Tenths — Part 1
Semester 4B · Chapter 12 · Lesson 1 · MATH-4B-C12-L01
Before you begin: prerequisite check
Recall: 4A common fractions and place value. Attempt these questions independently first.
What fraction is one half?
Show answer and reasoning
One of two equal parts is 1/2.
How many tenths make one whole?
Show answer and reasoning
Ten equal tenth parts make one whole.
What value does the 4 have in the number 4,308?
Show answer and reasoning
The digit is in the thousands place, so its value is four thousand.
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
One whole divided into ten equal parts creates tenths. Four shaded parts represent 4/10, which is written 0.4. The digit immediately to the right of the decimal point counts tenths. Ten tenths make one whole. Always use the same-sized whole when comparing fractions or decimal strips. In the number 2.4, two complete wholes and four tenths are present; it is not twenty-four tenths plus something extra—it is exactly twenty-four tenths.
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
Write 3/10 as a decimal and explain its tenths digit.
3 equal tenths of the same whole are written 0.3.
Check 1: try it yourself
Write 2/10 as a decimal and explain its tenths digit.
Show answer and reasoning
2 equal tenths of the same whole are written 0.2.
Worked example 2
A bar divided into ten equal segments has 1 shaded. Name the fraction and decimal.
Ten equal parts define tenths, so 1 parts mean 1/10 or 0.1.
Check 2: try it yourself
A bar divided into ten equal segments has 7 shaded. Name the fraction and decimal.
Show answer and reasoning
Ten equal parts define tenths, so 7 parts mean 7/10 or 0.7.
Worked example 3
How many tenths must be added to 0.6 to make one whole?
One whole is 10 tenths. Subtract 6 from 10 to find the missing parts.
Check 3: try it yourself
How many tenths must be added to 0.5 to make one whole?
Show answer and reasoning
One whole is 10 tenths. Subtract 5 from 10 to find the missing parts.
Guided practice
Write 6/10 as a decimal and explain its tenths digit.
Show answer and reasoning
6 equal tenths of the same whole are written 0.6.
A bar divided into ten equal segments has 9 shaded. Name the fraction and decimal.
Show answer and reasoning
Ten equal parts define tenths, so 9 parts mean 9/10 or 0.9.
How many tenths must be added to 0.2 to make one whole?
Show answer and reasoning
One whole is 10 tenths. Subtract 2 from 10 to find the missing parts.
What number is 5 tenths after zero on a line marked in tenths?
Show answer and reasoning
Move 5 equally spaced 0.1 intervals to reach 0.5.
Explain why the decimal 0.9 is the same quantity as 9 tenths.
Show answer and reasoning
A decimal tenths digit counts the same equal parts as numerator 9 over denominator 10.
Independent practice
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.
What number is 6 tenths after zero on a line marked in tenths?
Show answer and reasoning
Move 6 equally spaced 0.1 intervals to reach 0.6.
How many tenths must be added to 0.9 to make one whole?
Show answer and reasoning
One whole is 10 tenths. Subtract 9 from 10 to find the missing parts.
Write 1/10 as a decimal and explain its tenths digit.
Show answer and reasoning
1 equal tenths of the same whole are written 0.1.
Explain why the decimal 0.3 is the same quantity as 3 tenths.
Show answer and reasoning
A decimal tenths digit counts the same equal parts as numerator 3 over denominator 10.
Write 7/10 as a decimal and explain its tenths digit.
Show answer and reasoning
7 equal tenths of the same whole are written 0.7.
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.
Explain why the decimal 0.4 is the same quantity as 4 tenths.
Show answer and reasoning
A decimal tenths digit counts the same equal parts as numerator 4 over denominator 10.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Write 7/10 as a decimal and explain its tenths digit. Explain how place value or a model can check your result.
Show answer and reasoning
7 equal tenths of the same whole are written 0.7. A correct explanation should name the relevant fractional place values and verify the answer.
A learner claims: “0.3 means three whole units.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: 0.3 means three tenths of one whole. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Explain why the decimal 0.2 is the same quantity as 2 tenths.
Show answer and reasoning
A decimal tenths digit counts the same equal parts as numerator 2 over denominator 10.
What number is 2 tenths after zero on a line marked in tenths?
Show answer and reasoning
Move 2 equally spaced 0.1 intervals to reach 0.2.
Explain why the decimal 0.8 is the same quantity as 8 tenths.
Show answer and reasoning
A decimal tenths digit counts the same equal parts as numerator 8 over denominator 10.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.