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Chapter 8: Problem 60

How many 5 milliliter test tubes filled with water will it take to fill a 1 liter container?

Short Answer

Expert verified
200 test tubes are needed.

Step by step solution

01

Understand Unit Conversion

First, realize that 1 liter is equivalent to 1000 milliliters. This is important because it allows us to switch between liters and milliliters easily while solving the problem.
02

Set Up the Division Problem

Consider the total volume you need to fill and the capacity of each test tube. You need to know how many 5 milliliter test tubes are needed to make up 1000 milliliters. This is a division problem: 1000 milliliters divided by 5 milliliters per test tube.
03

Perform the Division

Calculate the division: \( \frac{1000}{5} = 200 \). This means you need 200 test tubes to make up 1000 milliliters.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Volume Measurement
Volume measurement is a critical concept in math and science. It describes the amount of three-dimensional space an object occupies. In this specific problem, we measure volume in milliliters and liters. Here's what you need to know:
  • Milliliters (mL): A metric unit of volume, where 1 milliliter is one-thousandth of a liter.
  • Liters (L): Another metric unit of volume, commonly used for liquids. 1 liter is equivalent to 1000 milliliters.
To solve volume measurement problems efficiently, it's important to understand unit conversions and their applications. In this problem, we start by converting 1 liter (L) into milliliters (mL). By recognizing that 1 liter equals 1000 milliliters, we can easily convert and work with smaller measurements like the 5 mL test tubes mentioned.
Setting Up a Division Problem
In this problem, once we convert the volume into milliliters, setting up a division problem becomes the logical next step. This is because we want to determine how many smaller volumes (the test tubes) are needed to make up a larger volume (1 liter).A division problem here is based on:
  • Numerator: The total volume needed, which is 1000 milliliters.
  • Denominator: The volume each test tube holds, which is 5 milliliters.
Division tells us how many times the denominator (volume of one test tube) fits into the numerator (total volume needed). Setting this up as a division equation allows us to calculate the number of test tubes required:\[ \text{Number of test tubes} = \frac{\text{Total volume in mL}}{\text{Volume of one test tube in mL}} \]
Approaching Math Problem Solving
Math problem solving often involves combining several concepts, like in this division problem. To solve successfully, it helps to:
  • Break down the problem into simpler parts. Here, we started with converting units from liters to milliliters.
  • Identify the goal of the problem. We want to find how many test tubes fill 1 liter.
  • Apply mathematical operations, such as division, to reach the solution.
Executing the division helps solve the problem effectively: Calculate how many 5 mL increments fill up 1000 mL. So by dividing 1000 by 5:\[ \frac{1000}{5} = 200 \]This answer, 200, tells us you need exactly 200 test tubes of 5 milliliters to fill a 1-liter container. This approach is adaptable and can help solve numerous other math problems with similar structures.

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