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## Texas Go Math Grade 5 Lesson 1.4 Answer Key Compare and Order Decimals

**Unlock the Problem**

The table lists some of the mountains in the United States that are over two miles high. How does the height of Cloud Peak in Wyoming compare to the height of Boundary Peak in Nevada?

One Way

Use place value.

Line up the decimal points. Start at the left. Compare the digits in each place-value position until the digits are different.

Since 9 > 8, then 2.495 > 2.488, and 2.488 < 2.495.

So, the height of Cloud Peak is greater than the height of Boundary Peak.

Another Way

Use a place-value chart to compare

Compare the height of Cloud Peak to Wheeler Peak.

Since 5 > 3, then 2.495 > 2.493, and 2.493 < 2.495.

So, the height of Cloud Peak is greater than the height of Wheeler Peak.

**Math Talk**

**Mathematical Processes**

Explain why it is important to line up the decimal points when comparing decimals.

Answer:

Decimals extend the number system beyond the simple ‘hundreds, tens, units’ into ‘tenths of units’, ‘hundredths of units’ and so on. The most important rule to remember is to line up the decimal points in your calculation, ensuring that the decimal point in the answer also lines up with the decimal points above it

**Example**

Mount Whitney in California is 2.745 miles high, Mount Rainier in Washington * is 2.729 miles high, and Mount Harvard in Colorado is 2.731 miles high. Order the heights of these mountains from least to greatest. Which mountain has the least height? Which mountain has the greatest height?

STEP 1

Line up the decimal points. There are the same number of ones. Circle the tenths and compare.

2.745 Whitney

2.729 Rainier

2.731 Harvard

There are the same number of tenths.

STEP 2

Underline the hundredths and compare. Order from least to greatest.

2.745 Whitney

2.729 Rainier

2.731 Harvard

Since 2.729 < 2.731 < 2.745, the heights in order from least to greatest are 2.729, 2.731, 2.745.

So,

Rainier has the least height and Whitney has the greatest height.

**Math Talk**

**Mathematical Processes**

Explain why you do not have to compare the digits in the thousandths place to order the heights of the 3 mountains.

Answer:

We know that,

The place-value of “Hundredths” is greater than the place-value of “Thousandths”

Hence, from the above,

We can conclude that

Since the place-value of hundredths is greater than the thousandths, you do not have to compare the digits in the thousandths place to order the heights of the 3 mountains

**Share and Show**

Question 1.

Use the place-value chart to compare the two numbers. What is the greatest place-value position where the digits differ?

Answer:

The given place-value chart is:

Now,

From the given place-value chart,

We can observe that

The given decimal numbers are: 3.472 and 3.445

Now,

We know that,

The place-value of “Hundredths” is greater than the place-value of “Thousandths”

Now,

When we compare the place-values,

We can observe that

7 hundredths > 4 hundredths

Hence, from the above,

We can conclude that

The greatest place-value position where the digits differ is: Hundredths

**Compare. Write <, >, or =.**

Question 2.

4.563 4.536

Answer:

The given decimal numbers are: 4.563 and 4.536

Now,

We know that,

The place-value of “Hundredths” is greater than the place-value of “Thousandths”

Hence,

4.563 > 4.536

Question 3.

5.640 5.64

Answer:

The given decimal numbers are: 5.640 and 5.64

Now,

From the given numbers,

We can observe that

All the place-values are the same

Hence,

5.640 = 5.64

Question 4.

8.673 8.637

Answer:

The given decimal numbers are: 8.673 and 8.637

Now,

We know that,

The place-value of “Hundredths” is greater than the place-value of “Thousandths”

Hence,

8.673 > 8.637

**Name the greatest place-value position where the digits differ. Name the greater number.**

Question 5.

3.579; 3.564

Answer:

The given decimal numbers are: 3.579 and 3.564

Now,

We know that,

The place-value of “Hundredths” is greater than the place-value of “Thousandths”

Hence,

3.579 > 3.564

Question 6.

9.572; 9.637

Answer:

The given decimal numbers are: 9.572 and 9.637

Now,

We know that,

The place-value of “Tenths” is greater than the place-value of “Hundredths”

Hence,

9.572 < 9.637

Question 7.

4.159; 4.152

Answer:

The given decimal numbers are: 4.159 and 4.152

Now,

We know that,

The place-value of “Thousandths” is greater than the place-value of “Ten thousandths”

Hence,

4.159 > 4.152

**Problem Solving**

**Order from greatest to least.**

Question 8.

2.007; 2.714; 2.09; 2.97

Answer:

The given decimal numbers are: 2.007, 2.714, 2.09, and 2.97

Now,

We know that,

The place-value of “Tenths” is greater than the place-value of “Hundredths” is greater than the “Thousandths”

Hence, from the above,

We can conclude that

The order of numbers from the greatest to the least is: 2.97, 2.714, 2.09, and 2.007

Question 9.

