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## Texas Go Math Grade 4 Lesson 2.4 Answer Key Relate Hundredths and Decimals

**Essential Question**

How can you record hundredths as fractions and decimals?

Answer:

We know that,

The representation of the hundredths in the place-value chart is: 0.01

So,

The representation of the hundredths in the form of a fraction is: \(\frac{1}{100}\)

Hence, from the above,

We can conclude that

The representation of the hundredths in the form of a fraction is: \(\frac{1}{100}\)

The representation of the hundredths in the form of a decimal number is 0.01

**Unlock the problem**

In the 2008 Summer Olympic Games, the winning time in the men’s 100-meter butterfly race was only \(\frac{1}{100}\) second faster than the second-place time. What decimal represents this fraction of a second?

• Circle the numbers you need to use.

Answer:

It is given that

In the 2008 Summer Olympic Games, the winning time in the men’s 100-meter butterfly race was only \(\frac{1}{100}\) second faster than the second-place time

Hence, from the above,

We can conclude that

The numbers we need to use are: 1 and 100

You can write hundredths as fractions or decimals.

**One Way,** Use a model and a place-value chart.

**Fraction**

Shade \(\frac{1}{100}\) of the model.

Write: 0.01

Read: one hundredth

**Decimal**

Complete the place-value chart. \(\frac{1}{100}\) is 1 hundredth.

Write: 0.01

Read: one hundredth

**Another Way** Use a number line.

Label the number line with equivalent decimals. Locate the point \(\frac{1}{100}\).

Now,

From the above Number line,

We can observe that

0.01 names the same amount as \(\frac{1}{100}\).

So,

The winning time was 0.01 seconds faster.

**Math Talk**

**Mathematical Processes**

Explain how the size of one-tenth is related to the size one hundredth.

Answer:

We know that,

One-hundredth is the tenth of the one-tenth

Hence, from the above,

We can conclude that

One-hundredth = \(\frac{1}{10}\) × One-tenth

Alicia Won her 400-meter freestyle race by 4\(\frac{25}{100}\) seconds. How can you write this mixed number as a decimal?

Example Use a number line.

Label the number line with equivalent mixed numbers and decimals Locate the point 4\(\frac{25}{100}\).

Now,

From the above Number line,

We can observe that

4.25 names the same amount as 4\(\frac{25}{100}\).

So,

Alicia won her race by 4.25 seconds.

**Share and Show**

Question 1.

Shade the model to show \(\frac{31}{100}\)

Write the amount as a decimal. ______________

Answer:

The given models are:

Now,

To represent \(\frac{31}{100}\) in a rectangle,

We will shade 31 boxes in a rectangle out of 100 boxes

Now,

To represent \(\frac{31}{100}\) in the form of a decimal,

Write 31 after the decimal point

So,

The representation of \(\frac{31}{100}\) in the given models is:

Hence, from the above,

We can conclude that

The representation of \(\frac{31}{100}\) in the form of a decimal is: 0.31

**Write the fraction or mixed number and the decimal shown by the model.**

Question 2.

Answer:

The given model is:

Now,

From the above model,

We can observe that

The representation of the given model in the form of a fraction = (The number of shaded parts) ÷ (The total number of parts)

= \(\frac{68}{100}\)

Now,

The representation of the given model in the form of a decimal number is: 0.68

Hence, from the above,

We can conclude that

The representation of the given model in the form of a fraction is: \(\frac{68}{100}\)

The representation of the given model in the form of a decimal number is: 0.68

**Go Math Lesson 2.4 4th Grade Answer Key Question 3.**

Answer:

The given model is:

Now,

From the above model,

We can observe that

The representation of the given model in the form of a fraction = (The number of shaded parts) ÷ (The total number of parts)

= \(\frac{8}{100}\)

Now,

The representation of the given model in the form of a decimal number is: 0.08

Hence, from the above,

We can conclude that

The representation of the given model in the form of a fraction is: \(\frac{8}{100}\)

The representation of the given model in the form of a decimal number is: 0.08

Question 4.

Answer:

The given model is:

Now,

The representation of the complete model is:

Now,

From the above model,

We can observe that

The representation of the marked point in the form of a mixed number is: 6\(\frac{19}{100}\)

The representation of the marked point in the form of a decimal number is: 6.19

Hence, from the above,

We can conclude that

The representation of the marked point in the form of a mixed number is: 6\(\frac{19}{100}\)

The representation of the marked point in the form of a decimal number is: 6.19

**Math Talk**

**Mathematical Processes**

Are 0.5 and 0.50 equivalent? Explain.

