Decimal Place Value
Question: What is the value of the digit 6 in 4.672?
A. 6 ones
B. 6 tenths
C. 6 hundredths
D. 6 thousandths
Answer: B. 6 tenths
The 6 is immediately to the right of the decimal point, so it is in the tenths place.
Question: Write 0.6 as a fraction in simplest form.
Answer: 3/5
0.6 = 6/10
Simplify by dividing by 2:
6/10 = 3/5
Question: Round 6.47 to the nearest tenth.
Answer: 6.5
The hundredths digit is 7, so round the tenths digit up.
Question: Which is greater?
0.7 or 0.65
Answer: 0.7
Rewrite 0.7 as 0.70.
Then:
0.70 > 0.65
Question: A student says:
“The 4 in 6.041 is in the tenths place.”
Is the student correct?
Answer: No.
The 4 is in the hundredths place.
In 6.041:
Question: What is the value of the digit 8 in 3.048?
Answer: 8 thousandths
The digits after the decimal are:
So the 8 represents 8 thousandths.
Question: Write 0.08 as a fraction in simplest form.
Answer: 2/25
0.08 = 8/100
Divide by 4:
8/100 = 2/25
Question: Round 8.324 to the nearest hundredth.
Answer: 8.32
The thousandths digit is 4, so the hundredths digit stays the same.
Question: Fill in the symbol:
4.308 ___ 4.380
Compare the digits:
4.308 < 4.380
Question: A student says:
“0.35 is greater than 0.4 because 35 is greater than 4.”
Is the student correct?
Answer: No.
Rewrite 0.4 as 0.40.
Then:
0.35 < 0.40
So 0.4 is greater.
Question: What digit is in the hundredths place in 7.263?
Answer: 6
In 7.263:
Question: Write 0.125 as a fraction in simplest form.
Answer: 1/8
0.125 = 125/1,000
Divide by 125:
125/1,000 = 1/8
Question: Round 5.678 to the nearest tenth.
Answer: 5.7
The hundredths digit is 7, so the tenths digit rounds up.
Question: Put these decimals in order from least to greatest:
2.4, 2.04, 2.44, 2.404
Answer: 2.04, 2.4, 2.404, 2.44
Rewrite 2.4 as 2.400:
2.040 < 2.400 < 2.404 < 2.440
Question: A student says:
“0.075 = 75/100.”
Is the student correct?
Answer: No.
There are three decimal places, so:
0.075 = 75/1,000
Simplifying:
75/1,000 = 3/40
So:
0.075 = 3/40
Question: A number has a 5 in the thousandths place, a 7 in the tenths place, and a 3 in the ones place.
What is the number?
Answer: 3.705
The place values are:
3 ones + 7 tenths + 0 hundredths + 5 thousandths
So the number is:
3.705
Question: Write 4 3/10 as a decimal.
Answer: 4.3
3/10 = 0.3
So:
4 3/10 = 4.3
Question: A measurement rounds to 3.42 when rounded to the nearest hundredth.
Which two numbers could have been the original measurement?
A. 3.414
B. 3.415
C. 3.426
D. 3.424
E. 3.429
Answer: B and D
3.415 rounds to 3.42.
3.424 rounds to 3.42.
Question: Which is the greatest?
6.205, 6.25, 6.052, 6.2055
Answer: 6.25
Rewrite the numbers with four decimal places:
Therefore, 6.25 is greatest.
Question: Two students are comparing 5.62 and 5.602.
Who is correct? Explain.
Answer: Maya is correct.
Rewrite:
5.62 = 5.620
Now compare:
5.620 > 5.602
Therefore:
5.62 > 5.602
Question: What is the value of the digit 4 in 8.0426?
Answer: 4 hundredths
The digits after the decimal are:
So the 4 represents 4 hundredths, or 0.04.
Question: Write 5.075 as a mixed number in simplest form.
Answer: 5 3/40
First:
5.075 = 5 75/1,000
Simplify:
75/1,000 = 3/40
So:
5.075 = 5 3/40
Question: A number has three decimal places and rounds to 7.56 when rounded to the nearest hundredth.
What is the greatest possible number and the least possible number it could be?
Answer:
Least possible: 7.555
Greatest possible: 7.564
Any number from 7.555 through 7.564 rounds to 7.56 to the nearest hundredth.
Question: Four runners recorded these times:
The fastest runner is the person with the smallest time.
Who finished fastest?
Answer: Carlos
Compare:
13.025 < 13.205 < 13.2055 < 13.25
So Carlos had the shortest time.
Question: A race has four runners:
Runner/Time
Eli14.203 seconds
Finn14.23 seconds
Grace14.023 seconds
Harper14.2035 seconds
Eli says:
“I finished first because my time is the longest.”
Is Eli correct? Explain.
Answer: No.
In a race, the smallest time is the fastest.
Compare the times:
14.023 < 14.203 < 14.2035 < 14.230
So Grace finished first.