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## Texas Go Math Grade 4 Lesson 1.4 Answer Key Round Numbers

**Essential Question**

How can you round numbers?

Answer:

The general rules for the rounding of numbers are:

a. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

Example:

38 rounded to the nearest ten is 40.

b. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

Example:

33 rounded to the nearest ten is 30.

In May 2008, the Mount Rushmore National Monument in South Dakota welcomed 138,202 visitors. A website reported that about 1 hundred thousand people visited the park during that month. Was the estimate reasonable?

- Underline what you are asked to find.
- Circle the information you will use.

An estimate tells you about how many or about how much. It is close to an exact amount. You can round a number to find an estimate.

**One Way Use a number**

To round a number to the nearest hundred thousand, find the hundred thousand it is between.

Answer:

Use a number line to see which hundred thousand 138,202 is closest to

138,202 is closer to 150,000 than 100,000

Hence,

1 hundred thousand is not a reasonable estimate for 138,202.

**Math Talk**

**Mathematical Process:**

Is 155,000 closer to 100,000 or 200,000? Explain

Answer:

The given number is: 155,000

Now,

We know that,

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

So,

155,000 should be close to 200,000 since 155 is close to 200 than 100

Hence, from the above,

We can conclude that

155,000 is closer to 200,000

Question 1.

What number is halfway between 100,000 and 200,000?

Answer:

The given numbers are: 100,000 and 200,000

Now,

We know that,

The half of the 2 numbers = \(\frac{a + b}{2}\)

Where,

a and b are 2 numbers

So,

The half of 100,000 and 200,000 = \(\frac{100,000 + 200,000}{2}\)

= \(\frac{300,000}{2}\)

= 150,000

Hence, from the above,

We can conclude that

150,000 is halfway between 100,000 and 200,000

Question 2.

How does knowing where the halfway point helps you find which hundred thousand 138,202 is closest to? Explain.

Answer:

The given number line is:

Now,

From the above number line,

We can observe that

138,202 is closer to 150,000

Now,

We know that

150,000 is halfway of 100,000 and 200,000

Hence, from the above,

We can conclude that

138,202 is closer to the halfway point by using the number line

**Another Way Use place value.**

Mount Rushmore is located 5,725 feet above sea level. About how high is Mount Rushmore above sea level, to the nearest thousand feet?

To round a number to the nearest thousand, find the thousands it is between.

Answer:

Look at the digit in the place-value position to the right.

Hence, from the above,

We can conclude that

Mount Rushmore is about 6,000 feet above sea level.

**Math Talk**

**Mathematical Process**

Explain how you know 5,700 is closer to 6,000 than to 5,000.

Answer:

We know that,

The half of the given numbers = \(\frac{a + b}{2}\)

So,

The halfway of 5,000 and 6,000 = \(\frac{5,000 + 6,000}{2}\)

= \(\frac{11,000}{2}\)

= 5,500

So,

5,700 > 5,500

So,

5,700 is closer to 6,000

Hence, from the above,

We can conclude that

5,700 is closer to 6,000 than 5,000 since the halfway of 5,000 and 6,000 is less than 5,700

Question 3.

What is 250,000 rounded to the nearest hundred thousand? Explain.

Answer:

The given number is: 250,000

Now,

We know that,

If the number is greater than or equal to the halfway of the neasrest hundred thousand of the given number, then the given number is rounded to the latter number

Now,

The numbers that are closer to hundred thousand for 250,000 are: 200,000 and 300,000

So,

The halfway of 200,000 and 300,000 = \(\frac{200,000 + 300,000}{2}\)

= \(\frac{500,000}{2}\)

= 250,000

Hence, from the above,

We can conclude that

300,000 is the number that 250,000 is rounded to the nearest hundred thousand

**Share and Show**

Question 1.

Suppose 255,113 people live in a city. Rounded to the nearest hundred thousand, about how many people live in the city? Explain.

_____________ > 255,113 > _____________

Answer:

The given number is: 255,113

Now,

We know that,

If the number is greater than or equal to the halfway of the neasrest hundred thousand of the given number, then the given number is rounded to the latter number

Now,

The numbers that are closer to hundred thousand for 255,113 are: 200,000 and 300,000

So,

The halfway of 200,000 and 300,000 = \(\frac{200,000 + 300,000}{2}\)

= \(\frac{500,000}{2}\)

= 250,000

Hence, from the above,

We can conclude that

The number of people live in the city is about 300,000 people

**Round to the place value of the underlined digit.**

Question 2.

934,567

Answer:

The given number is: 934,567

Now,

We know that,

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

Hence, from the above,

We can conclude that

934,567 is rounded to 930,000

Question 3.

641,267

Answer:

The given number is: 641,267

Now,

We know that,

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

Hence, from the above,

We can conclude that

641,267 is rounded to 640,000

Question 4.

1,234,890

Answer:

The given number is: 1,234,890

Now,

We know that,

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

Hence, from the above,

We can conclude that

1,234,890 is rounded to 1,230,000

Question 5.

347,456

Answer:

The given number is: 347,456

Now,

We know that,

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

Hence, from the above,

We can conclude that

347,456 is rounded to 350,000

**Problem Solving**

Question 6.

**H.O.T.**

**Multi-Step** **Apply** The number 2,00 is missing a digit. The number rounded to the nearest thousand is 3,000. List all of the possibilities for the missing digit. Explain your answer.

Answer:

It is given that

The number 2,00 is missing a digit. The number rounded to the nearest thousand is 3,000

Now,

We know that,

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

So,

The missing digit should be: 5,6,7,8, and 9 since the given number rounded to 3,000

Hence, from the above,

We can conclude that

The list of all the possibilities for the missing digit is: 5, 6, 7, 8, and 9

Question 7.

**H.O.T.**

**Multi-Step Evaluate Reasonableness** The 2008 population of Wyoming was counted as 532,668 people. What is a reasonable estimate of the 2008 population of Wyoming? Explain.

Answer:

It is given that

The 2008 population of Wyoming was counted as 532,668 people

Now,

We know that,

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

So,

The reasonable estimate of 532,668 is: 530,000

Hence, from the above,

We can conclude that

The reasonable estimate of the 2008 population of Wyoming is: 530,000

Question 8.

What is the greatest whole number that rounds to the number 277,300? What is the least whole number?

Answer:

The given whole number is: 277,300

Now,

We know that,

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

So,

The reasonable estimates of 277,300 is:

200,000 < 277,300 < 300,000

Hence, from the above,

We can conclude that

The greatest whole number that rounds to the number 277,300 is: 300,000

The least whole number that rounds to the number 277,300 is: 200,000

Question 9.

Sarah rounded the number 4,583,583 to 4,500,000 when her teacher asked her to round to the nearest hundred thousand. Jamal rounded the same number to 4,600,000 when asked to round to the nearest hundred thousand. Who is correct? Explain the error that was made.

Answer:

It is given that

Sarah rounded the number 4,583,583 to 4,500,000 when her teacher asked her to round to the nearest hundred thousand. Jamal rounded the same number to 4,600,000 when asked to round to the nearest hundred thousand

Now,

We know that,

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

So,

4,583,583 is closer to 4,600,000 than 4,500,000

Hence, from the above,

We can conclude that

Jamal is correct

The error made is that 4,583,383 is greater than halfway of 4,000,000 and 5,000,000 and so, the number should be the latter number i.e., greater than 4,583,583

Question 10.

What number is halfway between 34,000 and 35,000?

Answer:

The given numbersa re: 34,000 and 35,000

Now,

We know that,

The halfway of the given numbers = \(\frac{a + b}{2}\)

So,

The halfway of 34,000 and 35,000 = \(\frac{34,000 + 35,000}{2}\)

= \(\frac{69,000}{2}\)

= 34,500

Hence, from the above,

We can conclude that

34,500 is halfway between 34,000 and 35,000

**Daily Assessment Task**

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

Question 11.

The number of dogs at The Great North Dog Walk in 2011, rounded to the nearest thousand, is 23,000. Which could be the exact number of dogs?

(A) 22,742

(B) 23,500

(C) 23,603

(D) 22,455

Answer:

It is given that

The number of dogs at The Great North Dog Walk in 2011, rounded to the nearest thousand, is 23,000

Now,

We know that,

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

So,

The exact number should be greater than or equal to 22,500

Hence, from the above,

We can conclude that

The exact number of dogs is:

Question 12.

A sports website had 2,684,735 visitors last year. Jerry rounded the number of visitors to the nearest hundred thousand for a newspaper article. Which number shows how he rounded 2,684,735?

(A) 2,684,400

(B) 2,680,000

(C) 2,690,000

(D) 2,700,000

Answer:

It is given that

A sports website had 2,684,735 visitors last year. Jerry rounded the number of visitors to the nearest hundred thousand for a newspaper article

Now,

We know that,

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

So,

The number that is closer to 2,684,735 is: 2,684,000

Hence, from the above,

We can conclude that

The number that shows the rounded number of 2,684,735 is:

Question 13.

**Multi-Step** Rachael rounded 16,473 to the nearest hundred. Then she rounded her answer to the nearest thousand. What is the final number?

(A) 16,500

(B) 17,000

(C) 20,000

(D) 16,000

Answer:

It is given that

Rachael rounded 16,473 to the nearest hundred. Then she rounded her answer to the nearest thousand

Now,

We know that,

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

So,

The number that is to the nearest hundred for 16,473 is: 16,500

The number that is to the nearest thousand for 16,473 is: 17,000

Hence, from the above,

We can conclude that

The final number is:

**TEXAS Test prep**

Question 14.

About 300,000 people attended a festival. Which number could be the exact number of people that attended the festival?

(A) 389,001

(B) 249,899

(C) 252,348

(D) 351,213

Answer:

It is given that

About 300,000 people attended a festival

Now,

We know that,

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

So,

The exact number should be greater than or equal to 250,000

Hence, from the above,

We can conclude that

The exact number of people that attended the festival is:

**Texas Go Math Grade 4 Lesson 1.4 Homework and Practice Answer Key**

Question 1.

The number 5,00 is missing a digit. The number rounded to the nearest thousand is 5,000. List all of the possibilities for the missing digit. Explain your answer.

Answer:

It is given that

The number 5,00 is missing a digit. The number rounded to the nearest thousand is 5,000

Now,

We know that,

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

So,

The missing digit for 5,000 is: 0, 1, 2, 3, and 4

Hence, from the above,

We can conclude that

The list of all of the possibilities for the missing digit is: 0, 1, 2, 3, and 4

Question 2.

Andy and Elizabeth each rounded 2,639,456 to the nearest ten-thousand. Andy got 2,640,000. Elizabeth got 2,630,000. Who is correct? Explain the error that was made.

Answer:

It is given that

Andy and Elizabeth each rounded 2,639,456 to the nearest ten-thousand. Andy got 2,640,000. Elizabeth got 2,630,000

Now,

The given number is: 2,639,456

Now,

We know that,

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

So,

2,639,456 is closest to 2,640,000 since 639 is greater than 635

Hence, from the above,

We can conclude that

Andy is correct

The error made is that since 2,639,456 is greater than the halfway between 2,600,000 and 2,700,000, the given number must not be close to 2,630,000

Question 3.

What is the greatest whole number that rounds to 67400? What is the least whole number?

Answer:

The given number is: 67,400

Now,

We know that,

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

So,

The range of the numbers that 67,400 is in between:

67,000 < 67,400 < 68,000

Hence, from the above,

We can conclude that

The greatest whole number is: 68,000

The least whole number is: 67,000

Question 4.

What number is halfway between 170,000 and 180,000?

Answer:

The given numbers are: 170,000 and 180,000

Now,

We know that,

The halfway of the given numbers = \(\frac{a + b}{2}\)

So,

The halfway of 170,000 and 180,000 = \(\frac{170,000 + 180,000}{2}\)

= \(\frac{350,000}{2}\)

= 175,000

Hence, from the above,

We can conclude that

175,000 is halfway between 170,000 and 180,000

**Problem Solving**

Question 5.

A shopping channel shipped 467,023 packages last year. What is a reasonable estimate of the number of packages shipped? Explain.

Answer:

It is given that

A shopping channel shipped 467,023 packages last year

Now,

We know that,

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

So,

467,023 is closer to 470,000

Hence, from the above,

We can conclude that

The reasonable estimate of the number of packages shipped is: 470,000 packages

Question 6.

A parking lot covers 32,420 square feet. What is its area to the nearest thousand feet? Explain how you round the number.

Answer:

It is given that

A parking lot covers 32,420 square feet

Now,

We know that,

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

So,

32,420 is closest to 32,000

Hence, from the above,

We can conclude that

The area of the parking lot to the nearest thousand feet is: 32,000 square feet

**Lesson Check:**

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

Question 7.

The population of Forestville is 83,277. What is the population rounded to the nearest thousand?

(A) 83,000

(B) 80,000

(C) 84,000

(D) 90,000

Answer:

It is given that

The population of Forestville is 83,277

Now,

We know that,

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

So,

The number that is closest to 83,277 is: 83,000

Hence, from the above,

We can conclude that

The population of Forestville that is rounded to the nearest thousand is:

Question 8.

To the nearest hundred thousand, there were 700,000 visitors to an amusement park last year. Which could be the exact number of visitors?

(A) 784,312

(B) 756,107

(C) 685,280

(D) 641,888

Answer:

It is given that

To the nearest hundred thousand, there were 700,000 visitors to an amusement park last year

Now,

We know that,

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

So,

The number that should be closest to 700,000 should be greater than or equal to 650,000

Hence, from the above,

We can conclude that

The exact number of visitors is:

Question 9.

What is the greatest whole number that rounds to 54,300?

(A) 53,399

(B) 54,349

(C) 53,999

(D) 54,299

Answer:

The given number is: 54,300

Now,

We know that,

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

So,

The whole number that is closest to 54,300 should have the digits 0, 1, 2, 3, and 4

Hence, from the above,

We can conclude that

The greatest whole number that rounds to 54,300 is:

Question 10.

The number 15,56 rounded to the nearest thousand is 15,000. Which numbers could be the missing digit?

(A) 1, 2, 3, 4, 5

(B) 1, 2, 3, 4, 5, 6

(C) 0, 1, 2, 3, 4, 5

(D) 0, 1, 2, 3, 4

Answer:

It is given that

The number 15,56 rounded to the nearest thousand is 15,000

Now,

We know that,

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

So,

The digits for the given number should be: 0, 1, 2, 3, and 4

Hence, from the above,

We can conclude that

The numbers that could be the missing digit is:

Question 11.

**Multi-Step** A male elephant weighs 6,708 pounds. A female elephant weighs 5,823 pounds. To the nearest hundred, what is the total weight of the two elephants?

(A) 7,000 pounds

(B) 12,500 pounds

(C) 6,000 pounds

(D) 13,000 pounds

Answer:

It is given that

A male elephant weighs 6,708 pounds. A female elephant weighs 5,823 pounds

So,

The total weight of the elephants = 6,708 + 5,823

= 12,531 Pounds

Now,

We know that,

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

So,

12,531 is close to 12,500

Hence, from the above,

We can conclude that

The total weight of the elephants to the nearest hundred is:

Question 12.

**Multi-Step** To the nearest hundred, a factory-produced 3,600 jars of applesauce on Thursday and 4,200 jars of applesauce on Friday. To the nearest thousand, how many jars of applesauce did they produce on the two days?

(A) 7,800

(B) 7,000

(C) 8,400

(D) 8,000

Answer:

It is given that

To the nearest hundred, a factory-produced 3,600 jars of applesauce on Thursday and 4,200 jars of applesauce on Friday

So,

The total number of jars of applesauce did they produce on two days = 3,600 + 4,200

= 7,800 jars

Now,

We know that,

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

So,

7,800 is close to 8,000

Hence, from the above,

We can conclude that

To the nearest thousand, the number of jars of applesauce did they produce on the two days is: