Question

8 compare les masses à laide des symboles <, > ou =.
a) 125 g \square 1,25 kg
b) 2,34 kg \square 2345 g
c) 788 g \square 0,789 kg
d) 4,4 kg \square 400 g

Explanation:

To solve this, we need to compare masses by converting them to the same unit (either grams or kilograms) since \( 1 \, \text{kg} = 1000 \, \text{g} \). Let's solve each part:

Part (a): \( 125 \, \text{g} \) vs \( 1.25 \, \text{kg} \)

Step 1: Convert \( 1.25 \, \text{kg} \) to grams

Since \( 1 \, \text{kg} = 1000 \, \text{g} \), we multiply \( 1.25 \) by \( 1000 \):
\( 1.25 \, \text{kg} = 1.25 \times 1000 = 1250 \, \text{g} \)

Step 2: Compare \( 125 \, \text{g} \) and \( 1250 \, \text{g} \)

\( 125 < 1250 \), so \( 125 \, \text{g} < 1.25 \, \text{kg} \)

Part (b): \( 2.34 \, \text{kg} \) vs \( 2345 \, \text{g} \)

Step 1: Convert \( 2.34 \, \text{kg} \) to grams

\( 2.34 \, \text{kg} = 2.34 \times 1000 = 2340 \, \text{g} \)

Step 2: Compare \( 2340 \, \text{g} \) and \( 2345 \, \text{g} \)

\( 2340 < 2345 \), so \( 2.34 \, \text{kg} < 2345 \, \text{g} \)

Part (c): \( 788 \, \text{g} \) vs \( 0.789 \, \text{kg} \)

Step 1: Convert \( 0.789 \, \text{kg} \) to grams

\( 0.789 \, \text{kg} = 0.789 \times 1000 = 789 \, \text{g} \)

Step 2: Compare \( 788 \, \text{g} \) and \( 789 \, \text{g} \)

\( 788 < 789 \), so \( 788 \, \text{g} < 0.789 \, \text{kg} \)

Part (d): \( 4.4 \, \text{kg} \) vs \( 400 \, \text{g} \)

Step 1: Convert \( 4.4 \, \text{kg} \) to grams

\( 4.4 \, \text{kg} = 4.4 \times 1000 = 4400 \, \text{g} \)

Step 2: Compare \( 4400 \, \text{g} \) and \( 400 \, \text{g} \)

\( 4400 > 400 \), so \( 4.4 \, \text{kg} > 400 \, \text{g} \)

Final Answers:

a) \( 125 \, \text{g} \boldsymbol{<} 1.25 \, \text{kg} \)
b) \( 2.34 \, \text{kg} \boldsymbol{<} 2345 \, \text{g} \)
c) \( 788 \, \text{g} \boldsymbol{<} 0.789 \, \text{kg} \)
d) \( 4.4 \, \text{kg} \boldsymbol{>} 400 \, \text{g} \)

Answer:

To solve this, we need to compare masses by converting them to the same unit (either grams or kilograms) since \( 1 \, \text{kg} = 1000 \, \text{g} \). Let's solve each part:

Part (a): \( 125 \, \text{g} \) vs \( 1.25 \, \text{kg} \)

Step 1: Convert \( 1.25 \, \text{kg} \) to grams

Since \( 1 \, \text{kg} = 1000 \, \text{g} \), we multiply \( 1.25 \) by \( 1000 \):
\( 1.25 \, \text{kg} = 1.25 \times 1000 = 1250 \, \text{g} \)

Step 2: Compare \( 125 \, \text{g} \) and \( 1250 \, \text{g} \)

\( 125 < 1250 \), so \( 125 \, \text{g} < 1.25 \, \text{kg} \)

Part (b): \( 2.34 \, \text{kg} \) vs \( 2345 \, \text{g} \)

Step 1: Convert \( 2.34 \, \text{kg} \) to grams

\( 2.34 \, \text{kg} = 2.34 \times 1000 = 2340 \, \text{g} \)

Step 2: Compare \( 2340 \, \text{g} \) and \( 2345 \, \text{g} \)

\( 2340 < 2345 \), so \( 2.34 \, \text{kg} < 2345 \, \text{g} \)

Part (c): \( 788 \, \text{g} \) vs \( 0.789 \, \text{kg} \)

Step 1: Convert \( 0.789 \, \text{kg} \) to grams

\( 0.789 \, \text{kg} = 0.789 \times 1000 = 789 \, \text{g} \)

Step 2: Compare \( 788 \, \text{g} \) and \( 789 \, \text{g} \)

\( 788 < 789 \), so \( 788 \, \text{g} < 0.789 \, \text{kg} \)

Part (d): \( 4.4 \, \text{kg} \) vs \( 400 \, \text{g} \)

Step 1: Convert \( 4.4 \, \text{kg} \) to grams

\( 4.4 \, \text{kg} = 4.4 \times 1000 = 4400 \, \text{g} \)

Step 2: Compare \( 4400 \, \text{g} \) and \( 400 \, \text{g} \)

\( 4400 > 400 \), so \( 4.4 \, \text{kg} > 400 \, \text{g} \)

Final Answers:

a) \( 125 \, \text{g} \boldsymbol{<} 1.25 \, \text{kg} \)
b) \( 2.34 \, \text{kg} \boldsymbol{<} 2345 \, \text{g} \)
c) \( 788 \, \text{g} \boldsymbol{<} 0.789 \, \text{kg} \)
d) \( 4.4 \, \text{kg} \boldsymbol{>} 400 \, \text{g} \)