All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 1 Lesson 7 Compare Decimals will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 5 Answer Key Chapter 1 Lesson 7 Compare Decimals
Example 1
Luis downloaded two songs onto his MP3 player. Which song is longer?
One Way Use a number line.
Numbers to the right are greater than numbers to the left.
Since 3.8 is to the right of 3.6, 3.8 
3.6.
Answer:
When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller.
The above-given decimals to compare are 3.6 and 3.8
The one’s place is the same and the tenth’s place is different.
So, 3.8 is greater than the 3.6
Symbolically, we can write as 3.8 > 3.6
Another Way Line up the decimal points.
Answer:
Example 2
Write <, >, or = in the below to make a true sentence.
8.69 8.6 ____ ← Annexa zero to the right of 8.6 so that it has the same number of decimal places
as 8.69.
Since 9 > 0 in the hundredths place, 8.69 8.6.
Answer:
When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller.
8.69 > 8.60
Put ‘0’ in the hundredth place. Now compare the digits.
Since 9 is greater than zero.
Symbolically, we write 8.69 > 8.60
Guided Practice
Plot each decimal on the number line.
Write <, >, or = in each to make a true sentence.
Talk Math
Describe how you know if two decimals are equivalent.
Answer:
Decimal numbers are those whose whole number part and the fractional part are separated by a decimal point. Two decimals are said to be equivalent when they have the same value. The equivalent decimals are considered as, unlike fractions.
Equivalent decimals:
Two decimals are equivalent when they have the same value. For example, 0.5, 0.50, and 0.500 cover the same space. Hence we can see that these two decimals have the same value. Hence, these are equivalent decimals.
Question 1.
0.5 0.7
Answer:
When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller.
– compare the digits in the tenth place because the one’s place is the same for both decimals.
– Continue comparing until the digits are different.
compare 5 and 7
5 is lesser than 7
So, symbolically we represent 0.5 < 0.7
Question 2.
4.40 4.44
Answer:
When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller.
– Compare the digits.
– The one’s place and tenth place are having the same values.
– Now compare the hundredths place 0 and 4
– 0 is less than 4
– So we write symbolically as 4.40 < 4.44
Independent Practice
Plot each decimal on the number line. Write <, >, or = in each to make a true sentence.
Question 3.
4.4 4.1 
Answer: >
Explanation:
– compare the digits
– The one’s place is having the same digit. So compare the next digit.
– The tenth place is having the digits 4 and 1
– 4 is greater than 1
– Therefore, 4.4 is greater than 4.1
– Symbolically, 4.4 > 4.1
Question 4.
0.37 0.39 
Answer: <
Explanation:
– Compare the digits.
– The one’s place and tenth place are having the same values.
– Now compare the hundredths place 7 and 9
– 7 is less than 9
– So we write symbolically as 0.37 < 0.39
Question 5.
0.57 0.65 
Answer: <
Explanation:
– Compare the digits
– The one’s digit is the same for both numbers.
– Now compare the next digits. Compare the digits in the tenths place value.
– The digits are 5 and 6.
– 5 is less than 6
– Therefore, 0.57 is less than 0.65
– Symbolically, we can write 0.57 < 0.65
Write <, >, or = in each 
to make a true sentence.
Question 6.
2.15 2.150
Answer:
When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller.
The above-given digits are 2.15 and 2.150
– Here what we do is we put ‘0’ in the hundredth place in the first number.
– So, the numbers are 2.150 and 2.150
– Compare the digits.
– The digits in the place values are the same.
– Therefore, 2.150 is equal to 2.150
– Symbolically, we can write 2.150 = 2.150
Question 7.
0.006 0.1
Answer: <
Explanation:
When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller.
– The above-given digits are 0.006 and 0.1
– Now compare the digits
– The digit is the same in the one’s place value.
– Now compare the next digit that is 0 and 1
– 0 is less than 1. So 0.006 is less than 0.1
– Symbolically, we can write as 0.006 < 0.1
Question 8.
0.652 0.64
Answer: >
Explanation:
When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller.
– The above-given digits are 0.652 and 0.64
– The one’s and tenths digits are the same. Now compare the next digit that is present in the hundredth place.
– 5 and 4. 5 is greater than 4.
– Symbolically, we can write as 0.652 > 0.64
Question 9.
0.09 0.001
Answer:
When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller.
– The above-given digits are 0.09 and 0.001
– The one’s and tenths digits are the same. Now compare the next digit that is present in the hundredth place.
– 9 and 0. 9 is greater than 0.
– Symbolically, we can write as 0.09 > 0.001
Question 10.
7.31 7.304
Answer: >
Explanation:
When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller.
– The above-given digits are 7.31 and 7.304
– The one’s and tenths digits are the same. Now compare the next digit that is present in the hundredth place.
– 1 and 0. 1 is greater than 0.
– Symbolically, we can write as 7.31 > 7.304
Question 11.
2.800 2.8
Answer: =
Explanation:
When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller.
The above-given digits are 2.800 and 2.8
– Here what we do is we put ‘0’ in the hundredth place and the thousandth place in the second number.
– So, the numbers are 2.800 and 2.800
– Compare the digits.
– The digits in the place values are the same.
– Therefore, 2.800 is equal to 2.800
– Symbolically, we can write 2.800 = 2.800
Question 12.
0.5 0.7
Answer: <
Explanation:
When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller.
– The above-given digits are 0.5 and 0.7
– Now compare the digits
– The digit is the same in the one’s place value.
– Now compare the next digit which is 5 and 7
– 5 is less than 7. So 0.5 is less than 0.7
– Symbolically, we can write as 0.5 < 0.7
Question 13.
0.62 0.26
Answer: >
Explanation:
When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller.
– The above-given digits are 0.62 and 0.26
– Now compare the digits
– The digit is the same in the one’s place value.
– Now compare the next digit which is 6 and 2
– 6 is greater than 2. So 0.62 is greater than 0.26
– Symbolically, we can write as 0.62 > 0.26
Question 14.
3.7 3.70
Answer: =
Explanation:
When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller.
The above-given digits are 3.7 and 3.70
– Here what we do is we put ‘0’ in the hundredth place in the first number.
– So, the numbers are 3.70 and 3.70
– Compare the digits.
– The digits in the place values are the same.
– Therefore, 3.70 is equal to 3.70
– Symbolically, we can write 3.70 = 3.70
Problem Solving
For Exercises 15—17, use the table that shows the cost of posters of famous works of art.
Question 15.
Does the poster Relativity or the poster Women and Bird in the Night cost more?
Answer:
The cost of poster relativity = 11.49
The cost of women and Birds in the night = 18.98
Now compare the decimals.
– The digits are the same in the one’s place. Now compare the next digits.
– 8 and 1. 8 is greater than 1.
– So, 18.98 > 11.49
Therefore, Women and Birds in the Night cost is more.
Question 16.
Which poster costs less: From the Lake, No. 1 or Waterlillies?
Answer:
The cost of Lake, No. 1 = 16.99
The cost of waterlilies = 15.99
– Now compare the digits
– The one’s place digits are the same. Now compare the next digits.
– we need to write the less cost.
– 5 and 6. 5 is less than 6
– 15.99 < 16.99
Therefore, waterlilies are less cost.
Question 17.
Which poster costs less than Waterlillies?
Answer:
The cost of waterlilies = 15.99
Now observe the above-given box and write the cost which is less than 15.99
Relativity is having a less cost compared to all.
The cost of relativity = 11.49
Therefore, the answer is relativity.
Hot Problems
Question 18.
Mathematical PRACTICE 6 Explain to a Friend How many times greater is 46 than 0.46? Explain to a classmate.
Answer:
100 times greater; The value of each place is 10 times the value of the place to its right.
Question 19.
?Building on the Essential Question What are the similarities and differences between comparing whole numbers and comparing decimals?
Answer:
You can use a number line or place value to compare.
– When comparing the whole numbers, line up the digits starting with the one’s place.
– When comparing the decimals, line up the decimal points.
McGraw Hill My Math Grade 5 Chapter 1 Lesson 7 My Homework Answer Key
Practice
Write <, >, or = in each 
to make a true sentence.
Question 1.
3.976 4.007
Answer: <
Explanation:
When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller.
– The above-given digits are 3.976 and 4.007
– Now compare the digits
– The digits in the one’s place are 3 and 4
– 3 is less than 4. So, 3.976 is less than 4.007
– Symbolically, 3.976 < 4.007
Question 2.
89.001 89.100
Answer: <
Explanation:
When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller.
– The above-given digits are 89.001 and 89.100
– The one’s and tenths digits are the same. Now compare the next digit that is present in the hundredth place.
– 0 and 1. 0 is less than 1.
– Symbolically, we can write as 89.001 < 89.100
Question 3.
126.698 126.689
Answer: >
Explanation:
When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller.
– The above-given digits are 126.698 and 126.689
– The one’s, tenths, and hundredth digits are the same. Now compare the next digit.
– 9 and 8. 9 is greater than 8.
– Symbolically, we can write as 126.698 > 126.689
Question 4.
5.05 5.050
Answer: =
Explanation:
When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller.
The above-given digits are 5.05 and 5.050
– Here what we do is we put ‘0’ in the thousandth place in the first number.
– So, the numbers are 5.050 and 5.050
– Compare the digits.
– The digits in the place values are the same.
– Therefore, 5.050 is equal to 5.050
– Symbolically, we can write 5.050 = 5.050
Question 5.
9.087 9.807
Answer: <
Explanation:
When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller.
– The above-given digits are 9.087 and 9.807
– Now compare the digits
– The digits in the one’s place are the same.
– 0 is less than 8. So, 9.087 is less than 9.807
– Symbolically, 9.087 < 9.808
Question 6.
3.674 6.764
Answer: <
Explanation:
When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller.
– The above-given digits are 3.674 and 6.764
– Now compare the digits
– The digits in the one’s place are 3 and 6
– 3 is less than 6. So, 3.674 is less than 6.764
– Symbolically, 3.674 < 6.764
Question 7.
0.256 0.256
Answer: =
Explanation:
When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller.
– The above-given digits are 0.256 and 0.256
– Now compare the digits
– both are equal
– Symbolically, 0.256 = 0.256
Question 8.
2.7 2.82
Answer: <
Explanation:
When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller.
– The above-given digits are 2.7 and 2.82
– Now compare the digits
– The digit is the same in the one’s place value.
– Now compare the next digit which is 7 and 8
– 7 is less than 8. So 2.7 is less than 2.82
– Symbolically, we can write as 02.7 < 2.82
Question 9.
6.030 6.03
Answer: =
Explanation:
When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller.
The above-given digits are 6.030 and 6.03
– Here what we do is we put ‘0’ in the thousandth place in the second number.
– So, the numbers are 6.030 and 6.030
– Compare the digits.
– The digits in the place values are the same.
– Therefore, 6.030 is equal to 6.030
– Symbolically, we can write 6.030 = 6.030
Question 10.
7.89 7.189
Answer: >
Explanation:
When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller.
– The above-given digits are 7.89 and 7.189
– Now compare the digits
– The digit is the same in the one’s place value.
– Now compare the next digit which is 8 and 1
– 8 is greater than 1. So 7.89 is greater than 7.189
– Symbolically, we can write as 7.89 > 7.189
Question 11.
12.54 1.254
Answer: >
Explanation:
When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller.
– The above-given digits are 12.54 and 1.254
– Now compare the digits
– The digit is the same in the tenth place value.
– Now compare the next digit which is 2 and 0
– 2 is greater than 0. So 12.54 is greater than 1.254
– Symbolically, we can write as 12.54 > 1.254
Question 12.
0.981 2.3
Answer: <
Explanation:
When you compare the decimals, you need to check the digits before the decimal point and check if they are smaller than or greater than the other number. Second, if the digits before the decimal point are identical, you have to compare the first digit after the decimal point, which is the tenth digit and identify which is greater or smaller.
– The above-given digits are 0.981 and 2.3
– Now compare the digits
– The digits in the one’s place are 0 and 2
– 0 is less than 2. So, 0.981 is less than 2.3
– Symbolically, 0.981 < 2.3
Problem Solving
Question 13.
In January, the average low temperature in Montreal, Quebec, Canada, is 5.2°F. The average low temperature in Cape Town, South Africa, is 60.3°F. Which city is warmer in January?
Answer:
The average low temperature in January was 5.2
The average low temperature in Cape town = is 60.3
compared to both temperatures, Cape Town, South Africa city warmer in January.
Question 14.
In one year Detroit, Michigan, recorded 30.9 inches of snow and Chicago, Illinois, recorded 39.9 inches of snow. Which city had more snow?
Answer:
The snow recorded in Detroit, Michigan = 30.9
The snow recorded in Chicago, Illinois = 39.9
Now compare the digits.
– The one’s place digits are the same. Now compare the next digits.
– 0 and 9. 9 is greater than 0.
– So, 39.9 is greater than 30.9
Therefore, Chicago and Illinois cities are having more snow.
Question 15.
Mathematical PRACTICE 6 Explain to a Friend George was weighed at the doctor’s office. The scale read 67.20 pounds. The doctor wrote 67.2 pounds on George’s chart. Did the doctor make a mistake? Explain to a friend.
Answer:
no, if the zero after the decimal doesn’t have a number other than zero on either side then it’s insignificant. (or)
No, it wasn’t a mistake. 67.2 pounds is the actual weight of the doctor. He simply had to write it down the way he wanted, instead of writing 67.20.
Question 16.
The two fastest times in the past 20 years for the girls’ 200-meter run at Clarksville Elementary School are 27.97 seconds and 27.93 seconds. At yesterday’s track meet, Claire ran 27.99 seconds.
Was her time faster than either of the two fastest? Explain.
Answer:
Her time was 0.02 seconds short of being equal to the 2nd fastest time. In conclusion, no, she was slower. (or)
– No. She didn’t beat the record as she was 0.03 seconds short of beating the 2nd fastest, and 0.07 seconds for the 1st fastest.
Vocabulary Check
Question 17.
Write if the following statement is true or false.
Equivalent decimals are decimals that have the same value. ____
Answer: True
Two decimals are equivalent when they have the same value. For example, 0.5, 0.50, and 0.500 cover the same space. Hence we can see that these two decimals have the same value. Hence, these are equivalent decimals.
Test Practice
Question 18.
Which of the following symbols make the statement below true?
98.546 
98.654
A. < B. >
C. =
D. ≥
Answer: Option A is correct.
– The above-given numbers are 98.546 and 98.654
– The first two digits are the same. Now compare the next digit.
– 5 and 6. 5 is less than 6
– So, 98.546 is less than 98.654
– Symbolically, we can write as 98.546 < 98.654