Q1: Which decimal represents the point shown on the number line?
[Number line from 0 to 1 with a point at the 3rd mark out of 10 equal parts]
(a) 0.3
(b) 0.03
(c) 3.0
(d) 0.30
Solution:
Ans: (a) Explanation: The number line is divided into 10 equal parts between 0 and 1. Each part represents one tenth, or \(0.1\). The point is at the 3rd mark, which is \(0.1 + 0.1 + 0.1 = 0.3\). Option (b) is incorrect because 0.03 is much smaller (three hundredths). Option (c) is incorrect because 3.0 is greater than 1. Option (d) equals 0.3 but uses unnecessary zero.
Q2: Between which two whole numbers does the decimal 2.7 lie on the number line?
(a) 1 and 2
(b) 2 and 3
(c) 7 and 8
(d) 0 and 1
Solution:
Ans: (b) Explanation: The decimal \(2.7\) has a whole number part of 2 and a decimal part of 0.7. This means it is greater than 2 but less than 3, so it lies between 2 and 3 on the number line. Option (a) is incorrect because those numbers are less than 2.7. Option (c) confuses the decimal part with whole numbers. Option (d) is too small.
Q3: What is the value of point P on this number line?
[Number line from 4 to 5 with point P at the 6th mark out of 10 equal parts]
(a) 4.6
(b) 5.6
(c) 4.06
(d) 6.4
Solution:
Ans: (a) Explanation: The number line goes from 4 to 5 and is divided into 10 equal parts. Each part is \(0.1\). Point P is 6 marks from 4, so we count: \(4 + 0.6 = 4.6\). Option (b) is incorrect because it goes past 5. Option (c) shows hundredths instead of tenths. Option (d) reverses the digits.
Q4: Which decimal is closest to 1 on the number line?
(a) 0.8
(b) 0.5
(c) 0.2
(d) 0.95
Solution:
Ans: (d) Explanation: To find which decimal is closest to 1, we need to see which has the smallest distance from 1. The distance from 1 is: 0.8 is 0.2 away, 0.5 is 0.5 away, 0.2 is 0.8 away, and 0.95 is only 0.05 away. Therefore, 0.95 is closest to 1.
Q5: A number line shows marks at 1.0, 1.5, 2.0, 2.5, and 3.0. What is the distance between consecutive marks?
(a) 0.1
(b) 0.5
(c) 1.0
(d) 0.25
Solution:
Ans: (b) Explanation: To find the distance between consecutive marks, we subtract: \(1.5 - 1.0 = 0.5\). We can check: \(2.0 - 1.5 = 0.5\) and \(2.5 - 2.0 = 0.5\). Each mark is 0.5 (or five tenths) apart. Option (a) is too small. Option (c) is too large. Option (d) is one-quarter, not one-half.
Q6: Which of these decimals would be located to the RIGHT of 3.4 on a number line?
(a) 3.1
(b) 3.04
(c) 3.45
(d) 2.9
Solution:
Ans: (c) Explanation: On a number line, numbers to the right are greater. We need a number greater than \(3.4\). Comparing: 3.1 < 3.4,="" 3.04="">< 3.4,="">3.45 > 3.4, and 2.9 < 3.4.="" only="">3.45 is greater than 3.4, so it appears to the right.
Q7: A number line is divided into tenths between 0 and 1. How many marks (not counting 0) are there before reaching 1?
(a) 10
(b) 9
(c) 5
(d) 8
Solution:
Ans: (b) Explanation: When a number line is divided into tenths, the marks represent: 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and then 1.0. Not counting 0, but before reaching 1, there are 9 marks. Option (a) incorrectly counts 1 as well.
Q8: Which statement about decimals on the number line is TRUE?
(a) 0.7 is greater than 0.70
(b) 0.6 is located between 0.5 and 0.8
(c) 1.2 is closer to 2 than to 1
(d) 0.9 is less than 0.80
Solution:
Ans: (b) Explanation: Let's check each statement:
(a) 0.7 = 0.70, so they are equal, not greater. (b) 0.6 is between 0.5 and 0.8 ✓ This is TRUE.
(c) 1.2 is 0.2 from 1 and 0.8 from 2, so it's closer to 1.
(d) 0.9 > 0.80, not less than.
Section B: Fill in the Blanks
Q9: On a number line, decimals increase in value as you move to the __________.
Solution:
Ans: right Explanation: On a horizontal number line, numbers increase in value as you move from left to right. Numbers to the right are always greater than numbers to the left.
Q10: The decimal 0.1 represents one __________ on the number line.
Solution:
Ans: tenth Explanation: The decimal \(0.1\) is read as "one tenth" and represents one out of ten equal parts between 0 and 1 on the number line.
Q11: A number line from 0 to 1 divided into 10 equal parts has each part equal to __________.
Solution:
Ans: 0.1 Explanation: When the distance from 0 to 1 is divided into 10 equal parts, each part represents one tenth, which equals \(0.1\) or \(\frac{1}{10}\).
Q12: The decimal that comes exactly halfway between 2 and 3 on a number line is __________.
Solution:
Ans: 2.5 Explanation: The halfway point between two whole numbers is found by adding them and dividing by 2: \((2 + 3) \div 2 = 2.5\). This can also be thought of as 2 plus one-half, which is 2.5.
Q13: If a number line shows 4.2, 4.4, 4.6, and 4.8, the next mark would be at __________.
Solution:
Ans: 5.0 Explanation: The pattern shows that each mark increases by 0.2. Following this pattern: \(4.8 + 0.2 = 5.0\). The sequence continues with equal spacing of two-tenths.
Q14: The distance between 1.3 and 1.7 on a number line is __________.
Solution:
Ans: 0.4 Explanation: To find the distance between two points on a number line, we subtract the smaller from the larger: \(1.7 - 1.3 = 0.4\). The distance is four-tenths.
Section C: Word Problems
Q15: Maria is measuring rainfall for her science project. On Monday, it rained 0.3 inches, and on Tuesday, it rained 0.7 inches. Show both amounts on a number line from 0 to 1 inch divided into tenths. Which day had more rainfall and by how much?
Solution:
Ans:
On the number line, 0.3 is at the 3rd mark and 0.7 is at the 7th mark.
Tuesday had more rainfall.
Difference: \(0.7 - 0.3 = 0.4\) inches Final Answer: Tuesday had 0.4 inches more rainfall than Monday.
Q16: A number line shows the distances in kilometers that four students ran: Jake ran 2.3 km, Emma ran 2.8 km, Liam ran 2.5 km, and Sophia ran 2.1 km. If you arrange these distances on a number line from least to greatest, who ran the shortest distance and who ran the longest?
Solution:
Ans:
Arranging from least to greatest: 2.1, 2.3, 2.5, 2.8
Comparing the decimal parts: 0.1 < 0.3="">< 0.5=""><> Final Answer: Sophia ran the shortest distance (2.1 km) and Emma ran the longest distance (2.8 km).
Q17: A caterpillar crawls along a number line. It starts at 1.2 and moves to the right by 0.6 units. What is its new position on the number line?
Solution:
Ans:
Starting position: 1.2
Movement to the right: +0.6
Calculation: \(1.2 + 0.6 = 1.8\) Final Answer: The caterpillar's new position is 1.8.
Q18: A baker needs to measure 3.5 cups of flour. Her measuring number line shows marks at every 0.5 cups from 0 to 5 cups. Starting at 0, how many marks does she need to count to reach 3.5 cups?
Solution:
Ans:
Each mark represents 0.5 cups.
Marks are at: 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5
Counting: 1st mark (0.5), 2nd mark (1.0), 3rd mark (1.5), 4th mark (2.0), 5th mark (2.5), 6th mark (3.0), 7th mark (3.5) Final Answer: The baker needs to count 7 marks to reach 3.5 cups.
Q19: Tom drew a number line from 0 to 2 and divided it into 10 equal parts between each whole number. He placed a sticker at 0.4 and another sticker at 1.6. What is the total distance between the two stickers?
Solution:
Ans:
First sticker position: 0.4
Second sticker position: 1.6
Distance = \(1.6 - 0.4 = 1.2\) Final Answer: The total distance between the two stickers is 1.2 units.
Q20: A frog is sitting on a lily pad at position 5.3 on a number line. It jumps 0.9 units to the left. Where does the frog land?
Solution:
Ans:
Starting position: 5.3
Jump to the left means subtract: 5.3 - 0.9
Calculation: \(5.3 - 0.9 = 4.4\) Final Answer: The frog lands at position 4.4 on the number line.
The document Worksheet (with Solutions): Decimals On The Number Line is a part of the Grade 4 Course Math Grade 4.
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