0.386; 0.3; 0.683; 0.836

Answer:

The given decimal numbers are: 0.386, 0.3, 0.683, and 0.836

Now,

We know that,

The place-value of “Tenths” is greater than the place-value of “Hundredths” is greater than the “Thousandths”

Hence, from the above,

We can conclude that

The order of numbers from the greatest to the least is: 0.836, 0.683, 0.386, and 0.3

**H.O.T. Algebra** Find the unknown digit to make each statement true.

Question 10.

3.59 > 3.5 1 > 3.572

Answer:

Let the unknown digit be x

Hence, from the above,

We can conclude that

The unknown digit that make the given statement true is:

3.59 > 3.581 > 3.572

Where,

x = 0, 1, 2, ……. 8

Question 11.

6.837 > 6.83 > 6.835

Answer:

Let the unknown digit be x

Hence, from the above,

We can conclude that

The unknown digit that make the given statement true is:

6.837 > 6.836 > 6.835

Where,

x = 0, 1, 2, ……. 6

Question 12.

2.45 < 2. 6 < 2.461

Answer:

Let the unknown digit be x

Hence, from the above,

We can conclude that

The unknown digit that make the given statement true is:

2.45 < 2.46 < 2.461

Where,

x = 0, 1, 2, ……. 4

Question 13.

Dawn keeps track of her softball batting average each year. The first year, her batting average is .783. The second year, her batting average is .81. In which year did she have the greater batting average?

Answer:

It is given that

Dawn keeps track of her softball batting average each year. The first year, her batting average is .783. The second year, her batting average is .81

Now,

The given decimal numbers are: 0.783 and 0.81

Now,

We know that,

The place-value of “Tenths” is greater than the place-value of “Hundredths” is greater than the “Thousandths”

So,

0.81 > 0.783

Hence, from the above,

We can conclude that

In the second year, Dawn has the greatest batting average

**Problem Solving**

**Use the table for 14-16.**

Question 14.

**Use Math Language** How does the height of Steele Mountain compare to the height of Blackburn Mountain? Compare the heights using words.

Answer:

The given table is:

Now,

From the given table,

We can observe that

The height of Steele Mountain is: 3.152 miles

The height of Blackburn Mountain is: 3.104 miles

Now,

We know that,

The place-value of “Tenths” is greater than the place-value of “Hundredths” is greater than the “Thousandths”

So,

3.152 > 3.104

Hence, from the above,

We can conclude that

The height of Steele Mountain is greater than the height of Blackburn Mountain

Question 15.

**Write Math** Explain how to order the height of the mountains from greatest to least.

Answer:

The given table is:

Now,

We know that,

The place-value of “Tenths” is greater than the place-value of “Hundredths” is greater than the “Thousandths”

So,

The order of the heights from the greatest to the least is:

3.152 > 3.134 > 3.104

Hence, from the above,

We can conclude that

The order of the height of mountains from the greatest to the least is:

3.152 miles > 3.134 miles > 3.104 miles

Question 16.

**Multi-Step** What if the height of Blackburn Mountain were 0.05 mile greater. Would it then be the mountain with the greatest height? Explain.

Answer:

The given table is:

Now,

From the given table,

We can observe that

The height of the Blackburn Mountain is: 3.104 miles

The greatest height is: 3.152 miles

So,

The increased height of Blackburn Mountain = 0.05 + 3.104

= 3.154 miles

So,

3.154 miles > 3.152 miles

Hence, from the above,

We can conclude that

With the height of Blackburn Mountain 0.05 miles greater, Blackburn Mountain will have the greatest height

**Daily Assessment Task**

**Fill in the bubble completely to show your answer.**

Question 17.

The length of a piece of plastic for a science kit needs to be greater than 22.4 inches and less than 22.5 inches. Which length of plastic can be used?

A. 22.35 in

B. 22.51 in

C. 22.47 in.

D. 22.40 in.

Answer:

It is given that

The length of a piece of plastic for a science kit needs to be greater than 22.4 inches and less than 22.5 inches.

So,

The numbers ca also be written as: 22.40 inches and 22.50 inches

Hence, from the above,

We can conclude that

The length of the plastic that can be used is:

Question 18.

Louis is comparing the numbers 8.402 and 8.451. What is the least place value he needs to compare to decide which number is greater?

A. ones

B. tenths

C. hundredths

D. thousandths

Answer:

It is given that

Louis is comparing the numbers 8.402 and 8.451

Now,

The given numbers are: 8.402 and 8.451

Now,

We know that,

The place-value of “Tenths” is greater than the place-value of “Hundredths” is greater than the “Thousandths”

So,

We have to compare the hundredths place value to decide which number is greater

Hence, from the above,

We can conclude that

The least place value that he needs to compare to decide which number is greater is:

Question 19.

