Place Value
Which place is the 8 in 3.489?
Hundredths
Write “three and forty-seven hundredths” in standard form.
3.47
Complete the comparison using >, <, or =.
4.305 ___ 4.35
4.305 < 4.35
Round 7.846 to the nearest tenth.
7.8
A race time rounds to 10.3 seconds when rounded to the nearest tenth.
It is also faster than 10.32 seconds.
What is a possible race time?
10.31, 10.30, 10.29
Write 6.308 in expanded form.
6 + 0.3 + 0.008
Match the number to its correct name: 4.205
A. four and two tenths and 5 thousandths
B. four and twenty-five thousandths
C. four and two hundred zero fifths
D. four and two hundred five thousandths
D. four and two hundred five thousandths
Which number is greater: 5.68 or 5.608? Explain using place value.
5.68 is greater because the eight in the hundredths place is greater than the eight in the thousandths place.
Round 9.999 to the nearest tenth.
10.0
Two runners have times that both round to 8.6 seconds (nearest tenth).
One runner is faster than the other.
Give two possible times and tell which one is faster.
8.61 and 8.64 → 8.61 is faster
Complete the expanded form:
7.406 = (7 × ___) + (4 × ___) + (6 × ___)
7.406 = (7 × 1) + (4 × 0.1) + (6 × 0.001)
Write 4.085 in word form.
four and eighty-five thousandths
A student says 6.5 is less than 6.45 because 6.45 has more digits.
Is the student correct? Explain your reasoning.
No, 6.5 is greater because the 5 in the tenths place is greater than the 4 in the tenths place in 6.45.
Round 2.865 to the nearest tenth and nearest hundredth
2.9 and 2.87
You run 1.75 miles each day for 3 days.
Then you run 2.25 miles on the fourth day.
How far did you run in total? Show or explain your thinking.
7.5 miles
Fill in the blanks:
In 8.888, the value of the 8 in the tenths place is ___ times the value of the 8 in the thousandths place.
100
Which number matches “nine and five hundredths”?
a. 9.5
b. 9.05
c. 9.005
Order the numbers from least to greatest:
3.4, 3.04, 3.44
3.04, 3.4, 3.44
A number rounds to 8.7 when rounded to the nearest tenth.
Give one possible number and explain your reasoning.
Possible answers: 8.74, 8.73,8.72,8.71,8.70, 8.69, 8.68, 8.67, 8.66, 8.65
Explanation: When rounding to the nearest tenth, I look at the hundredths place. In 8.74, the hundredths digit is 4, which is less than 5, so the tenths digit stays the same. That means 8.74 rounds to 8.7.
A student says:
“If two prices both round to $3.50, they must be the same amount.”
Is the student correct? Explain and give an example.
No, the student is not correct.
Two different prices can round to the same number. For example, $3.46 and $3.54 both round to $3.50 when rounding to the nearest tenth.
A number has a 4 in the hundredths place and a 4 in the thousandths place.
How do their values compare?
The 4 in the hundredths is 10 times greater than the 4 in the thousandths place
What is wrong with this statement?
“0.45 is read as forty-five tenths.”
It should be forty-five hundredths
A runner finished a race in 15.382 seconds. Another runner finished in 15.4 seconds.
Which runner was faster? Use a comparison statement to explain.
15.382 < 15.4, so first runner is faster
A number rounds to 9.4 when rounded to the nearest tenth and to 9.37 when rounded to the nearest hundredth.
What could the number be? Explain your reasoning.
When I round to the nearest hundredth, I look at the thousandths place. The thousandths digit is 4, which is less than 5, so 9.374 rounds to 9.37.
When I round to the nearest tenth, I look at the hundredths place. The hundredths digit is 7, which is 5 or more, so I round the tenths up. That makes 9.374 round to 9.4.
A shopper buys items totaling $9.97 and pays with $10.02.
They expect to receive only one coin as change.
Explain how this is possible using decimal reasoning.
change is $0.05 → one nickel