## 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?
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?
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?
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?
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.
See margin.
Explanation:

Question 1.
17.001

Question 2.
987.6542

Question 3.
14.9284

Question 4.
7.2916

In 5 through 7, write the number in the form indicated.
See margin.
Explanation:

Question 5.
1.5629 in word form

Question 6.
568.0101 in short-word form

Question 7.
27.6003 in expanded form

Do you UNDERSTAND?
Question 8.
How do you use a decimal point to read and write very small numbers?
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?
See margin.
Explanation:

Question 10.
What is the decimal portion of 63.029? What is the whole number portion?
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
hundredths; 0.01
Explanation:

Question 12.
647.476
thousandths; 0.006
Explanation:

Question 13.
84.48
tenths; 0.4
Explanation:

Question 14.
327.0094
hundredths; 0
Explanation:

Question 15.
0.0521
thousandths; 0.002
Explanation

Question 16.
78.667
tenths; 0.6
Explanation

Question 17.
3.016
ones; 3
Explanation:

Question 18.
8.5914
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?
Ten thousandths
Explanation:

Question 20.
From left to right, what is the value Ten thousandths of the second 8 in the number?
0.0008
Explanation:

Question 21.
How would you write the number in short-word form?
22 and 9,808 ten thousandths
Explanation:

Question 22.
How would you write the number in word form?
See margin.
Explanation:

Question 23.
How would you write the number in expanded form?
(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.
Explanation:

Question 25.
Writing to Explain What would point from a number?
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
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
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
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.
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.
2 and 1 tenth
Explanation:

Question 2.
Write the length of an adult grizzly bear’s claw length in expanded form.
(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?
681.37 kg
Explanation:

Question 4.
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?
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?
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?