Decimals on a Number Line

Show your work for each problem.

1.
Where is $0.5$ located on a number line from $0$ to $1$ ?
1. a)Closer to 1
2. b)Exactly halfway between 0 and 1
3. c)Closer to 0
4. d)At 0
Answer: Exactly halfway between 0 and 1
$0.5$ means 5 tenths, which is exactly half. Half of the distance from 0 to 1 puts it exactly in the middle.
2.
What decimal is exactly halfway between $0$ and $1$ ?
Answer: 0.5
Halfway between 0 and 1 is $0.5$ . This is because $0.5 = \frac{1}{2}$ , which is exactly half.
3.
Which of these decimals is closest to $1$ ?
1. a) $0.5$
2. b) $0.9$
3. c) $0.1$
4. d) $0.3$
Answer: $0.9$
$0.9$ is closest to $1$ because it is only $0.1$ away from $1$ . On a number line, $0.9$ is the furthest right among these choices.
4.
$2.7$ lies between two consecutive whole numbers. What is the larger of the two?
Answer: 3
$2.7$ has a whole number part of $2$ and a decimal part of $0.7$ . So it lies between $2$ and $3$ , 7 tenths past 2. The larger of the two whole numbers is $3$ .
5.
On a number line, which direction are larger numbers?
1. a)Above
2. b)To the right
3. c)Below
4. d)To the left
Answer: To the right
On a standard horizontal number line, numbers increase as you move to the right. So $0.8$ is to the right of $0.3$ , and $2$ is to the right of $1$ .
6.
Place $1.4$ on a number line. Between which two whole numbers does it fall, and how many tenths past the first whole number?
Answer: Between 1 and 2, 4 tenths past 1
1. What is the whole number part of $1.4$ ? 1
2. What is the decimal part of $1.4$ ? 0.4
3. So $1.4$ is between which two consecutive whole numbers? 1 and 2
4. How many tenths past 1 is $1.4$ ? 4
7.
Which is greater: $0.8$ or $0.75$ ?
1. a)Cannot be determined
2. b) $0.75$
3. c) $0.8$
4. d)They are equal
Answer: $0.8$
$0.8 = 0.80$ , which is greater than $0.75$ . On a number line, $0.8$ is further to the right than $0.75$ .
8.
What decimal is located at the point that is $0.3$ units to the right of $2$ on a number line?
Answer: 2.3
Starting at $2$ and moving $0.3$ units to the right gives $2 + 0.3 = 2.3$ .
9.
Compare $0.6$ and $0.42$ . Which is greater and why?
Answer: $0.6 > 0.42$
1. How many hundredths is $0.6$ ? (Add a zero: $0.6 = 0.60$ ) 60
2. How many hundredths is $0.42$ ? 42
3. So which decimal is greater? 0.6
4. On a number line, which would be further right? 0.6
10.
Where is $0.25$ located between $0$ and $1$ ?
1. a)Three quarters of the way from 0 to 1
2. b)Halfway between 0 and 1
3. c)One quarter of the way from 0 to 1
4. d)Very close to 0
Answer: One quarter of the way from 0 to 1
$0.25 = \frac{25}{100} = \frac{1}{4}$ . One quarter means one fourth of the distance from 0 to 1, so $0.25$ is located one quarter of the way.
11.
A number line shows marks at every tenth from $0$ to $1$ . How many marks are there in total (including $0$ and $1$ )?
Answer: 11
The marks are at: $0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1$ . That's $11$ marks in total.
12.
Order from least to greatest: $0.9$ , $0.09$ , $0.5$ , $0.55$
Answer: $0.09 < 0.5 < 0.55 < 0.9$
1. Which decimal is the smallest (closest to 0)? 0.09
2. Which comes next after $0.09$ ? 0.5
3. Which comes after $0.5$ ? 0.55
4. Which is the largest? 0.9
13.
What decimal is exactly halfway between $0.2$ and $0.3$ ?
Answer: 0.25
Halfway between $0.2$ and $0.3$ is $0.25$ . You can find this by $(0.2 + 0.3) \div 2 = 0.5 \div 2 = 0.25$ .
14.
Which statement is TRUE about $0.19$ and $0.2$ ?
1. a) $0.19 > 0.2$
2. b) $0.19 = 0.2$
3. c)Cannot compare
4. d) $0.19 < 0.2$
Answer: $0.19 < 0.2$
$0.2 = 0.20$ . Comparing $0.19$ to $0.20$ : 19 hundredths is less than 20 hundredths. So $0.19 < 0.2$ .
15.
A thermometer shows a temperature between $36$ and $37$ degrees. The liquid stops at the 7th mark after $36$ , and there are 10 marks between each whole degree. What is the temperature?
Answer: $36.7$
1. What whole number do you start from? 36
2. With 10 marks per degree, what decimal does each mark represent? 0.1
3. How many tenths is the 7th mark? 7
4. What is the temperature? 36.7
16.
The part of a number line from $0.4$ to $0.5$ is divided into 10 equal parts. What decimal is at the 3rd mark after $0.4$ ?
Answer: 0.43
$0.4 = 0.40$ and $0.5 = 0.50$ , so the 10 parts are hundredths: $0.41$ , $0.42$ , $0.43$ , ... The 3rd mark after $0.4$ is $0.43$ .
17.
A runner completes a race in $12.45$ seconds. Another runner finishes in $12.5$ seconds. Who was faster?
Answer: The runner with 12.45 seconds
1. $12.5 = 12.50$ . How many hundredths past 12 is $12.5$ ? 50
2. Compare: is $12.45$ less than or greater than $12.50$ ? less than
3. In a race, is a smaller or a larger time better? smaller
4. Who was faster? The runner with 12.45 s