Hundredths — Part 2
Semester 4B · Chapter 12 · Lesson 4 · MATH-4B-C12-L04
Before you begin: prerequisite check
Recall: 12.03; place-value grouping. Attempt these questions independently first.
Write 13/100 as a two-decimal-place number.
Show answer and reasoning
13 hundredths are 0.13.
Write 51/100 as a two-decimal-place number.
Show answer and reasoning
51 hundredths are 0.51.
Write 32/100 as a two-decimal-place number.
Show answer and reasoning
32 hundredths are 0.32.
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
Decimals can be rewritten without changing their value. Four tenths and forty hundredths cover the same area of the same-sized whole: 0.4 = 0.40. A zero placed to the right of the last decimal digit changes the notation, not the quantity. Expanded form clarifies positions: 2.37 equals two wholes, three tenths, and seven hundredths. Compare or add decimals by matching place values, not by counting digits or comparing the digits as whole numbers.
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
Rename 0.1 as hundredths and write the equivalent decimal to two places.
Every tenth is ten hundredths; multiply the count by ten.
Check 1: try it yourself
How many hundredths are in 7 tenths?
Show answer and reasoning
Each tenth consists of 10 hundredths; 7×10=70.
Worked example 2
A student writes 0.6 = 0.60. Is this equation true, and why?
Both mean 60 hundredths. A trailing zero does not change the number.
Check 2: try it yourself
A student writes 0.5 = 0.50. Is this equation true, and why?
Show answer and reasoning
Both mean 50 hundredths. A trailing zero does not change the number.
Worked example 3
How many hundredths are in 8 tenths?
Each tenth consists of 10 hundredths; 8×10=80.
Check 3: try it yourself
Write 1 tenth and 4 hundredths as one decimal.
Show answer and reasoning
1 tenths is 10 hundredths, plus 4 more makes 14 hundredths.
Guided practice
Rename 0.7 as hundredths and write the equivalent decimal to two places.
Show answer and reasoning
Every tenth is ten hundredths; multiply the count by ten.
Is 0.60 greater than, less than, or equal to 0.6?
Show answer and reasoning
They describe the same 6 tenths; 0.60 simply writes the hundredths digit explicitly.
How many hundredths are in 2 tenths?
Show answer and reasoning
Each tenth consists of 10 hundredths; 2×10=20.
Is 0.10 greater than, less than, or equal to 0.1?
Show answer and reasoning
They describe the same 1 tenths; 0.10 simply writes the hundredths digit explicitly.
Write 7 tenths and 7 hundredths as one decimal.
Show answer and reasoning
7 tenths is 70 hundredths, plus 7 more makes 77 hundredths.
Independent practice
Rename 0.8 as hundredths and write the equivalent decimal to two places.
Show answer and reasoning
Every tenth is ten hundredths; multiply the count by ten.
A student writes 0.7 = 0.70. Is this equation true, and why?
Show answer and reasoning
Both mean 70 hundredths. A trailing zero does not change the number.
How many hundredths are in 4 tenths?
Show answer and reasoning
Each tenth consists of 10 hundredths; 4×10=40.
Rename 0.4 as hundredths and write the equivalent decimal to two places.
Show answer and reasoning
Every tenth is ten hundredths; multiply the count by ten.
Write 6 tenths and 2 hundredths as one decimal.
Show answer and reasoning
6 tenths is 60 hundredths, plus 2 more makes 62 hundredths.
Write 7 tenths and 6 hundredths as one decimal.
Show answer and reasoning
7 tenths is 70 hundredths, plus 6 more makes 76 hundredths.
A student writes 0.9 = 0.90. Is this equation true, and why?
Show answer and reasoning
Both mean 90 hundredths. A trailing zero does not change the number.
How many hundredths are in 1 tenth?
Show answer and reasoning
Each tenth consists of 10 hundredths; 1×10=10.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Rename 0.7 as hundredths and write the equivalent decimal to two places. Explain how place value or a model can check your result.
Show answer and reasoning
Every tenth is ten hundredths; multiply the count by ten. A correct explanation should name the relevant fractional place values and verify the answer.
A learner claims: “0.5 and 0.50 describe different numbers.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: 0.5 = 0.50 = 50/100, the same number. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Rename 0.2 as hundredths and write the equivalent decimal to two places.
Show answer and reasoning
Every tenth is ten hundredths; multiply the count by ten.
A student writes 0.4 = 0.40. Is this equation true, and why?
Show answer and reasoning
Both mean 40 hundredths. A trailing zero does not change the number.
How many hundredths are in 3 tenths?
Show answer and reasoning
Each tenth consists of 10 hundredths; 3×10=30.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.