Six metric length and distance conversion word problems on a math worksheet.

Let's solve each problem step by step.

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Problem 1:

Zach made a chart to show how many mm his plant grew each week for 7 weeks. Each block equals 5 mm of growth. How tall is the plant?

#### Solution:
1. Count the number of shaded blocks in the chart.
- There are 14 shaded blocks.
2. Each block represents 5 mm of growth.
- Total growth = \( 14 \times 5 \, \text{mm} = 70 \, \text{mm} \).
3. Convert millimeters to centimeters (since 1 cm = 10 mm):
- \( 70 \, \text{mm} = \frac{70}{10} \, \text{cm} = 7 \, \text{cm} \).

Answer: \( \boxed{7} \) centimeters

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Problem 2:

Susie begins a new walking program with 600 m on the first day. Each day, she will increase her walk by 200 m. How many kilometers will she walk on day 18 of her program?

#### Solution:
1. Identify the pattern:
- Day 1: \( 600 \, \text{m} \)
- Day 2: \( 600 + 200 = 800 \, \text{m} \)
- Day 3: \( 600 + 2 \times 200 = 1000 \, \text{m} \)
- General formula for day \( n \): \( 600 + (n-1) \times 200 \, \text{m} \).
2. For day 18:
- Distance = \( 600 + (18-1) \times 200 \)
- Distance = \( 600 + 17 \times 200 \)
- Distance = \( 600 + 3400 = 4000 \, \text{m} \).
3. Convert meters to kilometers (since 1 km = 1000 m):
- \( 4000 \, \text{m} = \frac{4000}{1000} \, \text{km} = 4 \, \text{km} \).

Answer: \( \boxed{4} \) kilometers

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Problem 3:

Trudy wants to surround her garden on all four sides with fencing. Her rectangular garden is 270 cm by 130 cm. How many meters of fencing will she need?

#### Solution:
1. Calculate the perimeter of the rectangular garden:
- Perimeter = \( 2 \times (\text{length} + \text{width}) \)
- Perimeter = \( 2 \times (270 + 130) \)
- Perimeter = \( 2 \times 400 = 800 \, \text{cm} \).
2. Convert centimeters to meters (since 1 m = 100 cm):
- \( 800 \, \text{cm} = \frac{800}{100} \, \text{m} = 8 \, \text{m} \).

Answer: \( \boxed{8} \) meters

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Problem 4:

Jin is training for the 50 meter dash. Each day that he trains, he runs the dash six times. Last week, he trained for four days. This week, he trained for five days. In two weeks, how far has Jin run?

#### Solution:
1. Calculate the distance Jin runs each day:
- Distance per day = \( 50 \, \text{m} \times 6 = 300 \, \text{m} \).
2. Calculate the total distance for last week (4 days):
- Distance last week = \( 300 \, \text{m/day} \times 4 \, \text{days} = 1200 \, \text{m} \).
3. Calculate the total distance for this week (5 days):
- Distance this week = \( 300 \, \text{m/day} \times 5 \, \text{days} = 1500 \, \text{m} \).
4. Calculate the total distance for two weeks:
- Total distance = \( 1200 + 1500 = 2700 \, \text{m} \).
5. Convert meters to kilometers (since 1 km = 1000 m):
- \( 2700 \, \text{m} = \frac{2700}{1000} \, \text{km} = 2.7 \, \text{km} \).

Answer: \( \boxed{2.7} \) kilometers

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Problem 5:

Lu is stringing beads to make a necklace. She is using 30 of the 8 mm beads, 70 of the 4 mm beads, and 40 of the 2 mm beads. How long will her finished necklace be?

#### Solution:
1. Calculate the total length contributed by each type of bead:
- Length from 8 mm beads: \( 30 \times 8 = 240 \, \text{mm} \).
- Length from 4 mm beads: \( 70 \times 4 = 280 \, \text{mm} \).
- Length from 2 mm beads: \( 40 \times 2 = 80 \, \text{mm} \).
2. Sum the lengths:
- Total length = \( 240 + 280 + 80 = 600 \, \text{mm} \).
3. Convert millimeters to centimeters (since 1 cm = 10 mm):
- \( 600 \, \text{mm} = \frac{600}{10} \, \text{cm} = 60 \, \text{cm} \).

Answer: \( \boxed{60} \) centimeters

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Problem 6:

Mara is building a wind chime. She needs string in the following lengths: six pieces of 20 cm, 3 pieces of 30 cm, and one piece of 40 cm. How much string does she need?

#### Solution:
1. Calculate the total length for each type of string:
- Length from 20 cm pieces: \( 6 \times 20 = 120 \, \text{cm} \).
- Length from 30 cm pieces: \( 3 \times 30 = 90 \, \text{cm} \).
- Length from 40 cm piece: \( 1 \times 40 = 40 \, \text{cm} \).
2. Sum the lengths:
- Total length = \( 120 + 90 + 40 = 250 \, \text{cm} \).
3. Convert centimeters to meters (since 1 m = 100 cm):
- \( 250 \, \text{cm} = \frac{250}{100} \, \text{m} = 2.5 \, \text{m} \).

Answer: \( \boxed{2.5} \) meters

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Final Answers:

1. \( \boxed{7} \) centimeters
2. \( \boxed{4} \) kilometers
3. \( \boxed{8} \) meters
4. \( \boxed{2.7} \) kilometers
5. \( \boxed{60} \) centimeters
6. \( \boxed{2.5} \) meters