Lesson 3 of 8 · Grades 4 to 5
Decimals on a number line
A number line is a ruler for every number, whole or not. Between two whole numbers there are ten tenths, and between two tenths there are ten hundredths. This lesson shows how to find the exact point for a decimal and how to read a decimal off a line.
Whole numbers and the space between
A number line is a ruler for numbers. Whole numbers sit at the big marks, and everything between them is taken up by decimals. To place tenths, split each whole step into ten equal jumps. Every jump is one tenth, or 0.1.
On the line below, the space from 0 to 1 is cut into ten equal parts. Each small tick is worth 0.1, and the fourth tick is 0.4.
Counting tenths
To read a point on a tenths line, count the jumps from the nearest whole number. Eight jumps from 0 land on 0.8. Six jumps past 1 land on 1.6, because the line keeps counting past the whole number instead of starting again.
Crossing a whole number
A decimal with a digit before the point names whole things as well as parts. The decimal 1.6 means one whole and six tenths. It is less than 2 and more than 1.5. When you order decimals on a line, the whole part tells you which part of the line to visit first, and the digits after the point tell you how far to move inside that gap.
Zooming in to hundredths
Between two tenths there is more room: each tenth gap holds ten hundredths. Zoom in on the space between 0.3 and 0.4 and you can mark hundredths such as 0.31, 0.32 and so on. The point 0.35 sits exactly halfway between 0.3 and 0.4.
Watch out for this
On a line from 1 to 2, each small tick is one tenth, not one whole. The point 1.2 is only a little past 1, not near 2. Check the labels at the big marks first, then count the small jumps between them.
Worked example
A lift starts at 0 on a marker line and rises in equal steps of 0.3. Where is the lift after four steps?
Step 1: each step is 0.3, so count in tenths: 0.3, 0.6, 0.9, 1.2.
Step 2: after three steps the lift is at 0.9, which is just short of one whole.
Step 3: the fourth step takes it past 1 to 1.2.
Step 4: check on the line: 1.2 is one whole and two tenths, two tenths to the right of 1.
Answer: 1.2.
Remember
- Split each whole step into ten equal jumps to make a tenths line.
- Count the jumps from the nearest whole number to read a point.
- A decimal like 1.6 means one whole and six tenths.
- Each tenth gap holds ten hundredths, so 0.35 is halfway between 0.3 and 0.4.
Try it
Answer the five questions below. Work them out first, then open each answer to check.
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A line from 0 to 1 is split into ten equal parts. Which decimal is at the third tick?
Show answer
0.3. Three equal jumps of one tenth land on three tenths.
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Which decimal is halfway between 0.6 and 0.8?
Show answer
0.7. It is one tenth away from each end.
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On a line from 1 to 2, which point is four tenths past 1?
Show answer
1.4. One whole and four tenths.
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Which is closer to 2: 1.8 or 2.3?
Show answer
1.8. It is two tenths away from 2, while 2.3 is three tenths away.
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Order from smallest to largest: 0.9, 0.4, 1.1.
Show answer
0.4, 0.9, 1.1. On a number line they appear in that order from left to right.
Puzzle · Halfway point
Puzzle time
A dot sits exactly halfway between 0.6 and 0.8 on a number line. Which decimal names the dot?
Show a hint
Halfway means the same distance from each end.
Show the answer
Answer: 0.7. 0.6 and 0.8 are two tenths apart, so the halfway decimal is one tenth above 0.6: 0.7.