**Multi-Step** Melinda compares four numbers. Which shows the numbers from least to greatest?

A. 3.04; 3.10; 3.529; 3.685

B. 3.10; 3.04; 3.529; 3.685

C. 3.10; 3.04; 3.685; 3.529

D. 3.04; 3.685; 3.529; 3.10

Answer:

It is given that

Melinda compares four numbers

Now,

We know that,

The place-value of “Tenths” is greater than the place-value of “Hundredths” is greater than the “Thousandths”

Hence, from the above,

We can conclude that

The numbers that have the order from the least to the greatest is:

**Texas Test Prep**

Question 20.

Mount Logan in the Yukon is 3.702 miles high. Mount McKinley in Alaska is 3.848 miles high and Pico de Orizaba in Mexico is 3.571 miles high. Order these mountains by height from greatest to least.

A. Logan, McKinley, Pico de Orizaba

B. McKinley, Logan, Pico de Orizaba

C. Pico de Orizaba, Logan, McKinley

D. Logan, Pico de Orizaba, McKinley

Answer:

It is given that

Mount Logan in the Yukon is 3.702 miles high. Mount McKinley in Alaska is 3.848 miles high and Pico de Orizaba in Mexico is 3.571 miles high

Now,

The given decimal numbers are: 3.702, 3.848, and 3.571

Now,

We know that,

The place-value of “Tenths” is greater than the place-value of “Hundredths” is greater than the “Thousandths”

So,

The order of the numbers from the greatest to the least is:

3.848 > 3.702 > 3.571

Hence, from the above,

We can conclude that

The height of the mountains fro the least to the greatest is:

### Texas Go Math Grade 5 Lesson 1.4 Homework and Practice Answer Key

**Compare. Write <, >, or =.**

Question 1.

9.23 9.32

Answer:

The given decimal numbers are: 9.23 and 9.32

Now,

We know that,

The place-value of “Tenths” is greater than the place-value of “Hundredths”

Hence,

9.23 < 9.32

Question 2.

7.20 7.2

Answer:

The given decimal numbers are: 7.20 and 7.2

Now,

We know that,

The number that has the last digit zero and the same number that does not have the last digit zero are the same

Hence,

7.20 = 7.2

Question 3.

1.994 1.493

Answer:

The given decimal numbers are: 1.994 and 1.493

Now,

We know that,

The place-value of “Tenths” is greater than the place-value of “Hundredths”

Hence,

1.994 > 1.493

**Order from greatest to least.**

Question 7.

7.081; 7.81; 7.002; 7.14

Answer:

The given decimal numbers are: 7.081, 7.81, 7.002, and 7.14

Now,

We know that,

The place-value of “Tenths” is greater than the place-value of “Hundredths” is greater than the “Thousandths”

Hence, from the above,

We can conclude that

The order of numbers from the greatest to the least is: 7.81, 7.14, 7.081, and 7.002

Question 8.

1.001; 1.1; 1.403; 1.078

Answer:

The given decimal numbers are: 1.001, 1.1, 1.403, and 1.078

Now,

We know that,

The place-value of “Tenths” is greater than the place-value of “Hundredths” is greater than the “Thousandths”

Hence, from the above,

We can conclude that

The order of numbers from the greatest to the least is: 1.403, 1.1, 1.078, and 1.001

Question 9.

0.04; 0.5; 0.021; 0.133

Answer:

The given decimal numbers are: 0.04, 0.5, 0.021, 0.133

Now,

We know that,

The place-value of “Tenths” is greater than the place-value of “Hundredths” is greater than the “Thousandths”

Hence, from the above,

We can conclude that

The order of numbers from the greatest to the least is: 0.5, 0.133, 0.040, and 0.021

Question 10.

4; 4.022; 4.002; 4.221

Answer:

The given decimal numbers are: 4, 4.022, 4.002, and 4.221

Now,

We know that,

The place-value of “Tenths” is greater than the place-value of “Hundredths” is greater than the “Thousandths”

Hence, from the above,

We can conclude that

The order of numbers from the greatest to the least is: 4.221, 4.022, 4.002, and 4

**Problem Solving**

**Find the unknown digit to make each statement true,**

Question 11.

5.345 > 5.34 > 5.343

Answer:

Let the unknown digit be x

Hence, from the above,

We can conclude that

The unknown digit that make the given statement true is:

5.345 > 5.344 > 5.343

Where,

x = 0, 1, 2, 3, and 4

Question 12.

8.25 < 8. 6 < 8.361

Answer:

Let the unknown digit be x

Hence, from the above,

We can conclude that

The unknown digit that make the given statement true is:

8.25 < 8.26 < 8.361

Where,

x = 0, 1, 2

Question 13.