Answer:

The given decimal numbers are: 0.5 and 0.50

Now,

We know that,

If zero is placed on the right side as the last digit in the decimal number, then that zero don’t have any value

So,

0.5 = 0.50

Hence, from the above,

We can conclude that

0.5 and 0.50 are equivalent

**Problem Solving**

Question 5.

**H.O.T Representations** Shade the grids to show three different ways to represent \(\frac{16}{100}\) using models.

Answer:

The given fraction is: \(\frac{16}{100}\)

Now,

To represent the given fraction in 3 different ways,

We have to write the equivalent fractions of \(\frac{16}{100}\)

So,

The equivalent fractions of the given fraction are:

\(\frac{16}{100}\) = \(\frac{4}{25}\) = \(\frac{8}{50}\)

So,

The representation of the above equivalent fractions in the models is:

Hence, from the above,

We can conclude that

The three ways to represent \(\frac{16}{100}\) are:

Question 6.

**Write Math** Explain how one whole, one-tenth, and one hundredth are related.

Answer:

We know that,

“One-whole” is represented as 1

“One-tenth” is \(\frac{1}{10}\) of 1

“One-hundredth” is \(\frac{1}{10}\) of “One-tenth” and \(\frac{1}{100}\) of 1

Hence, from the above,

We can conclude that

One-hundredth = \(\frac{1}{10}\) of “One-tenth” = \(\frac{1}{100}\) of 1

**Sense or Nonsense?**

Question 7.

**H.O.T. Multi-Step** The Memorial Library is 0.3 miles from the school. Whose statement makes sense? Whose statement is nonsense?

Explain your reasoning.

Answer:

It is given that

The Memorial Library is 0.3 miles from the school

Now,

The representation of 0.3 in the form of a fraction is: \(\frac{3}{10}\)

The representation of 0.3 in the word form is: Three tenths

Now,

According to the given information,

Gabe said he was going to walk three tenths miles

Tara said she was going to walk three miles

Hence, from the above,

We can conclude that

Tanya’s statement is nonsense

**Daily Assessment Task**

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

Question 8.

A house shaped like a ball has curved windows. The largest window is 2\(\frac{75}{100}\) meters tall. What is 2\(\frac{75}{100}\) written as a decimal?

(A) 0.275

(B) 2.175

(C)2.75

(D) 27.5

Answer:

It is given that

A house shaped like a ball has curved windows. The largest window is 2\(\frac{75}{100}\) meters tall

Now,

The given mixed number is: 2\(\frac{75}{100}\)

So,

2[llatex]\frac{75}{100}[/latex] = 2 + \(\frac{75}{100}\)

= 2 + 0.75

= 2.75

Hence, from the above,

We can conclude that

The representation of 2\(\frac{75}{100}\) as a decimal is:

Question 9.

Barry made the model below to show the distance he and his sister hiked while on vacation. Which decimal does the model show?

(A) 4.80

(B) 3.80

(C) 4.08

(D) 3.08

Answer:

It is given that

Barry made the model below to show the distance he and his sister hiked while on vacation

Now,

The given model is:

Now,

From the above model,

We can observe that

The representation of the model in the form of a fraction = (The number of shaded parts) ÷ (The total number of parts)

= \(\frac{380}{100}[latex]

= 3.80

Hence, from the above,

We can conclude that

The representation of the model in the form of a decimal number is:

Question 10.

A quilt is made up of 100 equal squares. There is a star on 35 of the squares. Which decimal represents the part of the quilt with stars?

(A) 35

(B) 3.5

(C) 1.35

(D) 0.35

Answer:

It is given that

A quilt is made up of 100 equal squares. There is a star on 35 of the squares

Now,

The part of the quilt with stars = (The number of stars present) ÷ (The total number of squares)

= [latex]\frac{35}{100}\)

= 0.35

Hence, from the above,

We can conclude that

The representation of the part of the quilt with the stars in the form of a decimal is:

**TEXAS Test Prep**

Question 11.

Which are the fraction and decimal shown by the model?

(A) 12\(\frac{9}{10}\); 12.9

(B) 1\(\frac{29}{100}\); 1.29

(C) 1\(\frac{09}{100}\); 1.09

(D) 2\(\frac{90}{100}\); 2.90

Answer:

The given model is:

Now,

From the above model,

We can observe that

The representation of the above model in the form of a fraction = (The number of shaded parts) ÷ (The total number of parts)

= \(\frac{129}{100}\)

= 1\(\frac{29}{100}\)

= 1 + \(\frac{29}{100}\)

= 1 + 0.29

= 1.29

Hence, from the above,

We can conclude that

The representation of the fraction and decimal for the given model is:

### Texas Go Math Grade 4 Lesson 2.4 Homework and Practice Answer Key

**Relate Hundredths and Decimals**

Question 1.

