question: put 0.4, 3/8, −1/2, 3/5 in order, from smallest to largest.
0.4, 38, −12, 35
1 Write each as a decimal
To compare, we write every number the same way: as a decimal.
A decimal is tenths, hundredths or thousandths.
8 times 125 is 1000.
So we multiply the top and the bottom by 125.
375 thousandths is 0.375.
So 3/8 is 0.375.
= 38 = 3 × 1258 × 125 = 3751000 = 0.375
2 times 5 is 10.
So we multiply the top and the bottom by 5.
5 tenths is 0.5.
The minus sign stays in front: −0.5.
= −12 = −1 × 52 × 5 = −510 = −0.5
5 times 2 is 10.
So we multiply the top and the bottom by 2.
6 tenths is 0.6.
So 3/5 is 0.6.
= 35 = 3 × 25 × 2 = 610 = 0.6
2 Same number of digits
Zeros at the end of a decimal do not change it: 0.4 is the same as 0.400.
So we give every number 3 digits after the point.
= 0.400, 0.375, −0.500, 0.600
3 Compare
Now they all have 3 digits after the point.
So we can forget the point and compare them like whole numbers: 375 < 400 < 600.
= 0.375 < 0.400 < 0.600
375 < 400 < 600
Careful!
More digits does not mean bigger.
Compare 0.375 with 0.400.
Careful: not 0.375 > 0.4 ✗
Negative numbers are smaller than every positive number.
So they come first.
= −0.500 < 0.375 < 0.400 < 0.600
4 Write the answer
Now we write the numbers as they were given, in the same order: −1/2, 3/8, 0.4, 3/5.
= −12 < 38 < 0.4 < 35
5 Check
Let's check on a number line.
Smaller numbers are further to the left.
We put a dot for each number.
From left to right: −1/2, 3/8, 0.4, 3/5.
The same order.
So the answer is right!
left to right: same order
Let's look back.
First: write each as a decimal.
Then: same number of digits.
Then: compare.
Then: write the answer.
Last: check.
Answer = −12 < 38 < 0.4 < 35
▶ Watch it solved
