All the solutions provided in McGraw Hill My Math Grade 4 Answer Key PDF Chapter 10 Lesson 7 Compare and Order Decimals will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 4 Answer Key Chapter 10 Lesson 7 Compare and Order Decimals
To compare decimals, you can use a number line or place value.
Math in My World
Example 1
At recess, Austin and his friends decided to have two races. One was 0.2 mile, and the other was 0.4 mile. Which race was longer?
One Way:
Use a number line.
Graph 0.4 and 0.2.
0.4 is to the right of 0.2.
So, 0.4 > 0.2.
Another Way:
Use place value.
Line up the decimal points. Then compare the digits in each place-value position.
In the tenths place, 4 > 2.
So, 0.4 > 0.2.
So, the longer race was the one that was ____________.
Notice that you can only compare 0.4 and 0.2 because they refer to the same whole, which is one mile.
Answer: 0.4
Example 2
Order 0.15, 0.38, and 0.3 from greatest to least
1. Line up the decimal points.
2. Place a zero to the right of 0.3 so all the numbers have the same number of decimal places.
3. Compare the digits in each place-value position.
In the tenths place, 1 < 3. So, 0.15 is the least decimal. In the hundredths place, 8 > 0. So, 0.38 is the greatest decimal.
The order from greatest to least is ____________, _____________ and ____________.
Check:
Answer: 0.38, 0.3 and 0.15
Talk Math
Explain how to compare 0.4 and 0.40.
Answer: 0.4 = 0.40
Before comparing, place a zero to the right of 0.4 so both the numbers have the same number of decimal places.
Now, compare the digits in each place-value position.
Here, In the tenths place, 4=4. So, in hundredths place, 0=0.
So, 0.4 = 0.40
In other way,
0.4 and 0.40 are equivalent numbers. As 0.4 is noted as 4 tenths, which is 4 divided by 10. Similarly, 0.40 is noted as 40 hundredths, which is 40 divided by 100. Therefore, both the values are same and they are equivalent numbers.
Guided Practice
Compare. Use >, <, or =.
Question 1.
0.2 
0.6
Answer: 0.2 < 0.6
compare the digits in each place-value position.
Here, In the tenths place, 2 < 6.
So, 0.2 < 0.6.
Question 2.
0.4 0.04
Answer: 0.4 > 0.04
Before comparing, place a zero to the right of 0.4 so both the numbers have the same number of decimal places.
Now, compare the digits in each place-value position.
Here, In the tenths place, 4 > 0.
So, 0.4 > 0.04
Question 3.
0.6 0.60
Answer: 0.6 = 0.60
Before comparing, place a zero to the right of 0.6 so both the numbers have the same number of decimal places.
Now, compare the digits in each place-value position.
Here, In the tenths place, 6=6. So, in hundredths place, 0=0.
So, 0.6 = 0.60
Question 4.
0.57 0.7
Answer: 0.57 < 0.7
Before comparing, place a zero to the right of 0.7 so both the numbers have the same number of decimal places.
Now, compare the digits in each place-value position.
Here, In the tenths place, 5 < 7.
So, 0.57 < 0.7
Order from greatest to least.
Question 5.
0.2, 0.02, 0.4
Answer: 0.4, 0.2, 0.02
Place a zero to the right of 0.2 and 0.4 so all the numbers have the same number of decimal places.
0.20, 0.02, 0.40
Now, Compare the digits in each place-value position.
In the tenths place, 0 is less than 2 & 4. So, 0.02 is the least decimal. In between 0.2 and 0.4, 2 in tenths place is less than 4. So, 0.4 is the greatest decimal.
Question 6.
0.51, 0.34, 0.46
Answer: 0.51, 0.46, 0.34
Compare the digits in each place-value position.
In the tenths place, 3 is less than 4 &5. So, 0.34 is the least decimal. In between 0.46 and 0.51, 4 in tenths place is less than 5. So, 0.51 is the greatest decimal.
Independent Practice
Compare. Use >, <, or =. Draw a number line to check your work.
Question 7.
0.5 0.7
Answer: 0.5 < 0.7
compare the digits in each place-value position.
Here, In the tenths place, 5 < 7.
So, 0.5 < 0.7
Question 8.
0.56 0.58
Answer: 0.56 < 0.58
compare the digits in each place-value position.
Here, In the tenths place, 5 = 5. So, in hundredths place, 6 < 8.
So, 0.56 < 0.58
Question 9.
0.8 0.80
Answer: 0.8 = 0.80
Before comparing, place a zero to the right of 0.8 so both the numbers have the same number of decimal places.
Now, compare the digits in each place-value position.
Here, In the tenths place, 8=8. So, in hundredths place, 0=0.
So, 0.8 = 0.80
Question 10.
0.38 0.3
Answer: 0.38 > 0.3
Before comparing, place a zero to the right of 0.3 so both the numbers have the same number of decimal places.
Now, compare the digits in each place-value position.
Here, In the tenths place, 3 =3. So, in hundredths place, 8 > 0.
So, 0.38 > 0.3
Question 11.
0.90 0.9
Answer: 0.90 = 0.9
Before comparing, place a zero to the right of 0.9 so both the numbers have the same number of decimal places.
Now, compare the digits in each place-value position.
Here, In the tenths place, 9=9. So, in hundredths place, 0=0.
So, 0.90 = 0.9
Question 12.
0.2 0.02
Answer: 0.2 > 0.02
Before comparing, place a zero to the right of 0.2 so both the numbers have the same number of decimal places.
Now, compare the digits in each place-value position.
Here, In the tenths place, 2 > 0.
So, 0.2 > 0.02
Question 13.
0.87 0.78
Answer: 0.87 > 0.78
compare the digits in each place-value position.
Here, In the tenths place, 8 > 7.
So, 0.87 > 0.78
Question 14.
0.48 0.5
Answer: 0.48 < 0.5
Before comparing, place a zero to the right of 0.5 so both the numbers have the same number of decimal places.
Now, compare the digits in each place-value position.
Here, In the tenths place, 4 < 5.
So, 0.48 < 0.5
Question 15.
0.07 0.7
Answer: 0.07 < 0.7
Before comparing, place a zero to the right of 0.7 so both the numbers have the same number of decimal places.
Now, compare the digits in each place-value position.
Here, In the tenths place, 0 < 7.
So, 0.07 < 0.7
Order from least to greatest.
Question 16.
0.5, 0.55, 0.6
Answer: 0.5, 0.55, 0.6
Place a zero to the right of 0.5 and 0.6 so all the numbers have the same number of decimal places.
0.50, 0.55, 0.60
Now, Compare the digits in each place-value position.
In the tenths place, 5 < 6 and in hundredths place, 0 < 5. So, 0.5 is the least decimal and 0.6 is the greatest decimal.
Question 17.
0.35, 0.53, 0.3
Answer: 0.3, 0.35, 0.53
Place a zero to the right of 0.3 so all the numbers have the same number of decimal places.
0.35, 0.53, 0.30
Now, Compare the digits in each place-value position.
In the tenths place, 3 < 5 and in hundredths place, 0 < 5. So, 0.3 is the least decimal and 0.53 is the greatest decimal.
Question 18.
0.38, 0.4, 0.36
Answer: 0.36, 0.38, 0.4
Place a zero to the right of 0.4 so all the numbers have the same number of decimal places.
0.36, 0.38, 0.40
Now, Compare the digits in each place-value position.
In the tenths place, 3 < 4 and in hundredths place, 6 < 8. So, 0.36 is the least decimal and 0.4 is the greatest decimal.
Question 19.
0.16, 0.6, 0.61
Answer: 0.16, 0.6, 0.61
Place a zero to the right of 0.6 so all the numbers have the same number of decimal places.
