Aimathic – Compare decimals – Free Math Worksheets

Compare decimals

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Difficulty: 1 – 5

5158334

Order the prices from least to greatest: $\$1.49$, $\$1.94$, $\$1.44$, $\$1.99$

Hints

- Compare the whole-dollar amounts first. - If those are equal, compare the tenths digits. - If the tenths digits are also equal, compare the hundredths digits.

Solution

1. All four prices have $1$ in the ones place. 2. Compare the tenths digits. Prices with $4$ tenths are less than prices with $9$ tenths. 3. Within each pair, compare the hundredths digits. 4. The order is $\$1.44 < \$1.49 < \$1.94 < \$1.99$.

Answer

$\$1.44 < \$1.49 < \$1.94 < \$1.99$

5158364

Write $<$, $>$, or $=$ in each circle. a) $\$14.80 \bigcirc \$18.40$ b) $\$6.07 \bigcirc \$6.70$ c) $\$22.55 \bigcirc \$22.55$

Hints

- Compare the whole-dollar amounts first. - If the dollars are equal, compare the cents. - Pay attention to place value.

Solution

1. For a), compare the whole-dollar amounts. Since $14 < 18$, $\$14.80 < \$18.40$. 2. For b), the whole-dollar amounts are equal. Compare the cents: $7 < 70$, so $\$6.07 < \$6.70$. 3. For c), the amounts are identical, so they are equal.

Answer

a) $<$ b) $<$ c) $=$

5197644

Write $<$, $>$, or $=$ to compare each pair of money amounts. a) $400\,\text{cents} \;\dots\; \$4$ b) $\$6 \;\dots\; 60\,\text{cents}$ c) $250\,\text{cents} \;\dots\; \$2$

Hints

- Convert both amounts to the same unit. - One dollar equals $100$ cents. - Check carefully whether each amount is written in dollars or cents.

Solution

1. Convert each dollar amount to cents. 2. $\$4 = 400$ cents, so the amounts are equal. 3. $\$6 = 600$ cents, and $600 > 60$. 4. $\$2 = 200$ cents, and $250 > 200$.

Answer

a) $=$ b) $>$ c) $>$

5119284

Insert $<$, $>$, or $=$. First rewrite the decimals as fractions with denominator $100$. a) $0.3 \;\square\; 0.03$ b) $0.05 \;\square\; \frac{5}{100}$ c) $1.2 \;\square\; \frac{120}{100}$ d) $0.08 \;\square\; 0.01$

Hints

- Rewrite each decimal in hundredths. - Once the denominators match, compare the numerators. - Pay close attention to place value and zeros.

Solution

1. For a), $0.3 = \frac{30}{100}$ and $0.03 = \frac{3}{100}$. Since $30 > 3$, $0.3 > 0.03$. 2. For b), $0.05 = \frac{5}{100}$, so the values are equal. 3. For c), $1.2 = \frac{12}{10} = \frac{120}{100}$, so the values are equal. 4. For d), $0.08 = \frac{8}{100}$ and $0.01 = \frac{1}{100}$. Since $8 > 1$, $0.08 > 0.01$.

Answer

a) $0.3 > 0.03$ b) $0.05 = \frac{5}{100}$ c) $1.2 = \frac{120}{100}$ d) $0.08 > 0.01$

5158344

Order these prices from greatest to least. Pay attention to dollars and cents: $30$ cents, $\$0.03$, $\$3.03$, $\$3.30$, $33$ cents

Hints

- Convert all amounts to the same unit. - One dollar equals $100$ cents. - Compare the resulting whole numbers.

Solution

1. Express every amount in cents: $30$, $3$, $303$, $330$, and $33$ cents. 2. Order the values: $330 > 303 > 33 > 30 > 3$. 3. Match them to the original forms.

Answer

$\$3.30 > \$3.03 > 33\,\text{cents} > 30\,\text{cents} > \$0.03$

5158354

Order the prices from least to greatest: $\$5.50$, $500$ cents, $\$0.55$, $\$5.05$, $5$ cents

Hints

- Convert every amount to cents. - Pay attention to the zero in the tenths place of $\$5.05$. - Compare the cent values as whole numbers.

Solution

1. Express each amount in cents: $550$, $500$, $55$, $505$, and $5$ cents. 2. Order the values: $5 < 55 < 500 < 505 < 550$. 3. Match the ordered values to the original forms.

Answer

$5\,\text{cents} < \$0.55 < 500\,\text{cents} < \$5.05 < \$5.50$

5158374

Write $<$, $>$, or $=$ to compare each pair. a) $\$1.05 \bigcirc 105\,\text{cents}$ b) $\$3.80 \bigcirc 38\,\text{cents}$ c) $\$0.09 \bigcirc 90\,\text{cents}$

Hints

- Convert both amounts in each pair to cents. - One dollar equals $100$ cents. - Watch the zero placeholders in decimal notation.

Solution

1. $\$1.05 = 105$ cents, so the amounts are equal. 2. $\$3.80 = 380$ cents, and $380 > 38$. 3. $\$0.09 = 9$ cents, and $9 < 90$.

Answer

a) $=$ b) $>$ c) $<$

5103184

Find a fraction with denominator $10$ that is greater than $\frac{1}{4}$ and less than $\frac{2}{5}$. Explain why there is exactly one solution.

Hints

- Convert the two boundary fractions to decimals. - List the tenths near those decimals. - Remember that the fraction must be strictly greater than one boundary and strictly less than the other.

Solution

1. Write the boundary fractions as decimals: $\frac{1}{4}=0.25$ and $\frac{2}{5}=0.4$. 2. Fractions with denominator $10$ represent tenths. The tenths near this interval are $\frac{2}{10}=0.2$, $\frac{3}{10}=0.3$, and $\frac{4}{10}=0.4$. 3. Only $0.3$ is strictly between $0.25$ and $0.4$. Therefore, the only solution is $\frac{3}{10}$.

Answer

$\frac{3}{10}$. It is the only tenth strictly between $0.25$ and $0.4$.

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