Comparing Decimals

Show your work for each problem.

1.
Which symbol makes this statement true? $0.7 \, \square \, 0.4$
1. a) $>$
2. b) $=$
3. c) $<$
4. d)None of these
Answer: $>$
$0.7 > 0.4$ because 7 tenths is greater than 4 tenths.
2.
Which decimal is the smallest? $0.8$ , $0.3$ , $0.6$ , $0.9$
1. a) $0.8$
2. b) $0.9$
3. c) $0.3$
4. d) $0.6$
Answer: $0.3$
$0.3$ is the smallest because 3 tenths is less than 6, 8, or 9 tenths.
3.
$0.5$ written with two decimal places is $0.50$ . How many hundredths is that?
Answer: 50
$0.5 = 0.50$ , which is 50 hundredths. Adding a zero to the right of the last decimal digit doesn't change the value: 5 tenths = 50 hundredths.
4.
Which is greater: $0.6$ or $0.2$ ? Write the greater number.
Answer: 0.6
$0.6 > 0.2$ because 6 tenths is greater than 2 tenths.
5.
Is $0.5$ equal to $0.50$ ?
1. a)Yes, they are equal
2. b)No, $0.50$ is greater
3. c)No, $0.5$ is greater
4. d)Cannot be determined
Answer: Yes, they are equal
Yes! $0.5 = 0.50$ . Adding zeros to the right doesn't change the value. Both represent 5 tenths.
6.
Which is greater: $0.5$ or $0.47$ ?
1. a)Cannot compare
2. b) $0.5$
3. c)They are equal
4. d) $0.47$
Answer: $0.5$
$0.5 > 0.47$ . Write as $0.50$ vs $0.47$ . At the tenths place, $5 > 4$ , so $0.5$ is greater.
7.
Which is smaller: $0.09$ or $0.1$ ? Write the smaller number.
Answer: 0.09
$0.09 < 0.1$ . Write as $0.09$ vs $0.10$ . Since $9 < 10$ hundredths, $0.09$ is smaller.
8.
A runner finishes in $12.45$ seconds and another in $12.39$ seconds. Write the faster time.
Answer: 12.39
$12.39$ seconds is faster because $12.39 < 12.45$ . The smaller time wins the race!
9.
Which is the greatest? $0.125$ , $0.5$ , $0.3$ , $0.09$
1. a) $0.09$
2. b) $0.125$
3. c) $0.3$
4. d) $0.5$
Answer: $0.5$
$0.5$ is greatest. Compare tenths: $0.5$ has 5 tenths, $0.3$ has 3, $0.125$ has 1, $0.09$ has 0.
10.
Order from least to greatest: $0.8$ , $0.35$ , $0.6$
Answer: $0.35 < 0.6 < 0.8$
1. How many hundredths is $0.8$ ? 80
2. How many hundredths is $0.6$ ? 60
3. Compare 80, 35 and 60 hundredths. Which decimal is the smallest? 0.35
4. Which decimal comes second, in the middle? 0.6
11.
Compare $0.3$ and $0.29$ . Which is greater?
Answer: $0.3 > 0.29$
1. How many hundredths is $0.3$ ? 30
2. How many hundredths is $0.29$ ? 29
3. Which is more: 30 hundredths or 29 hundredths? 30
4. So which number is greater, $0.3$ or $0.29$ ? 0.3
12.
Product A costs 2.49 dollars and Product B costs 2.5 dollars. Which is cheaper? Write the price.
Answer: 2.49
$2.49 < 2.50$ . Product A at 2.49 dollars is 1 cent cheaper than Product B at 2.50 dollars.
13.
Order from greatest to least: $1.5$ , $1.45$ , $1.52$ , $1.4$
Answer: $1.52 > 1.5 > 1.45 > 1.4$
1. Write the numbers as hundredths. How many hundredths is $1.5$ ? 150
2. How many hundredths is $1.4$ ? 140
3. Now compare 150, 145, 152 and 140 hundredths. Which number is the greatest? 1.52
4. Which number comes second? 1.5
5. Which number comes third? 1.45
14.
A gymnast needs a score of at least $9.5$ to qualify. Her scores are $9.45$ , $9.52$ , and $9.48$ . How many scores qualify?
Answer: 1
1. The qualifying score is $9.5 = 9.50$ . How many hundredths past 9 is it? 50
2. Is $9.45$ greater than or equal to $9.50$ ? no
3. Is $9.52$ greater than or equal to $9.50$ ? yes
4. Is $9.48$ greater than or equal to $9.50$ ? no
5. How many scores qualify? 1
15.
Which list shows decimals in order from least to greatest?
1. a) $0.08, 0.75, 0.3, 0.9$
2. b) $0.9, 0.75, 0.3, 0.08$
3. c) $0.3, 0.08, 0.75, 0.9$
4. d) $0.08, 0.3, 0.75, 0.9$
Answer: $0.08, 0.3, 0.75, 0.9$
As hundredths: 8, 30, 75, 90. In order: $0.08 < 0.3 < 0.75 < 0.9$ .
16.
Three packages weigh $2.35$ kg, $2.4$ kg, and $2.305$ kg. Which package is heaviest?
Answer: $2.4$ kg
1. How many thousandths past 2 is $2.35$ ? 350
2. How many thousandths past 2 is $2.4$ ? 400
3. $2.305$ is 305 thousandths past 2. Which is the most: 350, 400 or 305 thousandths? 400
4. So which package is the heaviest? Write its weight in kg. 2.4