0.16, 0.60, 0.61
Now, Compare the digits in each place-value position.
In the tenths place, 1 < 6. So, 0.16 is the lease decimal. In hundredths place, 0 < 1. So, 0.61 is the greatest decimal.
Circle whether each statement is true or false. Use the number line to compare.
Question 20.
0.46 > 0.48
true
false
Answer: False
0.48 is to the right of 0.46.
So, 0.46 < 0.48.
Question 21.
0.49 > 0.43
true
false
Answer: True
0.49 is to the right of 0.43.
So, 0.49 > 0.43.
Question 22.
0.42 > 0.47
true
false
Answer: False
0.47 is to the right of 0.42.
So, 0.47 > 0.42.
Question 23.
0.50 < 0.45
true
false
Answer: False
0.50 is to the right of 0.45.
So, 0.50 > 0.45.
Problem Solving
Question 24.
The distance from Scarlett’s house to the elementary school is 0.3 mile. The distance from Scarlett’s house to the middle school is 0.9 mile. Which distance is shorter?
Answer: The distance from Scarlett’s house to the elementary school is shorter, which is 0.3 mile.
The distance from Scarlett’s house to the elementary school = 0.3
The distance from Scarlett’s house to the middle school = 0.9
Compare the digits in each place-value position,
In tenths place, 3 < 9. So, 0.3 < 0.9.
Therefore, The distance from Scarlett’s house to the elementary school is shorter.
Question 25.
On a vegetable tray, 0.5 of the vegetables are carrots and 0.2 of the vegetables are broccoli. Of what vegetable is there more?
Answer: carrots are more, which is 0.5
0.5 of the vegetables are carrots and 0.2 of the vegetables are broccoli
Compare the digits in each place-value position,
In tenths place, 5 > 2. So, 0.5 > 0.2.
Therefore, carrots are more.
HOT Problems
Question 26.
Mathematical PRACTICE Use Number Sense What number is halfway between 0.36 and 0.48 on a number line?
Answer: 0.42
It is 0.06 more than 0.36 and 0.06 less than 0.48
To find a halfway point (which is also the average), add the numbers together and divide by 2.
0.36 + 0.48 = 0.84 and the halfway point is 0.42
Question 27.
Mathematical PRACTICE Find the Error Miles wrote the 3 numbers below in order from least to greatest. Find and correct his mistake.
Answer: \(\frac{19}{100}\), 0.27, 0.29 is the correct order from least to greatest
\(\frac{19}{100}\) = 0.19 in decimal
Now, 0.27, 0.19, 0.29
Compare the digits in each place-value position,
In tenths place, 1 < 2, So, 0.19 is the least number. In hundredths place, 7 > 9, So, 0.29 is the greatest number.
Therefore, \(\frac{19}{100}\), 0.27, 0.29 is the correct order from least to greatest
Question 28.
Building on the Essential Question How can I use models to compare decimals?
Answer: There are few simple models we can use to compare decimals. They are mentioned below:
1) Using number line:
Indicate the numbers that you want to compare on the number line. The numbers which are on the right when compared to adjacent indicated number is noted as greatest number. Observe example 1 for better understanding.
2) Using place value:
Line up the decimal points in the place value chart. Then compare the digits of every number in each place-value position such as in tenths place, hundredths place and so on. Observe example 1 for better understanding.
McGraw Hill My Math Grade 4 Chapter 10 Lesson 7 My Homework Answer Key
Practice
Compare. Use >, <, or =.
Question 1.
0.9 0.4
Answer: 0.9 > 0.4
compare the digits in each place-value position.
Here, In the tenths place, 9 > 4.
So, 0.9 > 0.4
Question 2.
0.32 0.37
Answer: 0.32 < 0.37
compare the digits in each place-value position.
Here, In the tenths place, 3 = 3. So, in hundredths place, 2 < 7.
