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Here you will learn about decimal number lines, including what decimal number lines are and how to use them.
Students will first learn about decimal number lines as part of numbers and operations in base 10 in 5th grade. They will build on this knowledge as part of the number system in 6th grade.
A decimal number line is a number line that includes decimal increments and can help us to visualize decimal numbers.
Decimals are numbers that have parts that are not whole. They represent values in between whole numbers such as tenths, hundredths, thousandths, and so on.
For example, this number line goes up from 0 to 1 by tenths (0.1).
Below, the number 0.638 has been marked on a decimal number line. Its position has been estimated between 0.6 and 0.7, but closer to 0.6.
If you zoom in between 0.6 and 0.7 to a number line that goes up by hundredths (0.01), you can position the decimal 0.638 more accurately. This time the position has been estimated between 0.63 and 0.64, but closer to 0.64.
If you zoom in once again between 0.63 and 0.64 to a number line that goes up by thousandths (0.001), then you can place the decimal 0.638 in its exact position.
Tenths, hundredths and thousandths are common decimal scales, but they are not the only ones you can use. Decimal number lines can use any decimal scale as long as the intervals are split into equal parts.
For example, this decimal number line goes up from 0 to 1 by two-tenths (0.2).
For example, this decimal number line goes up from 0 to 5 by five-tenths (0.5).
For example, this decimal number line goes up from 0 to 2 by twenty-five hundredths (0.25).
Decimal number lines can also be used to represent negative numbers.
For example, this decimal number line goes up from -3 to 2 by five-tenths (0.5).
How does this relate to 5th grade math and 6th grade math?
In order to fill in values on a decimal number line:
Use this worksheet to check your 5th grade and 6th grade studentsβ understanding of decimal number line. 15 questions with answers to identify areas of strength and support!
DOWNLOAD FREEUse this worksheet to check your 5th grade and 6th grade studentsβ understanding of decimal number line. 15 questions with answers to identify areas of strength and support!
DOWNLOAD FREEFill in the scale.
The bottom of the scale is 7, the top of the scale is 8 and there are 5 intervals.
2Calculate the length of each interval by finding the difference in the top and bottom of the scale and dividing by the number of intervals.
To calculate the length of an interval step you can use the formula.
(\text{Top of the scale } - \text{ Bottom of the scale}) \; \div \text{ Number of intervals}This gives,
(8-7)\div 5=0.2So the scale goes up by two-tenths (0.2).
3Fill in the missing values.
Start from 7 and go up the scale, adding 0.2 each time.
Fill in the scale.
Consider the bottom and top of the scale and the number of intervals.
The bottom of the scale is 5, the top of the scale is 9 and there are 8 intervals.
Calculate the length of each interval by finding the difference in the top and bottom of the scale and dividing by the number of intervals.
To calculate the length of an interval step you can use the formula.
(\text{Top of the scale } - \text{ Bottom of the scale}) \; \div \text{ Number of intervals}
This gives,
(9-5)\div 8=0.5
So the scale goes up by five-tenths (0.5).
Fill in the missing values.
Start from 5 and go up the scale, adding 0.5 each time.
Fill in the scale.
Consider the bottom and top of the scale and the number of intervals.
The bottom of the scale is 12, the top of the scale is 14 and there are 5 intervals.
Calculate the length of each interval by finding the difference in the top and bottom of the scale and dividing by the number of intervals.
To calculate the length of an interval step you can use the formula.
(\text{Top of the scale } - \text{ Bottom of the scale}) \; \div \text{ Number of intervals}
This gives,
(14-12)\div 5=0.4
So the scale goes up by four-tenths (0.4).
Fill in the missing values.
Start from 12 and go up the scale, adding 0.4 each time.
Find the missing value.
Consider the bottom and top of the scale and the number of intervals.
The bottom of the scale is 5.2, the top of the scale is 6.0 and there are 8 intervals.
Calculate the length of each interval by finding the difference in the top and bottom of the scale and dividing by the number of intervals.
To calculate the length of an interval step you can use the formula.
(\text{Top of the scale } - \text{ Bottom of the scale}) \; \div \text{ Number of intervals}
This gives,
(6.0-5.2)\div 8=0.1
So the scale goes up by one-tenth (0.1).
Fill in the missing values.
Start from 5.2 and go up the scale, adding 0.1 each time.
The missing value is 5.6.
Find the missing value.