6.48 > 6.4 1 > 6.470

Answer:

Let the unknown digit be x

Hence, from the above,

We can conclude that

The unknown digit that make the given statement true is:

6.48 > 6.471 > 6.470

Where,

x = 0, 1, 2, ……. 7

Question 14.

Jack travels 2.45 miles to school. Wanda travels 2.31 miles to school. Compare the distances using words.

Answer:

It is given that

Jack travels 2.45 miles to school. Wanda travels 2.31 miles to school

Now,

We know that,

The place-value of “Tenths” is greater than the place-value of “Hundredths” is greater than the “Thousandths”

So,

2.45 > 2.31

Hence, from the above,

We can conclude that

Jack travels more miles than Wanda to school

Question 15.

In a jumping contest, Marcus jumped 1.02 meters, Gustavo jumped 1.29 meters, and Loreena jumped 1.202 meters. Who won the jumping contest?

Answer:

It is given that

In a jumping contest, Marcus jumped 1.02 meters, Gustavo jumped 1.29 meters, and Loreena jumped 1.202 meters

Now,

The given decimal numbers are: 1.02, 1.29, and 1.202

Now,

We know that,

The place-value of “Tenths” is greater than the place-value of “Hundredths” is greater than the “Thousandths”

So,

1.29 > 1.202 > 1.02

Hence, from the above,

We can conclude that

Gustavo won the jumping contest

**Lesson Check**

**Fill in the bubble completely to show your answer.**

Question 16.

Which number has the greatest value?

A. 9.382

B. 9.47

C. 9.09

D. 9.7

Answer:

We know that,

The place-value of “Tenths” is greater than the place-value of “Hundredths” is greater than the “Thousandths”

Hence, from the above,

We can conclude that

The number that has the greatest value is:

Question 17.

Kerry is comparing the numbers 9.207 and 9.210. What is the least place value she, needs to compare to decide which number is greater?

A. ones

B. thousandths

C. hundredths

D. tenths

Answer:

It is given that

Kerry is comparing the numbers 9.207 and 9.210

Now,

We know that,

The place-value of “Tenths” is greater than the place-value of “Hundredths” is greater than the “Thousandths”

So,

We have to compare the “Hundredths” place value to find the greatest number in the given decimal numbers

Hence, from the above,

We can conclude that

The least place value Kerry needs to compare to decide which number is greater is:

Question 18.

Which number has the least value?

A. 7.034

B. 7.304

C. 7.403

D. 7.003

Answer:

We know that,

The place-value of “Tenths” is greater than the place-value of “Hundredths” is greater than the “Thousandths”

Hence, from the above,

We can conclude that

The number that has the least value is:

Question 19.

In 5.820, what is the place-value position of the 0?

A. thousandths

B. tenths

C. hundredths

D. ones

Answer:

The given decimal number is: 5.820

Now,

The representation of 5.820 in the place value chart is:

Hence, from the above,

We can conclude that

The place value position of 0 in 5.820 is:

Question 20.

**Multi-Step** Jenna compares the lengths of her pet fish. The table shows the lengths of the fish. Which shows the lengths in order from greatest to least?

A. Spots, Oscar, Gus, Gem

B. Oscar, Spots, Gem, Gus

C. Gus, Oscar, Gem, Spots

D. Spots, Oscar, Gem, Gus

Answer:

It is given that

Jenna compares the lengths of her pet fish. The table shows the lengths of the fish

Now,

The given table is:

Now,

We know that,

The place-value of “Tenths” is greater than the place-value of “Hundredths” is greater than the “Thousandths”

So,

From the given table,

We can observe that

The order of the numbers that are from the greatest to the least is:

4.7 > 4.32 > 4.21 > 4.055

So,

The order of the lengths of Jenna’s pet fish is:

Sports > Oscar > Gem > Gus

Hence, from the above,

We can conclude that

The lengths of Jenna’s pet fishes in order from the least to the greatest is:

Question 21.

**Multi-Step** Look at the table in Question 20. What if Gem grew 0.5 inches. Which would then show the lengths in order from greatest to least?

A. Gem, Spots, Gus, Oscar

B. Gus, Oscar, Gem, Spots

C. Gem, Spots, Oscar, Gus

D. Spots, Oscar, Gem, Gus

Answer:

The given table is:

Now,

The present length of Gem = (The old length of gem) + 0.5

= 0.5 + 4.21

= 4.71 inches

So,

The order of the lengths of Jenna’s pet fish according to the new size of Gem is:

Gem > Sports > Oscar > Gus

Hence, from the above,

We can conclude that

The order of the lengths of pet fish from the greatest to the least after the increase of Gem’s length by 0.5 inches is: