## Envision Math 6th Grade Textbook Answer Key Topic 1.4 Decimal Place Value

**Decimal Place Value**

How can you read very small decimal numbers? One gallon equals 3.7854 liters. How do you read this number?

Answer:

A decimal is a number that uses a decimal point and has one or more digits to the right of the decimal point.

**Another Example**

What are different ways to write decimals?

Answer:

The atomic mass of the chemical chromium is 51.9961.

Use a place-value chart to write the decimal in different forms.

Standard form: 51.9961

Short-word form: 51 and 9,961 ten thousandths

Word form: fifty-one and nine thousand nine hundred sixty-one ten thousandths

Expanded form: (5 × 10) + (1 × 1) + (9 × 0.1) + (9 × 0.01) + (6 × 0.001) + (1 × 0.0001) = 50 + 1 + 0.9 + 0.09 + 0.006 + 0.0001

**Explain It**

Question 1.

What is the purpose of the decimal point in a decimal number?

Answer:

It separates the whole number portion of the number from the decimal portion of the number.

Explanation:

Question 2.

If the first digit to the right of the decimal were removed from the number above, how would you write it in different forms?

Answer:

51.0961; 51 and 961 ten thousandths; fifty-one and nine hundred sixty-one ten thousandths; (5 × 10) + (1 × 1) + (9 × 0.01) + (6 × 0.001) + (1 × 0.0001) = 50 + 1 + 0.09 + 0.006 + 0.0001

Explanation:

Use a place-value chart to help you read a decimal.

Short-word form: 3 and 7,854 ten thousandths

Standard form: 3.7854

**Guided Practice**

**Do you know HOW?**

In 1 through 4, write the place and value of the underlined digit.

Answer:

See margin.

Explanation:

Question 1.

17.001

Answer:

Question 2.

987.6542

Answer:

Question 3.

14.9284

Answer:

Question 4.

7.2916

Answer:

In 5 through 7, write the number in the form indicated.

Answer:

See margin.

Explanation:

Question 5.

1.5629 in word form

Answer:

Question 6.

568.0101 in short-word form

Answer:

Question 7.

27.6003 in expanded form

Answer:

**Do you UNDERSTAND?**

Question 8.

How do you use a decimal point to read and write very small numbers?

Answer:

See margin.

Explanation:

Question 9.

In the example at the top of the page, how do you know that 0.005 is the value of the digit 5?

Answer:

See margin.

Explanation:

Question 10.

What is the decimal portion of 63.029? What is the whole number portion?

Answer:

See margin.

Explanation:

**Independent Practice**

Tips: All digits to the left of the decimal point are whole numbers, and all digits to the right of the decimal point are decimals.

Write the place and value of the underlined digit.

Question 11.

1,957.01

Answer:

hundredths; 0.01

Explanation:

Question 12.

647.476

Answer:

thousandths; 0.006

Explanation:

Question 13.

84.48

Answer:

tenths; 0.4

Explanation:

Question 14.

327.0094

Answer:

hundredths; 0

Explanation:

Question 15.

0.0521

Answer:

thousandths; 0.002

Explanation

Question 16.

78.667

Answer:

tenths; 0.6

Explanation

Question 17.

3.016

Answer:

ones; 3

Explanation:

Question 18.

8.5914

Answer:

ten thousandths; 0.0004

Explanation:

**Independent Practice**

Use the place-value chart to answer 19 through 23.

Question 19.

What is the place value of the last digit?

Answer:

Ten thousandths

Explanation:

Question 20.

From left to right, what is the value Ten thousandths of the second 8 in the number?

Answer:

0.0008

Explanation:

Question 21.

How would you write the number in short-word form?

Answer:

22 and 9,808 ten thousandths

Explanation:

Question 22.

How would you write the number in word form?

Answer:

See margin.

Explanation:

Question 23.

How would you write the number in expanded form?

Answer:

(2 × 10) + (2 × 1) + (9 × 0.1) + (8 × 0.01) + (8 × 0.0001)

**Problem Solving**

Question 24.

Number Sense Write a decimal that has the digit 9 in the tenths place and happen if you removed the decimal the ten-thousandths place.

Answer:

Sample answer: 1.9009

Explanation:

Question 25.

Writing to Explain What would point from a number?

Answer:

The number would become a whole number, and its value would be greater.

Explanation:

Use this data table to answer items 26 through 29.

Question 26.

Number Sense Which place do you use to tell that the new record is faster?

A. tens

B. tenths

C. hundreds

D. thousandths

Answer:

B. tenths

Explanation:

Question 27.

Which is the word form of the new record?

A. one hundred fifty-four and one hundred sixty-five thousandths

B. one hundred fifty-four and twenty-five thousandths

C. one hundred fifty-four and twenty-five hundredths

D. one hundred fifty-four

Answer:

C. one hundred fifty-four and twenty-five hundredths

Explanation:

Question 28.

Think About the Process Which expression tells how to find how much faster the new record was?

A. 154.165 + 154.25

B. 154.25 – 154.165

C. 154.165 × 154.25

D. 154.25 ÷ 154.165

Answer:

B. 154.25 – 154.165

Explanation:

Question 29.

Writing to Explain Explain why writing the new record as 154.250 mph does not change its value.

Answer:

Sample answer: The 0 in the thousandths place has a value of 0.

Explanation:

**Mixed Problem Solving**

Use the table above to answer 1 through 3.

Question 1.

Write the height of an adult grizzly bear in short-word form.

Answer:

2 and 1 tenth

Explanation:

Question 2.

Write the length of an adult grizzly bear’s claw length in expanded form.

Answer:

(1 × 10) + (1 × 0.1) + (6 × 0.01)

Explanation:

Question 3.

If newborn grizzlies weigh about 0.45 kg, how many kilograms do grizzly bears gain from the time they are newborn until they are adults?

Answer:

681.37 kg

Explanation:

Question 4.

Answer:

If a bear ran at a speed of 54.078 km/h, then increased its speed two-hundredths of a kilometer per hour, how fast would it be running?

Answer:

54.098 km/h

Explanation:

Question 5.

The grizzly bear disappeared from the state of California in 1922. How many years before 2009 did the grizzly disappear?

Answer:

87 years

Explanation:

Question 6.

The female grizzly has one to four cubs every other year. If a female has four cubs every other year for 12 years, how many cubs would she have given birth to?

Answer:

24 cubs

Explanation:

Question 7.

If one cub weighed 0.45 kg and another cub weighed 1.23 kg, how much more would the heavier cub weigh than the lighter one?

Answer:

0.78 kg

Explanation: