my homework lesson 4 represent decimals answer key

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McGraw-Hill My Math Grade 5 Volume 1

Textbook: mcgraw-hill my math grade 5 volume 1 isbn: 9780021150243.

Use the table below to find videos, mobile apps, worksheets and lessons that supplement McGraw-Hill My Math Grade 5 Volume 1 book.

Chapter 1: Place Value

Lesson 1: place value through millions, lesson 2: compare and order whole numbers through millions, lesson 3: hands on: model fractions and decimals, lesson 4: represent decimals, lesson 5: hands on: understand place value, lesson 6: place value through thousandths, lesson 7: compare decimals, lesson 8: order whole numbers and decimals, chapter 2: multiply whole numbers, lesson 1: prime factorization, lesson 2: hands on: prime factorization patterns, lesson 3: powers and exponents, lesson 4: multiplication patterns, lesson 5: hands on: use partial products and the distributive property, lesson 6: the distributive property, lesson 7: estimate products, lesson 8: multiply by one-digit numbers, lesson 9: multiply by two-digit numbers, chapter 3: divide by a one-digit divisor, lesson 1: relate division to multiplication, lesson 2: hands on: division models, lesson 3: two-digit dividends, lesson 4: division patterns, lesson 5: estimate quotients, lesson 6: hands on: division models with greater numbers, lesson 7: hands on: distributive property and partial quotients, lesson 8: divide three- and four-digit dividends, lesson 9: place the first digit, lesson 10: quotients with zeros, lesson 11: hands on: use models to interpret the remainder, lesson 12: interpret the remainder, chapter 4: divide by a two-digit divisor, lesson 1: estimate quotients, lesson 2: hands on: divide using base-ten blocks, lesson 3: divide by a two-digit divisor, lesson 4: adjust quotients, lesson 5: divide greater numbers, chapter 5: add and subtract decimals, lesson 1: round decimals, lesson 2: estimate sums and differences, lesson 3: hands on: add decimals using base-ten blocks, lesson 4: hands on: add decimals using models, lesson 5: add decimals, lesson 6: addition properties, lesson 7: hands on: subtract decimals using base-ten blocks, lesson 8: hands on: subtract decimals using models, lesson 9: subtract decimals, chapter 6: multiply and divide decimals, lesson 1: estimate products of whole numbers and decimals, lesson 2: hands on: use models to multiply, lesson 3: multiply decimals by whole numbers, lesson 4: hands on: use models to multiply decimals, lesson 5: multiply decimals, lesson 6: multiply decimals by powers of ten, lesson 7: multiplication properties, lesson 8: estimate quotients of decimals, lesson 9: hands on: divide decimals, lesson 10: divide decimals by whole numbers, lesson 11: hands on: use models to divide decimals, lesson 12: divide decimals, lesson 13: divide decimals by powers of ten, chapter 7: expressions and patterns, lesson 1: hands on: numerical expressions, lesson 2: order of operations, lesson 3: write numerical expressions, lesson 4: hands on: generate patterns, lesson 5: patterns, lesson 6: ordered pairs, lesson 7: graph patterns.

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4th grade (Eureka Math/EngageNY)

Unit 1: module 1: place value, rounding, and algorithms for addition and subtraction, unit 2: module 2: unit conversions and problem solving with metric measurement, unit 3: module 3: multi-digit multiplication and division, unit 4: module 4: angle measure and plane figures, unit 5: module 5: fraction equivalence, ordering, and operations, unit 6: module 6: decimal fractions, unit 7: module 7: exploring measurement with multiplication.

Curriculum  /  Math  /  5th Grade  /  Unit 1: Place Value with Decimals  /  Lesson 5

Place Value with Decimals

Lesson 5 of 13

Criteria for Success

Tips for teachers, anchor tasks.

Problem Set

Target Task

Additional practice.

Explain patterns in the number of zeros of the quotient when dividing a whole number by 10. Recognize that in a multi-digit whole number, a digit in any place represents $${\frac{1}{10}}$$  as much as it represents in the place to its left.

Common Core Standards

Core standards.

The core standards covered in this lesson

Number and Operations in Base Ten

5.NBT.A.1 — Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

5.NBT.A.2 — Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

Foundational Standards

The foundational standards covered in this lesson

4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

Number and Operations—Fractions

4.NF.B.4.B — Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)

The essential concepts students need to demonstrate or understand to achieve the lesson objective

• Divide whole numbers by 10 (e.g., $$5,000 \div 10$$ , $$4,320 \div 10$$ ).
• Multiply whole numbers by $$\frac{1}{10}$$  or 0.1 and see that this is equivalent to dividing those whole numbers by 10. 
• Generalize the pattern that dividing a whole number by 10 results in the digits in the number shifting one place to the right (MP.8).
• Understand that a digit in one place represents $$\frac{1}{10}$$  of what it represents in the place to its left.

Suggestions for teachers to help them teach this lesson

Students will only divide in cases where the quotient is a whole number. Students will divide by 10 with decimal quotients in Topic B. 

Lesson Materials

• Millions Place Value Chart (2 per student) — Students might need more or less depending on their reliance on this tool.
• Base ten blocks (8 thousands, 80 hundreds, 70 tens, 50 ones per student or small group) — Students might not need these depending on their reliance on concrete materials. You could just use one set for the teacher if materials are limited.

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

a.   Solve. 

• $$50\div10=$$ ___________
• $$8,700\div 10=$$ ___________
• $$90,060 \div 10 =$$  ___________
• $$204,000 \div 10 =$$  ___________

b.   What do you notice about Part (a)? What do you wonder?

Guiding Questions

a.    Solve.

• $${70 \div 10}$$
• $${70 \times {1\over 10}}$$
• $$70\times0.1$$

Write a whole number in which the value of the digit 3 is $$\frac{1}{10}$$ the value of the digit 3 in 23,456. Explain how you know the number you wrote is correct. 

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

Discussion of Problem Set

• Look at #1b. What did you get? (Note: They should have gotten 10 if they were paying close attention. Same with #2f.) 
• Look at #5. Do you agree or disagree? If you agree, what are the two correct answers? Prove that they are both correct. 
• Look at #7. What kind of picture did you draw? 

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

a.    $$380\div10=$$ ________

b.    $$4,820 \times \frac{1}{10}=$$ ________

Student Response

Explain what happened to the value of the 8 in both problems in #1.

An example response to the Target Task at the level of detail expected of the students.

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Extra Practice Problems

Answer keys for Problem Sets and Extra Practice Problems are available with a Fishtank Plus subscription.

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Topic A: Place Value with Whole Numbers

Build whole numbers to 1 million by multiplying by 10 repeatedly.

5.NBT.A.1 5.NBT.A.2

Use whole numbers to denote powers of 10. Explain patterns in the number of zeros when multiplying any powers of 10 by any other powers of 10. 

Explain patterns in the number of zeros of the product when multiplying a whole number by 10. Recognize that in a multi-digit whole number, a digit in any place represents 10 times as much as it represents in the place to its right. 

Explain patterns in the number of zeros of the product when multiplying a whole number by powers of 10. 

Explain patterns in the number of zeros of the quotient when dividing a whole number by powers of 10. 

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Topic B: Place Value with Decimals

Build decimal numbers to thousandths by dividing by 10 repeatedly. 

Explain patterns in the placement of the decimal point when a decimal is multiplied by any power of 10. Recognize that in a multi-digit decimal, a digit in any place represents 10 times as much as it represents in the place to its right.

Explain patterns in the placement of the decimal point when a decimal is divided by a power of 10. Recognize that in a multi-digit decimal, a digit in any place represents $${\frac{1}{10}}$$  as much as it represents in the place to its left.

Topic C: Reading, Writing, Comparing, and Rounding Decimals

Read and write decimals to thousandths using base-ten numerals, number names, and expanded form. 

5.NBT.A.3.A

Compare multi-digit decimals to the thousandths based on meanings of the digits using $${>}$$ , $${<}$$ , or $$=$$  to record the comparison.

5.NBT.A.3.B

Use place value understanding to round decimals to the nearest whole. 

Use place value understanding to round decimals to any place.

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

Refer to our Texas Go Math Grade 4 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from 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.

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?

Share and Show

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

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 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?

Daily Assessment Task

Fill in the bubble completely to show your answer.

TEXAS Test Prep

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

Relate Hundredths and Decimals

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

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Math Expressions Grade 4 Unit 7 Lesson 8 Answer Key Relate Fractions and Decimals

Solve the questions in Math Expressions Grade 4 Homework and Remembering Answer Key Unit 7 Lesson 8 Answer Key Relate Fractions and Decimals to attempt the exam with higher confidence. https://mathexpressionsanswerkey.com/math-expressions-grade-4-unit-7-lesson-8-answer-key/

Math Expressions Common Core Grade 4 Unit 7 Lesson 8 Answer Key Relate Fractions and Decimals

Math Expressions Grade 4 Unit 7 Lesson 8 Homework

Use the visual to fill in each blank.

\(\frac{40}{100}\) = __40___ of __100___ equal parts and the decimal __0.4___.

\(\frac{4}{10}\) = ____4____ of ___10_____ equal parts and the decimal ___0.4______. Explanation: Number of dots given in the picture =100 Then count the shaded part of dots in the whole = 40 \(\frac{40}{100}\) = 0.4 Number of columns in a whole = 10 \(\frac{4}{10}\) = 0.4

\(\frac{110}{100}\) = _1.1___ of equal parts, \(\frac{11}{10}\) = 110_____ of __100____ equal parts,

1\(\frac{1}{10}\) = __1___ whole and _1__ of __10___ equal parts, and the decimal __1.1___. Explanation: Each whole consists of 100 dots Then count the shaded part of dots = 110 \(\frac{110}{100}\) = 1.1 Number of columns in a whole = 10 \(\frac{1}{10}\) = 0.1

\(\frac{25}{100}\) = ___50___ of __100_____ equal parts, \(\frac{1}{4}\) = ___1____ of ___2____ equal parts, and the decimal __0.5______. Explanation: Number of dots given in the picture =100 Then count the shaded part of dots = 50 \(\frac{50}{100}\) = 0.5 \(\frac{1}{2}\) = 0.5

Math Expressions Grade 4 Unit 7 Lesson 8 Remembering

Convert each measurement.

Question 1. 12 hrs = __________ min Answer: 720 min Explanation: 12 hrs = __720__ min 12 x 60 min = 720 min

Question 2. 2 months = __________ wks Answer: 8.57 wks Explanation: 2 months = ____8.57____ wks 60/7 = 8.57 weeks

Question 3. 43 min = ___________ sec Answer: 2580 sec Explanation: 43 min = ____2580____ sec 43 x 60 = 2580 sec

Question 4. 6 days = ___________ hrs Answer: 144 hrs Explanation: 6 days = 144 hrs 6 x 24 = 144 hrs

Write the equivalent mixed number.

Question 5. \(\frac{12}{5}\) = ____________ Answer: 2\(\frac{2}{5}\) Explanation: Simplify the given fraction division \(\frac{12}{5}\) We get the quotient 2 and remainder 2 2\(\frac{2}{5}\)

Question 6. \(\frac{19}{4}\) = ____________ Answer: 4\(\frac{3}{4}\) Explanation: Simplify the given fraction division \(\frac{19}{4}\) We get the quotient 4 and remainder 3 4\(\frac{3}{4}\)

Question 7. \(\frac{15}{2}\) = ____________ Answer: 7\(\frac{1}{2}\) Explanation: Simplify the given fraction division \(\frac{15}{2}\) We get the quotient 14 and remainder 1 7\(\frac{1}{2}\)

Question 8. \(\frac{29}{3}\) = ____________ Answer: 9\(\frac{2}{3}\) Explanation: Simplify the given fraction division \(\frac{29}{3}\) We get the quotient 9 and remainder 2 9\(\frac{2}{3}\)

Question 9. \(\frac{49}{8}\) = ____________ Answer: 6\(\frac{1}{8}\) Explanation: Simplify the given fraction division \(\frac{49}{8}\) We get the quotient 6 and remainder 1 6\(\frac{1}{8}\)

Question 10. \(\frac{37}{6}\) = ____________ Answer: 6\(\frac{1}{6}\) Explanation: Simplify the given fraction division \(\frac{37}{6}\) We get the quotient 6 and remainder 1 6\(\frac{1}{6}\)

Question 11. How many times did Emmy get her hair cut in the year? Answer: 12 times Explanation: Add all the lengths of hair cut in the year to know, how many times she has done her hair cut. OR Add all the doted marks on the number line shown above

Question 12. How much longer was the length of hair Emmy had cut most often than the length of hair she had cut least often? Answer: \(\frac{1}{4}\)

Explanation: \(\frac{3}{4}\) three times ( longer was the length of hair Emmy had cut most often)

\(\frac{2}{4}\) Four times ( the length of hair she had cut least often)

\(\frac{3}{4}\) – \(\frac{2}{4}\) = \(\frac{1}{4}\)

Question 13. Stretch Your Thinking Milo has 3 quarters in his right pocket and 8 dimes in his left pocket. Show the amount of money Milo has in each pocket as a sum of fractions and as a sum of decimals. In which pocket is there more money? Answer: Left Pocket \(\frac{8}{10}\) > \(\frac{3}{4}\) Explanation: 3 quarters in his right pocket = \(\frac{1}{4}\)+\(\frac{1}{4}\)+\(\frac{1}{4}\) =\(\frac{3}{4}\) 8 dimes in his left pocket = \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) =\(\frac{8}{10}\) \(\frac{8}{10}\) > \(\frac{3}{4}\)

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Eureka Math Grade 4 Module 6 Lesson 6 Answer Key

Engage ny eureka math 4th grade module 6 lesson 6 answer key, eureka math grade 4 module 6 lesson 6 problem set answer key.

Answer: 1 x 15/100 = 1.15.

Answer: 2 x 47/100 = 2.47.

Answer: 2 x 95/100 = 2.95.

Answer: 7 x 52/100 = 7.52.

Question 3. Write the equivalent fraction and decimal for each of the following numbers. a. 1 one 2 hundredths b. 1 one 17 hundredths c. 2 ones 8 hundredths d. 2 ones 27 hundredths e. 4 ones 58 hundredths f. 7 ones 70 hundredths

Answer: a.1\(\frac{2}{100}\).

Explanation: In the above-given question, given that, 1 one 2 hundredths. 1 x 2/100. 202/100. 2.02.

Answer: b.1\(\frac{17}{100}\).

Explanation: In the above-given question, given that, 1 one 17 hundredths. 1 x 17/100. 117/100. 1.17.

Answer: c.2\(\frac{8}{100}\).

Explanation: In the above-given question, given that, 2 one 8 hundredths. 2 x 8/100. 208/100. 2.08.

Answer: d.2\(\frac{27}{100}\).

Explanation: In the above-given question, given that, 2 one 27 hundredths. 2 x 27/100. 227/100. 2.27.

Answer: e.4\(\frac{58}{100}\).

Explanation: In the above-given question, given that, 4 one 58 hundredths. 4 x 58/100. 458/100. 4.58.

Answer: f.7\(\frac{70}{100}\).

Explanation: In the above-given question, given that, 7 one 70 hundredths. 7 x 70/100. 770/100. 7.70.

Answer: a.7 ones 13 hundredths.

Explanation: In the above-given question, given that, 7 one 13 hundredths. 7 x 13/100. 713/100. 7.13.

Answer: b.7 ones 3 hundredths.

Explanation: In the above-given question, given that, 7 one 3 hundredths. 7 x 3/100. 73/100. 0.73.

Answer: c.7 ones 3 tenths.

Explanation: In the above-given question, given that, 7 one 3 tenths. 7 x 3/10. 73/10. 7.3.

Answer: d.7 tens 3 ones.

Eureka Math Grade 4 Module 6 Lesson 6 Exit Ticket Answer Key

Answer: a.7 ones 20 hundredths.

Answer: a.1 ones 75 hundredths.

Question 2. Write the equivalent fraction and decimal for each number. a. 8 ones 24 hundredths b. 2 ones 6 hundredths

Answer: a.8\(\frac{24}{100}\).

Explanation: In the above-given question, given that, 8 one 24 hundredths. 8 x 24/100. 824/100. 8.24.

Answer: b.2\(\frac{6}{100}\).

Explanation: In the above-given question, given that, 2 one 6 hundredths. 2 x 6/100. 206/100. 2.06.

Eureka Math Grade 4 Module 6 Lesson 6 Homework Answer Key

Answer: 2 x 35/100 = 2.35.

Answer: 3 x 17/100 = 3.17.

Explanation: In the above-given question, given that, 3 x 17/100. 3 x 100 + 17. 317/100. 3.17.

Answer: 3 x 25/100 = 2.47.

Question 3. Write the equivalent fraction and decimal for each of the following numbers. a. 2 ones 2 hundredths b. 2 ones 16 hundredths c. 3 ones 7 hundredths d. 1 one 18 hundredths e. 9 ones 62 hundredths f. 6 ones 20 hundredths

Answer: a.2\(\frac{2}{100}\).

Explanation: In the above-given question, given that, 2 one 2 hundredths. 2 x 2/100. 202/100. 2.02.

Answer: b.2\(\frac{16}{100}\).

Explanation: In the above-given question, given that, 2 one 16 hundredths. 2 x 16/100. 216/100. 2.16.

Answer: c.3\(\frac{7}{100}\).

Explanation: In the above-given question, given that, 3 one 7 hundredths. 3 x 7/100. 307/100. 3.07.

Answer: d.1\(\frac{18}{100}\).

Explanation: In the above-given question, given that, 1 one 18 hundredths. 1 x 18/100. 118/100. 1.18.

Answer: e.9\(\frac{62}{100}\).

Explanation: In the above-given question, given that, 9 one 62 hundredths. 9 x 62/100. 962/100. 9.62.

Answer: f.6\(\frac{20}{100}\).

Explanation: In the above-given question, given that, 6 one 20 hundredths. 6 x 20/100. 620/100. 6.20.

Answer: a.4 ones 18 hundredths.

Explanation: In the above-given question, given that, 4 one 18 hundredths. 4 x 18/100. 418/100. 4.18.

Answer: b.4 ones 8 hundredths.

Explanation: In the above-given question, given that, 4 one 8 hundredths. 4 x 8/100. 408/100. 4.08.

Answer: c.4 ones 8 tenths.

Explanation: In the above-given question, given that, 4 one 8 tenths. 4 x 8/10. 48/10. 4.8.

Answer: d.4 tens 8 ones.

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