So, 0.32 < 0.37
Question 3.
0.9 0.90
Answer: 0.9 = 0.90
Before comparing, place a zero to the right of 0.9 so both the numbers have the same number of decimal places.
Now, compare the digits in each place-value position.
Here, In the tenths place, 9=9. So, in hundredths place, 0=0.
So, 0.90 = 0.9
Order from least to greatest.
Question 4.
0.7, 0.27, 0.43
Answer: 0.27, 0.43, 0.7
Place a zero to the right of 0.7 so all the numbers have the same number of decimal places.
0.70, 0.27, 0.43
Now, Compare the digits in each place-value position.
In the tenths place, 2 < 4 < 7. So, 0.27 is the lease decimal and 0.7 is the greatest decimal.
Question 5.
0.4, 0.22, 0.72
Answer: 0.22, 0.4, 0.72
Place a zero to the right of 0.4 so all the numbers have the same number of decimal places.
0.40, 0.22, 0.72
Now, Compare the digits in each place-value position.
In the tenths place, 2 < 4 < 7. So, 0.22 is the lease decimal and 0.72 is the greatest decimal.
Problem Solving
Question 6.
Eli lives 0.7 mile from his school. He lives 0.25 mile from his friend’s house. Does Eli live closer to his school or his friend’s house?
Answer: Eli lives closer to his friend’s house, which is 0.25 mile
Eli lives 0.7 mile from his school.
Eli lives 0.25 mile from his friend’s house.
Now, compare both the numbers 0.7 and 0.25
Place a zero to the right of 0.7 so both the numbers have the same number of decimal places.
By comparing the digits in each place-value position, in tenths place, 2 < 7. So, 0.25 is the closest distance.
Question 7.
Alana spent 0.35 of a dollar on a ring at the arcade and 0.72 of a dollar on a snack. Did Alana spend more on the ring or the snack?
Answer: Alana spent more on snack, which is 0.72 dollar
Alana spent 0.35 of a dollar on a ring at the arcade and 0.72 of a dollar on a snack
Now, compare both the numbers 0.35 and 0.72
By comparing the digits in each place-value position, in tenths place, 3 < 7. So, she spent more on snack, which is 0.72
Question 8.
Mathematical PRACTICE Identify Structure Tristan has a box of toys. Four out of 100 toys are red, 0.52 of the toys are green, and 0.1 of the toys are blue. Write the decimals in order from greatest to least.
Answer: 0.52, 0.1, 0.04
Four out of 100 toys = 0.04 are red
0.52 of the toys are green
0.1 of the toys are blue
Place a zero to the right of 0. so all the numbers have the same number of decimal places.
0.04, 0.52, 0.10
Now, Compare the digits in each place-value position.
In the tenths place, 0 < 1 < 5. So, 0.04 is the lease decimal and 0.52 is the greatest decimal.
Question 9.
Mathematical PRACTICE Model Math Write a real-world problem that compares 0.4 and 0.29. Then solve the problem.
Answer: Emili spent 0.4 of a dollar on a toy and she spent 0.29 dollar on a candy. Which one you think she spent the most of a dollar?
compare both the numbers 0.4 and 0.29
By comparing the digits in each place-value position, in tenths place, 4 > 2. So, she spent more on a toy, which is 0.4 of a dollar.
Test Practice
Question 10.
Which decimals are ordered from least to greatest?
(A) 0.25, 0.9, 0.35
(B) 0.9, 0.25, 0.35
(C) 0.25, 0.35, 0.9
(D) 0.9, 0.35, 0.25
Answer: C (0.25, 0.35, 0.9)
Place a zero to the right of 0.9 so all the numbers have the same number of decimal places.
0.25, 0.35, 0.90
Now, Compare the digits in each place-value position.
In the tenths place, 2 < 3 < 9. So, 0.25, 0.35, 0.9 are ordered from least to greatest.