Comparing Tenths

Which is greater: $0.6$ or $0.4$?

Look at the ones place: Both have $0$ in the ones place = Ones are equal

Compare the tenths place: $6$ tenths vs $4$ tenths = $6 > 4$

Write the comparison: Since $6 > 4$, we have $0.6 > 0.4$ = $0.6 > 0.4$

Answer: $0.6$ is greater than $0.4$

Different Number of Decimal Places

Compare $0.5$ and $0.47$

Make the same number of decimal places: Write $0.5$ as $0.50$ = $0.50$ vs $0.47$

Compare ones place: Both have $0$ ones = Equal

Compare tenths place: $5$ tenths vs $4$ tenths = $5 > 4$

Write the answer: Since $5 > 4$ in tenths, $0.50 > 0.47$ = $0.5 > 0.47$

Answer: $0.5$ is greater than $0.47$

Comparing with Whole Numbers

Order from least to greatest: $1.3$, $0.9$, $1.15$

Compare ones places first: $0.9$ has $0$ ones; $1.3$ and $1.15$ have $1$ one = $0.9$ is smallest

Compare $1.3$ and $1.15$: Make same decimal places: $1.30$ vs $1.15$ = Ones equal, compare tenths

Compare tenths: $3$ tenths vs $1$ tenth: $3 > 1$ = $1.30 > 1.15$

Order all three: Smallest to largest = $0.9, 1.15, 1.3$

Answer: From least to greatest: $0.9$, $1.15$, $1.3$

Mistake: Thinking $0.17 > 0.9$ because $17 > 9$

Why: Students sometimes ignore the decimal point and compare as if they were whole numbers.

Correct: Line up decimal points: $0.17$ vs $0.90$. Since $1 < 9$ in the tenths place, $0.17 < 0.9$

Mistake: Thinking more digits means a larger number

Why: Having more decimal places doesn't mean a larger value. Place value matters!

Correct: $0.5$ (one decimal place) is greater than $0.432$ (three decimal places) because $5 > 4$ in tenths

Mistake: Forgetting to add trailing zeros when comparing

Why: Different decimal places make comparison harder.

Correct: Write $0.3$ as $0.30$ to compare with $0.28$. Now it's clear: $30 > 28$ hundredths

Shopping and Prices

Comparing prices to find the best deal requires decimal comparison.

A store sells pencils for 0.75 euros and pens for 0.80 euros. Which costs less?

Sports Times and Scores

In racing and gymnastics, small decimal differences determine winners.

Runner A finishes in 12.45 seconds, Runner B in 12.39 seconds. Runner B wins because $12.39 < 12.45$.

Q: Is $0.5$ the same as $0.50$?

A: Yes! Adding zeros to the right of the last decimal digit doesn't change the value. $0.5 = 0.50 = 0.500$

Q: How do I compare $0.09$ and $0.1$?

A: Write them with the same decimal places: $0.09$ vs $0.10$. Since $9 < 10$ hundredths, $0.09 < 0.1$

Q: Why is $0.3$ greater than $0.29$?

A: Write $0.3$ as $0.30$. Now compare: $30$ hundredths vs $29$ hundredths. Since $30 > 29$, we have $0.3 > 0.29$