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Complete the following conversions.

a) [tex]$256 \, \text{m} = \quad \text{cm} = \quad \text{mm}$[/tex]

b) [tex]$3446 \, \text{mg} = \quad \text{g} = \quad \text{kg}$[/tex]

c) [tex]$598 \, \text{kL} = \quad \text{L} = \quad \text{mL}$[/tex]

d) [tex]$118.75 \, \text{km} = \quad \text{km} + \quad \text{m}$[/tex]

e) [tex]$6755 \, \text{g} = \quad \text{kg} + \quad \text{g}$[/tex]

f) [tex]$28.7 \, \text{kg} = \quad \text{kg} + \quad \text{g}$[/tex]

Sagot :

GinnyAnswer
Let's proceed step-by-step with the conversions.

### a) [tex]$256 \, m$[/tex]

1. Convert meters to centimeters: \\
[tex]\( 1 \, m = 100 \, cm \)[/tex] \\
Therefore, [tex]\( 256 \, m = 256 \times 100 = 25600 \, cm \)[/tex].

2. Convert centimeters to millimeters: \\
[tex]\( 1 \, cm = 10 \, mm \)[/tex] \\
Therefore, [tex]\( 25600 \, cm = 25600 \times 10 = 256000 \, mm \)[/tex].

Summary:
[tex]$ 256 \, m = 25600 \, cm = 256000 \, mm $[/tex]

### b) [tex]$3446 \, mg$[/tex]

1. Convert milligrams to grams: \\
[tex]\( 1000 \, mg = 1 \, g \)[/tex] \\
Therefore, [tex]\( 3446 \, mg = \frac{3446}{1000} = 3.446 \, g \)[/tex].

2. Convert grams to kilograms: \\
[tex]\( 1000 \, g = 1 \, kg \)[/tex] \\
Therefore, [tex]\( 3.446 \, g = \frac{3.446}{1000} = 0.003446 \, kg \)[/tex].

Summary:
[tex]$ 3446 \, mg = 3.446 \, g = 0.003446 \, kg $[/tex]

### c) [tex]$598 \, kL$[/tex]

1. Convert kiloliters to liters: \\
[tex]\( 1 \, kL = 1000 \, L \)[/tex] \\
Therefore, [tex]\( 598 \, kL = 598 \times 1000 = 598000 \, L \)[/tex].

2. Convert liters to milliliters: \\
[tex]\( 1 \, L = 1000 \, mL \)[/tex] \\
Therefore, [tex]\( 598000 \, L = 598000 \times 1000 = 598000000 \, mL \)[/tex].

Summary:
[tex]$ 598 \, kL = 598000 \, L = 598000000 \, mL $[/tex]

### d) [tex]$118.75 \, km$[/tex]

1. Separate into kilometers and meters: \\
The integer part remains in kilometers, and the decimal part is converted to meters. \\
[tex]\( 118 \, km \)[/tex] is the integer part \\
To find the meters: \\
[tex]\( 0.75 \, km = 0.75 \times 1000 = 750 \, m \)[/tex]

Summary:
[tex]$ 118.75 \, km = 118 \, km + 750 \, m $[/tex]

### e) [tex]$6755 \, g$[/tex]

1. Convert grams to kilograms: \\
[tex]\( 1000 \, g = 1 \, kg \)[/tex] \\
Therefore, [tex]\( 6755 \, g = \frac{6755}{1000} = 6.755 \, kg \)[/tex].

2. Separate kilograms and grams: \\
[tex]\( 6 \, kg \)[/tex] is the integer part \\
To find the gram remainder: \\
[tex]\( 6.755 \, kg = 6 \, kg \)[/tex] and the remainder: \\
[tex]\( 0.755 \, kg = 0.755 \times 1000 = 755 \, g \)[/tex]

Summary:
[tex]$ 6755 \, g = 6.755 \, kg = 6 \, kg + 755 \, g $[/tex]

### f) [tex]$28.7 \, kg$[/tex]

1. Separate kilograms and grams: \\
The integer part remains in kilograms, and the decimal part is converted to grams. \\
[tex]\( 28 \, kg \)[/tex] is the integer part \\
To find the gram remainder: \\
[tex]\( 0.7 \, kg = 0.7 \times 1000 = 700 \, g \)[/tex]

Summary:
[tex]$ 28.7 \, kg = 28 \, kg + 700 \, g $[/tex]

These are the final answers for each conversion problem:

- [tex]\( 256 \, m = 25600 \, cm = 256000 \, mm \)[/tex]
- [tex]\( 3446 \, mg = 3.446 \, g = 0.003446 \, kg \)[/tex]
- [tex]\( 598 \, kL = 598000 \, L = 598000000 \, mL \)[/tex]
- [tex]\( 118.75 \, km = 118 \, km + 750 \, m \)[/tex]
- [tex]\( 6755 \, g = 6.755 \, kg = 6 \, kg + 755 \, g \)[/tex]
- [tex]\( 28.7 \, kg = 28 \, kg + 700 \, g \)[/tex]
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