The fully shaded grid shows 1. Explain how these three models are related.

Problem Solving

Answer:

It is given that

The fully shaded grid shows 1

Now,

The given model is:

Now,

From the above model,

We can observe that

The first model is shaded only one-tenth of the second model

The second model is shaded only one-tenth of the third model

So,

The relationship between the models is:

1st model = \(\frac{1}{10}\) of 2nd model = \(\frac{1}{100}\) of 3rd model

Hence, from the above,

We can conclude that

The relationship between the models is:

1st model = \(\frac{1}{10}\) of 2nd model = \(\frac{1}{100}\) of 3rd model

**Go Math Lesson 2.4 Homework Answer Key Grade 4 Question 2.**

Emma and Charles saw this sign along the highway.

Emma said, “It is seventy-five hundredths of a mile to Waterslide Park.”

Charles said, “It is seven and five-tenths miles to Waterslide Park.”

Whose statement makes sense? whose statement is nonsense? Explain your reasoning.

Answer:

It is given that

Emma said, “It is seventy-five hundredths of a mile to Waterslide Park.”

Charles said, “It is seven and five-tenths miles to Waterslide Park.”

Now,

The representation of seventy-five hundredths in the Standard form is: 0.75

The representation of seven and five-tenths in the Standard form is: 7.5

It is given that

The Waterslide park is: 0.75 miles

Hence, from the above,

We can conclude that

Emma’s statement makes sense

Charles’s statement makes not sense

Question 3.

Jake said he has \(\frac{8}{100}\) of a dollar in his pocket. Margie said that the decimal for \(\frac{8}{100}\) is 0.8. What error did she make? What is the decimal form for \(\frac{8}{100}\)?

Answer:

It is given that

Jake said he has \(\frac{8}{100}\) of a dollar in his pocket. Margie said that the decimal for \(\frac{8}{100}\) is 0.8

Now,

The representation of \(\frac{8}{100}\) in the decimal form is: 0.08

Now,

0.8 represents only one digit after the decimal point

But,

From the given fraction,

The digits after the decimal point must have 2

So,

The error made by Margie is:

The misinterprettion of digits after the decimal point

Hence, from the above,

We can conclude that

The error made by Margie is:

The misinterprettion of digits after the decimal point

The representation of \(\frac{8}{100}\) in the decimal form is: 0.08

**Lesson Check**

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

Question 4.

What is the decimal for \(\frac{73}{100}\)?

(A) 7.3

(B) 0.73

(C) 73

(D) 100.73

Answer:

The given fraction is: \(\frac{73}{100}\)

Now,

The representation of \(\frac{73}{100}\) in the decimal form is: 0.73

Hence, from the above,

We can conclude that

The representation of \(\frac{73}{100}\) in the decimal form is:

Question 5.

A fully shaded grid shows 1. Which is the correct fraction or decimal for this model?

(A) 231

(B) 2.31

(C) 2\(\frac{3}{100}\)

(D) \(\frac{231}{100}\)

Answer:

It is given that

A fully shaded grid shows 1

Now,

The given model is:

Now,

From the above model,

We can observe that

The representation of the given model in the form of a decimal number = 1 + 1 + \(\frac{31]{100}\)

= 2 + 0.31

= 2.31

= \(\frac{231}{100}\)

= 2\(\frac{31}{100}\)

Hence, from the above,

We can conclude that

The correct representation of the fraction and decimal for the given model is:

Question 6.

Which fraction is marked with a dot on this number line?

(A) 4\(\frac{7}{10}\)

(B) 4\(\frac{7}{100}\)

(C) 4\(\frac{17}{100}\)

(D) 4\(\frac{17}{10}\)

Answer:

The given model is:

Now,

The representation of the complete model is:

Now,

From the above model,

We can observe that

The dotted marked point is represented as: 4.17

So,

The representation of 4.17 in the form of a mixed number is: 4\(\frac{17}{100}\)

Hence, from the above,

We can conclude that

The representation of the dotted line on the number line in the form of a fraction is:

**Go Math Grade 4 Lesson 2.4 Homework Answer Key Question 7.**

**Multi-Step** A dollar is 100 cents. A quarter is 25 cents. What fraction of a dollar is a quarter?

(A) \(\frac{4}{100}\)

(B) \(\frac{100}{25}\)

(C) \(\frac{25}{10}\)

(D) \(\frac{25}{100}\)

Answer:

It is given that

A dollar is 100 cents. A quarter is 25 cents

So,

The fraction of a dollar is a quarter = \(\frac{25]{100}\)

Hence, from the above,

We can conclude that

The fraction of a dollar is a quarter is: