Understanding Decimal Place Values

Show your work for each problem.

1.
In the number , which digit is in the tenths place?
1. a)5
2. b)7
3. c)2
4. d)4
Answer: 2
In , the digit is in the tenths place (first position after the decimal point). The is in the hundredths place and the is in the thousandths place.
2.
What is the value of the digit in ?
1. a)
2. b)
3. c)
4. d)
Answer:
In , counting from the decimal: 0 is in tenths, 8 is in hundredths. The value of 8 in the hundredths place is (8 hundredths).
3.
What is the place value name for the digit in ?
Answer: thousandths
In : 1 is in tenths, 2 is in hundredths, and 6 is in thousandths. The third position after the decimal point is the thousandths place.
4.
What is the value of the digit in ?
Answer: 0.5
In , the digit 5 is in the tenths place. Its value is (five tenths or ).
5.
Which decimal has a in the hundredths place?
1. a)
2. b)
3. c)
4. d)
Answer:
In , the 3 is in the hundredths place (second position after decimal). In , the 3 is in tenths. In , the 3 is in thousandths. In , the 3 is in the ones place.
6.
Write in expanded form
Answer: 7 + 0.4 + 0.08 + 0.002
1. What is the value of the 7 (ones place)? 7
2. What is the value of the 4 (tenths place)? 0.4
3. What is the value of the 8 (hundredths place)? 0.08
4. What is the value of the 2 (thousandths place)? 0.002
7.
Which digit has a greater value in : the or the ?
Answer: 4
The 4 is in the hundredths place (value ), and the 7 is in the thousandths place (value ). Since , the digit 4 has a greater value.
8.
What number is represented by ?
1. a)
2. b)
3. c)
4. d)
Answer:
. The 5 is ones, 3 is tenths, 6 is hundredths, and 1 is thousandths.
9.
Compare: Which is greater, or ?
Answer: 0.45
1. Write 0.45 with three decimal places 0.450
2. Compare the tenths place of both numbers 4 = 4
3. Compare the hundredths place of both numbers 5 > 0
4. Which number is greater? 0.45
10.
How many times greater is the value of the in than the value of the in ?
Answer: 10
In , the 2 has value (2 tenths). In , the 2 has value (2 hundredths). Since , the 2 in is 10 times greater.
11.
A price tag shows €15.79. What is the value of each digit?
Answer: 10 + 5 + 0.7 + 0.09
1. What is the value of the 1 in 15.79? 10
2. What is the value of the 5? 5
3. What is the value of the 7? 0.7
4. What is the value of the 9? 0.09
12.
If you move the digit from the tenths place to the thousandths place, how does its value change?
1. a)It becomes 100 times smaller
2. b)It stays the same
3. c)It becomes 10 times smaller
4. d)It becomes 10 times greater
Answer: It becomes 100 times smaller
In tenths: . In thousandths: . Moving 2 places right means dividing by . So .
13.
Order from least to greatest: , , ,
Answer: 0.053, 0.305, 0.35, 0.503
1. Write all numbers with 3 decimal places 0.305, 0.350, 0.053, 0.503
2. Which has the smallest tenths digit? 0.053
3. Of the remaining, which is next smallest? 0.305
4. What is the final order? 0.053, 0.305, 0.35, 0.503
14.
A runner's time is 12.045 seconds. The judge says the 4 represents 4 hundredths of a second. Is the judge correct? Answer yes or no.
Answer: yes
The judge is correct. In 12.045: the 0 is in the tenths place, the 4 is in the hundredths place, and the 5 is in the thousandths place. The digit 4 is indeed in the hundredths place, so its value is 0.04 seconds (4 hundredths of a second).
15.
Create a number where the digit 5 appears twice: once with value 0.5 and once with value 0.005
Answer: 0.505
1. Which place has value 0.5? tenths
2. Which place has value 0.005? thousandths
3. What digit goes in the hundredths place? 0
4. Write the complete number 0.505
16.
How many hundredths are in ?
Answer: 47
, which means 47 hundredths. You can also think: 4 tenths = 40 hundredths, plus 7 hundredths = 47 hundredths.
17.
Write the decimal that has 2 tens, 4 ones, 0 tenths, 8 hundredths, and 3 thousandths
Answer: 24.083
1. What is the value of 2 tens? 20
2. What is the whole number part? 24
3. What comes after the decimal? (0 tenths, 8 hundredths, 3 thousandths) 0.083
4. Write the complete number 24.083
18.
A scientist measures 0.625 grams. Express this as tenths, hundredths, and thousandths separately.
Answer: 6 tenths, 2 hundredths, 5 thousandths
1. How many tenths are in 0.625? 6
2. How many hundredths (just the digit)? 2
3. How many thousandths (just the digit)? 5
4. Check: 0.6 + 0.02 + 0.005 = ? 0.625