Tenths — Part 2
Semester 4B · Chapter 12 · Lesson 2 · MATH-4B-C12-L02
Before you begin: prerequisite check
Recall: 12.01. Attempt these questions independently first.
Write 4/10 as a decimal and explain its tenths digit.
Show answer and reasoning
4 equal tenths of the same whole are written 0.4.
A bar divided into ten equal segments has 5 shaded. Name the fraction and decimal.
Show answer and reasoning
Ten equal parts define tenths, so 5 parts mean 5/10 or 0.5.
How many tenths must be added to 0.1 to make one whole?
Show answer and reasoning
One whole is 10 tenths. Subtract 1 from 10 to find the missing parts.
Key vocabulary
- tenth
- one of ten equal parts of a whole
- hundredth
- one of one hundred equal parts
- equivalent decimals
- two notations for the same amount
- midpoint
- exact halfway point between rounding benchmarks
Understand the concept
A decimal number line places quantities between whole-number benchmarks using equal intervals. Between zero and one, ten equal jumps each represent one tenth. The point 0.7 is seven such jumps from zero. Between two and three, the point 2.3 is three tenths after two. Every tick has to use the same numeric spacing, even when you draw the line by hand. A decimal point doesn't turn a number into two unrelated whole numbers; the scale connects them continuously.
Fully worked examples and immediate checks
Read each example, predict how to begin, then follow its numerical explanation. The check below it is a fresh problem.
Worked example 1
On a number line from 2 to 3 divided into ten equal intervals, what decimal is at the 9th tick after 2?
Each interval is 0.1, so add 9 tenths to 2 to get 2.9.
Check 1: try it yourself
On a number line from 1 to 2 divided into ten equal intervals, what decimal is at the 5th tick after 1?
Show answer and reasoning
Each interval is 0.1, so add 5 tenths to 1 to get 1.5.
Worked example 2
On a number line from 3 to 4 divided into ten equal intervals, what decimal is at the 4th tick after 3?
Each interval is 0.1, so add 4 tenths to 3 to get 3.4.
Check 2: try it yourself
On a number line from 0 to 1 divided into ten equal intervals, what decimal is at the 5th tick after 0?
Show answer and reasoning
Each interval is 0.1, so add 5 tenths to 0 to get 0.5.
Worked example 3
On a number line from 0 to 1 divided into ten equal intervals, what decimal is at the 3rd tick after 0?
Each interval is 0.1, so add 3 tenths to 0 to get 0.3.
Check 3: try it yourself
On a number line from 5 to 6 divided into ten equal intervals, what decimal is at the 9th tick after 5?
Show answer and reasoning
Each interval is 0.1, so add 9 tenths to 5 to get 5.9.
Guided practice
On a number line from 4 to 5 divided into ten equal intervals, what decimal is at the 3rd tick after 4?
Show answer and reasoning
Each interval is 0.1, so add 3 tenths to 4 to get 4.3.
On a number line from 5 to 6 divided into ten equal intervals, what decimal is at the 6th tick after 5?
Show answer and reasoning
Each interval is 0.1, so add 6 tenths to 5 to get 5.6.
On a number line from 4 to 5 divided into ten equal intervals, what decimal is at the 4th tick after 4?
Show answer and reasoning
Each interval is 0.1, so add 4 tenths to 4 to get 4.4.
On a number line from 4 to 5 divided into ten equal intervals, what decimal is at the 8th tick after 4?
Show answer and reasoning
Each interval is 0.1, so add 8 tenths to 4 to get 4.8.
On a number line from 1 to 2 divided into ten equal intervals, what decimal is at the 4th tick after 1?
Show answer and reasoning
Each interval is 0.1, so add 4 tenths to 1 to get 1.4.
Independent practice
On a number line from 5 to 6 divided into ten equal intervals, what decimal is at the 3rd tick after 5?
Show answer and reasoning
Each interval is 0.1, so add 3 tenths to 5 to get 5.3.
On a number line from 4 to 5 divided into ten equal intervals, what decimal is at the 9th tick after 4?
Show answer and reasoning
Each interval is 0.1, so add 9 tenths to 4 to get 4.9.
On a number line from 2 to 3 divided into ten equal intervals, what decimal is at the 7th tick after 2?
Show answer and reasoning
Each interval is 0.1, so add 7 tenths to 2 to get 2.7.
On a number line from 1 to 2 divided into ten equal intervals, what decimal is at the 8th tick after 1?
Show answer and reasoning
Each interval is 0.1, so add 8 tenths to 1 to get 1.8.
On a number line from 2 to 3 divided into ten equal intervals, what decimal is at the 6th tick after 2?
Show answer and reasoning
Each interval is 0.1, so add 6 tenths to 2 to get 2.6.
On a number line from 2 to 3 divided into ten equal intervals, what decimal is at the 8th tick after 2?
Show answer and reasoning
Each interval is 0.1, so add 8 tenths to 2 to get 2.8.
On a number line from 2 to 3 divided into ten equal intervals, what decimal is at the 5th tick after 2?
Show answer and reasoning
Each interval is 0.1, so add 5 tenths to 2 to get 2.5.
On a number line from 4 to 5 divided into ten equal intervals, what decimal is at the 6th tick after 4?
Show answer and reasoning
Each interval is 0.1, so add 6 tenths to 4 to get 4.6.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
On a number line from 3 to 4 divided into ten equal intervals, what decimal is at the 2nd tick after 3? Explain how place value or a model can check your result.
Show answer and reasoning
Each interval is 0.1, so add 2 tenths to 3 to get 3.2. A correct explanation should name the relevant fractional place values and verify the answer.
A learner claims: “0.8 lies between 8 and 9 on the number line.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: 0.8 lies between 0 and 1, eight tenths after zero. Explain the relevant quantities or properties, not merely the final answer.
Exit check
On a number line from 1 to 2 divided into ten equal intervals, what decimal is at the 9th tick after 1?
Show answer and reasoning
Each interval is 0.1, so add 9 tenths to 1 to get 1.9.
On a number line from 5 to 6 divided into ten equal intervals, what decimal is at the 5th tick after 5?
Show answer and reasoning
Each interval is 0.1, so add 5 tenths to 5 to get 5.5.
On a number line from 4 to 5 divided into ten equal intervals, what decimal is at the 2nd tick after 4?
Show answer and reasoning
Each interval is 0.1, so add 2 tenths to 4 to get 4.2.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.