Consider the bottom and top of the scale and the number of intervals.
The bottom of the scale is 14, the top of the scale is 17 and there are 6 intervals.
Calculate the length of each interval by finding the difference in the top and bottom of the scale and dividing by the number of intervals.
To calculate the length of an interval step you can use the formula.
(\text{Top of the scale } - \text{ Bottom of the scale}) \; \div \text{ Number of intervals}
This gives,
(17-14)\div 6=0.5
So the scale goes up by five-tenths (0.5).
Fill in the missing values.
Start from 14 and go up the scale, adding 0.5 each time.
The missing value is 16.5.
Find the missing value.
Consider the bottom and top of the scale and the number of intervals.
The bottom of the scale is 7.1, the top of the scale is 7.5 and there are 8 intervals.
Calculate the length of each interval by finding the difference in the top and bottom of the scale and dividing by the number of intervals.
To calculate the length of an interval step you can use the formula.
(\text{Top of the scale } - \text{ Bottom of the scale}) \; \div \text{ Number of intervals}
This gives,
(7.5-7.1)\div 8=0.05
So the scale goes up by five-hundredths (0.05).
Fill in the missing values.
Start from 7.1 and go up the scale, adding 0.05 each time.
The missing value is 7.45.
1. Find the missing value.
The bottom of the scale is 6, the top of the scale is 7 and there are 5 intervals.
To calculate the length of an interval step you can use the formula:
(\text{Top of the scale } – \text{ Bottom of the scale}) \; \div \text{ Number of intervals}
This gives,
(7-6)\div 5=0.2
Start from 6 and go up the scale, adding 0.2 each time.
The missing value is 6.4.
2. Find the missing value.
The bottom of the scale is 2.1, the top of the scale is 2.7 and there are 6 intervals.
To calculate the length of an interval step you can use the formula:
(\text{Top of the scale } – \text{ Bottom of the scale}) \; \div \text{ Number of intervals}
This gives,
(2.7-2.1)\div 6=0.1
Start from 2.1 and go up the scale, adding 0.1 each time.
The missing value is 2.3.
3. Find the missing value.
The bottom of the scale is 5.2, the top of the scale is 5.3 and there are 10 intervals.
To calculate the length of an interval step you can use the formula:
(\text{Top of the scale } – \text{ Bottom of the scale}) \; \div \text{ Number of intervals}
This gives,
(5.3-5.2)\div 10=0.01
Start from 5.2 and go up the scale, adding 0.01 each time.
The missing value is 5.25.
4. Find the missing value.
The bottom of the scale is 16.2, the top of the scale is 18.2 and there are 5 intervals.
To calculate the length of an interval step you can use the formula:
(\text{Top of the scale } – \text{ Bottom of the scale}) \; \div \text{ Number of intervals}
This gives,
(18.2-16.2)\div 5=0.4
Start from 16.2 and go up the scale, adding 0.4 each time.
The missing value is 17.8.
5. Find the missing value.
The bottom of the scale is 6.5, the top of the scale is 9.0 and there are 10 intervals.
To calculate the length of an interval step you can use the formula:
(\text{Top of the scale } – \text{ Bottom of the scale}) \; \div \text{ Number of intervals}
This gives,
(9.0-6.5)\div 10=0.25
Start from 6.5 and go up the scale, adding 0.25 each time.
The missing value is 7.25.
6. Find the missing value.
The bottom of the scale is 5.5, the top of the scale is 7.3 and there are 6 intervals.
To calculate the length of an interval step you can use the formula:
(\text{Top of the scale } – \text{ Bottom of the scale}) \; \div \text{ Number of intervals}
This gives,
(7.3-5.5)\div 6=0.3
Start from 5.5 and go up the scale, adding 0.3 each time.
The missing value is 6.4.
Decimal number lines can help students understand decimal place value and be used to order and compare decimals. They are also helpful as models for adding, subtracting, multiplying or dividing decimals. Students will also use decimal number lines when creating graphs and plotting data.
There is value in having students explore decimal number lines by drawing them themselves. However, there are drawbacks as it can be more time consuming and ensuring that all the intervals are equal can be difficult. For each activity, use discretion to decide whether providing students with premade number lines or letting them create their own is more appropriate for the learning goal.
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Prepare for math tests in your state with these 3rd Grade to 8th Grade practice assessments for Common Core and state equivalents.
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